~~~~~=~ Technical Bulletin No. 560 ~ April 1937

UNITED STATES DEPARTMENT OF AGRICULTURE

WASHINGTON, D. C.

YIELD, STAND, AND VOLUME TABLES FOR EVEN-AGED UPLAND OAK FORESTS

By G. LUTHER SCHNUR

A88oc~ate silviculturist, Allegheny Forest Experiment Station,1 Forest Service

CONTENTS

PageIntroduction•.. • -- _ 1 The upland oak rorests, 3 The yield tables______________________________ 6

Basic data - -- ---_ -.__ 10 Elimination of plots -__ 11 Yield analyses____________________________ 12 Accuracy of the yield tables, _ 33 Use of tables for yield prediction in under-

stocked stands__________________________ 34

Page The yield tables-Continued.

Effect of density and species composition on yield __ .________________ 35 The stand tables.

.~

40 Discussion and application of stand tablea, 66

The volume tables____________________________ 60Literature cited • ••• 86

INTRODUCTION

The upland oak region comprises 100 million acres, or one-fifth of the commercial forest area of the United States. It contains 43 billion cubic feet, or one-third of the total stand of hardwoods; and furnishes 2X billion cubic feet, or 40 percent, of the annual cut of such species. In addition, it is favorably located in respect to the great industrial regions and centers of population. "It is recognized as the great center of the Nation's hardwood resources" (26).2

There are two 'principal forest types in the region (26),3 the chestnut­chestnut oak-yellow poplar type, and the oak-hickory type (fig, 1). These have been further divided (27) into 21 cover types, practically all of which are represented in this study.

Forest management in this extensive region has been dependent on a number of volume and Yield studies (6,8,!J, 12, 18,29,30) based on local data, some of which were very meager. Since the advent of the chestnut blight (Endothia parasitica), oak stands in the eastern part of the region have lost one of their fastest-growing components. This has altered the growth capacity of many stands and accordingly lessened the usefulness of some of the earlier yield tables. Recently, Yield tables (15) and yields for the average SIte (1) for oak in Penn.. sylvania have been published

1 Maintained at Philadelphia, Pa., in cooperation with the University of Pennsylvania. 2 Italic numbers in parentheses refer to Literature Cited, p. 86. a Shantz and Zon's oak-pine type was not included in this study because of th~lqw percentage of oak that

generally occurs and the resulting higher percentage of the faster growing p

115807°-37--1

2 TECHNICAL BULLETIN 560, U. S. DEPl'. OF AGRICULTURE

The present study, begun on a somewhat local basis more than 10 years ago," was expanded in 1928 to include all portions of the upland oak region. The yield, stand} and volume tables presented 5 were

MILES 390Q

Upland Oak Forests

f~~~~ O~k-Chestnu~-YellowPoplar

~Oak-HicKory

OKLA.

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FIGURE V-The upland oak forest region, showing location of temporary sample plots. One or more plots were obtained in each designated locality.

computed from measurements obtained on sample plots and from trees cut on logging operations throughout the region.

'Prior to 1921, W. W. Ashe, F. W. Basley, E. H. Frothingham, Russel Watson, and W. D. Sterrett worked on di1ferent phases of an oak growth study. Some of the results were publlshed in 1931 (9). In 19~J. h.owever, the present study grew out of the former and was undertaken by Frothingham and E. F. ~cuarthy at the Appalachian Forest Experiment Station. It was intensified by the establishment of a large number of plots, but was limited to the southern Appalachian Mountain region. Five years later it became a joint .project of the Allegheny, Appalachian, and Central States Forest Experiment Stations, under the direction of McCarthy, at that time director of the Central States Station. Under McCarthy'ssupervision the field data were collected and the preliminary analyses and compilations were made. When McCarthy left the Forest Service, the project was assigned to the Allegheny Station for completion.

• The volume tables ~~l"e computed under the direction of Donald Bruce and L. H. Reineke by their alinement chart met.qQ~..Jii.·.t. .T h.e yield and stand tables were computed under the direction of the author,Wechho is indebted, J¥»fMi~!'~i;,~ Schumacher for invaluable aid in outlining the study and in selection of t

YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 3

THE UPLAND OAK FORESTS

The upland oak forests are mostly second-growth sprout stands; the author estimates the remaining areas of virgin upland oak to be 350,000 acres, or only about 0.3 percent of the total upland oak area. A great number of tree species make uf the forest. The average percentage composition and frequency 0 occurrence of the various species, as found in the present study, are shown in table 1. Although the 15 species of oak and 50 associated species found in the region occur in innumerable combinations, from pure stands to mixtures including a great number of species, the five important oaks-white, black, scarlet, chestnut, and red-make up an average of 83 percent of the stand basal area.

41

nique.

TABLE I.-Stand composition and Jrequency oJ occurrence oj species on sample plots

[Composition and frequency of occurrence on the plots]

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All plots Site 40 (35-44) Site 50 (45-54) Site 60 (51Hl4) Site 70 (65-74) Bite 80 (7.Hl4)

Stand Stand Stand Stand Stand Stand Species composition Fre­ composition Fre­ composition Fre· composition Fre­ composition Fre­ composition Fre­

quen­ quen­ quen­ quen­ quen­ quen­cyof cy of cv or cyof cyof ev ot

Basal Nom- occur- Basal Nnm­ occur- Basal Nom- occur- Basal Nom- occur- Basal Num­ occur- Basal Num­ occur­ber of rence ber of rence ber of renee ber of renee ber of renee berof rencearea trees area trees area trees area trees area trees area trees

-­----­-­--­-­--­--­-­-­-­-­-­-­-­-­-­Per· e«: Per- Per- Per- Per- Per- Per- Per- Per- Per- Per- Per- Per- Per· Per- Per- Per­cent cent cent cent cent cent cent cent cent cent cent cent cent cent cent cent cent centoak (QturCUB alba L.) _______________ 28.23 31. 29 95.30 20.70 23.23 75.00 31.00 34.95 91.07 29.77 32.07 95.98 28.29 31. 25 97.79 18.04 24.31 93.33

lak (Q. rJelutina La M.).____________ 19.11 13.45 91. 58 15.63 11. 75 75.00 10.64 7.24 73.21 16.99 12.15 94.26 22.84 15.90 95.59 29.79 20.89 96.67oak (Q. coccineaMuenchh.) ________ 17.08 10.85 79.70 6.57 5.10 75.00 15.02 8.96 76.79 18.28 11.55 86.21 16.17 10.50 75.00 18.76 12.26 70.00 ut oak (Q. montana Wllld.) ________ 13.73 13.50 63.36 21.80 22.95 75.00 16.57 15.20 62.50 13.25 13.00 66.67 13.33 13.48 63.24 10.70 10.01 43.33 :lk (Q. borealiB maxima (Marsh.) ) --------_.- -----­-----­--­ --------­ 4.65 3.45 51.98 6.67 5.42 50.00 5.27 4.00 50.00 5.46 4.10 58.05 3.86 2.80 48.53 2.55 1.63 36.67 ~ (Q. Btellata Wang.) _______________ .90 1. 07 13.37 2.00 2. 35 25.00 1. 52 1. 57 12.50 .25 1.54 18.97 .30 .41 8.09 .15 .33 6.67m red oak (Q. rubta L.). ___________ .60 .47 4.21 ------­ ------­ ------­ .00 .08 3.57 1.29 .20 2.87 .78 .56 3.68 2.94 2.47 16.67 r (Q. palUBtris Muenchh.) __________ .40 .27 1. 73 ------­ ------- ---.--­ .81 .99 1. 79 .04 .02 1.15 .44 .21 2.94 3.10 2.49 3.33 ~ck oak (Q. marilandtca Muenchh.)_ .14 .17 1.24 ------­ ------- ------. ------- ------. ------. .01 .04 1.15 .01 .03 1.47 -----.- --_ .._-­ ------­miscellaneous-Hill's (Q. ellipsoi·E.!. Hill), bear (Q. tlici/oliaWang.),'f chinquapin (Q. prinoides Willd.) __ .14 .10 1.98 ------­ ------- ------­ .79 .35 5.36 .04 .05 2.30 .02 .08 .74 -----..- ------­ ------­swamp-swamp white (Q. bicolor

~ri:Z~~'M~1r~~~~~_~~:_ ~~~~:~_ .05 .05 2.97 ------­ ------­ ------­ .02 .. 04 3.57 .05 .04 3.45 .03 .04 2.21 .13 .09 3.33 -­--­-­--­--­--­--­--­--­-­-­-­--­-­--­--­-­-­rotal ____________ •__________________ 85.03 74.67 ------­ 73.37 70.80 ------­ 81. 70 73.38 ------­ 85.43 74.76 ------­ 86.07 75.26 ------­ 86.16 74.48 -- ----­--­= -­-­--­-­-­--­--­--­-­--­--­-­--­--­-­-­

'Y I-bitternut (Hicoria cordi/ormis ng.) Britt.) , bigleaf shagbark (H.i08a (Michx.) Barg.) ________________ 2.69 6.08 70.05 9.80 13.70 75.00 3.44 5.95 67.86 2.37 5.92 69.54 2.62 6.21 72.79 2.58 5.90 70.00la pine (Pinustlirgtntana Mill.) _____ 1.86 1.10 14.11 7.87 4.68 50.00 3.67 1.96 17.86 2.41 1.43 16.09 .56 .41 5.56 .64 .41 13.33 nit (Castanea dentata (Marsh.).h.) ______________________________ . __ 1.84 1.62 24.50 3.80 2.45 25.00 2.83 2.14 28.57 1. 51 1. 55 24.14 1.86 1.57 24.26 1,56 1.35 20.00aple (Acer rubrum L.) ______________ 1.31 4.23 52.21 1.20 1.35 50.00 1.64 5.51 46.43 1. 37 5.10 59.77 1.12 2.72 47.06 1.40 4.48 43.33 r poplar (Liriodendron tuliP~~ra L.)_ .84 .77 20.30 ------­ ------­ ------­ .18 .19 10.71 .71 .51 16.09 1.20 1.11 25.00 1.14 1:68 36.67 >18ck (liTaxinuB nigra Mars .), red le1ln81/1oonica Marsh.) _______________ .62 .97 21.04 ____ • __ ------­ ------­ .21 .51 10.71 .69 1.05 19.54 .77 1.18 27.21 .44 .68 26.67

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Group A, miscellaneolls-hophornbeam (Ostrf/a tJirginiana (Mill.) Koch), blue beech (Carpinus caroltniana Walt.),persimmon (Diospyros tJirginiana L.),sourwood (O:rtdendron arboreuan (L.)de 0.), holly (1 exopaca Aiton), sassafras (Sassafras t'ariifolium (Salisb.) Ktze.) ____ .57 1.43 30.20 .62 1.,28 50.00 .38 .87 21.43 .33 1.06 30.46 .66 1. 54 29.41 1. 67 3.66 43Red gum (Liquidambar styraciflua L.) _____ .54 .77 5.20 ------­ .65 .87 5.75 .71 1.12 7.35 .26 .21 3Black gum (Nyssa Bf/lvatica Marsh.) _______ .48 1.71 37.62 1. 22 2.78 so. 00 .44 2.17 42.86 .56 1.87 39.66 .40 1. 49 33.82 .36 .88 30Shortleaf pine tPmue echinata Mill) _______ .47 .31 4.21 ------­ ------- ------­ .80 .43 7.14 .44 .30 5.17 .22 .22 .74 1.24 .66 10Black locust (Robinia pseudoacaciaL.) ____ .44 .29 15.10 1. 55 1.08 25.00 .67 .39 19.64 .53 .33 17.82 .23 .20 10.29 .18 .19 10Pitch pine (Pinus rigida Mill.) ____________ .43 .29 4.95 ------­ ------­ .19 .14 5.36 .55 .28 6.32 .48 .43 4.41 ------­ ------­ ---­Group B, miscellaneous-red mulberry

(Morus rubra L,) redbud (Cerciscanaden­sis L.), staghorn sumach (Rhus Atrta (L.)Sudw.), hawthorns (Oratae~ spp.),dogwood (Cornus florida L. , service­berry (Amelanchier canadensis (L.)Med., A. laevis Weig.) __________________ .41 2.09 35.15 ------­ .15 25.00 .52 2.13 44.64 . •48 2.24 37.36 .32 2.16 31. 62 .15 .86 23.Northern white pine (Pinus strobus L.) _____ .35 .29 7.18 ------- ------... ------­ .33 .30 7.14 .35 .30 9.77 .42 .32 5.15 .03 .08 3.White ash (Fraxinus americana L.) ________ .30 .54 11.63 ------­ ------­ ------­ .44 .44 16.07 .13 .26 9.20 .41 .75 13.97 .50 1.11 10.Unknown or dead chestnut. ______ •_______ .26 .26 3.71 ------­ ------- ------­ .63 .77 3.57 .31 .27 5.17 .08 .06 2.21 .15 .21 3.Black walnut (Juglan8 nigra L.) __________ .20 .15 8.42 --- ---­ ______ w ------­ .15 .09 3.57 .17 .16 7.47 .22 .12 8.82 .36 •39 20. Beech (Fagus grandi/olia Ebrh.) ___________ .18 .56 12.13 .30 .75 25.00 .13 .20 7.14 .13 .34 8.62 .24 .95 18.38 .27 .79 13­Black cherry (Prunus serotina Ehrh.) _____ .18 .12 4.95 ------- ------­ ------­ .19 .33 7.14 .13 .08 4.02 .27 .11 5.88 .01 .03 3.Pignut hickory (Hicoria glabra (Mill.)Sweet). ________________________________ .

.18 .42 3.47 ------­ ------­ ------­ .22 .47 1. 79 .17 .31 2.87 .17 .50 5.15 .25 .71 3.Largetooth aspen (Populus grandidentataMichx.) ___________________________ .. ___ . .13 .08 2.23 ----...-- ------- ------­ .21 .10 3.57 .17 .10 1. 72 .04 .03 1. 47 .18 .11 6.Sugar maple (Acer saccharum Marsh.) ____ . .12 .36 10.89 .27 .98 25.00 .27 .57 10.71 .04 .17 6.90 .14 .40 14. 71 .23 .74 13.Shagbark hickory (Hicoria ovata (Mill.)Britt.) __________________________________

.11 .20 1.76 ----..-- ------.. -- ..---­ .32 .55 1. 79 .13 .25 2.30 .01 .03 .74 .02 .08 3.Aspen (Populus tremuloides Michx.) ______ .09 .07 2.23 ------­ ----- -- ------­ .33 .27 5.36 .01 .01 1. 15 .11 .06 2.21 .01 .03 3.Chokecherry (Prunu« virginiana L.) _______ .07 .08 3.47 ------- ------­ ------­ .05 .06 1. 79 .02 .03 1.72 .15 .16 5.88 .01 .03 3.Butternut (Jugla1l8 cinerea-L.) ____________ .06 .04 2.97 ----.. -­ ... _----- ..-..--_ .... .02 .02 1. 79 .06 .05 2.30 .10 .06 5.15 ------­ ------­---­..Cucumber magnolia (Magnolia accumtnataI",Uding mountain magnolia (M.raseri Walt.) ______________________ •_____

.05 .08 2.48 ----- -­ ------.. ------­ .04 .06 3.57 .02 .03 1.72 .09 .16 3.68 -----­.. ------­ ----­-American (Ulmus americana L.)slippery (U.fulva Micbx.) __________ .05 .18 4. 46 ----.. -­ ------­ --..---- ------- ------- ------­ .07 .18 4.02 .07 .29 7.35 .01 .04 3.. ore (Platanus occidentalis L.) _______ .04 .04 2.72 ------- ------­ ------- ..------ --.. ---- ------­ .01 .01 .57 .08 .08 5.15 .18 .19 10..·t birch (Betula lenta L.) ______________ .03 .04 2.23 ------- ------­ ------­ ------- --..---- ------­ .01 .01 .53 .06 .10 5.88 ------­ ------­ ----­rn hemlock (TltU(Jacanademis Carr.)_ .03 .04 .50 ----...-- ------- ------­ ------- -----_ .. --- -..-- ------­ ------­ ------­ .08 .10 1.47 ------- ------­ ---_ .

rit~)~t__ ~~~~r:: __~~~~~~~_~!~~ __ ~~:~_ •02 .07 .74 ------- -----­ .. ------­ ------- ----....... -..----­ .02 .11 .57 .02 .04 .74 .01 .12 3.Basswood (Tilia glabra Vent.), inclUdin~ (T. heterophf/lla michauxii (Nutt.) Sarg. _ .01 .03 1. 24 ---- .. -­ ------- ------­ ------­ ------­ ---­ ..-­ .01 .03 1.72 .01 .04 1. 47 ------­ ------­ ---_..Eastern red cedar (Juniperus tliroiniallaL.) _________________________ •______ • ____ •

.01 .02 2. 23 ------­ p-----­ ------- ..._----­ -----...- ----.._­ .01 .03 3.45 .01 .02 2.21 ------­ ------­ ----­I Undesignated hickories included.

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6 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE

The majority of the forests are understocked, unhealthy, and in a run-down condition, owing mainly to indiscriminate cutting and grazing, and to fire, disease, and insects. The chestnut blight alone has reduced the stocking and changed the composition (13) of more than one-third of these forests. However, well-stocked stands made up of both sprouts and seedlings are occasionally found throughout the region. Some of these are the result of one, two, or even three clear cuttings. For as long as 100 years, many timber areas near the sites of old iron furnaces were periodically clear cut for charcoal and at present appear to represent very nearly the growth capacity of the sites on which they are found." A large number of the study plots were located in such stands. Their yields furnish a measure of the volume of timber that can be obtained under what are thought to be the best natural growing conditions for even-aged stands. Even though the great bulk of the upland oak forests are now understocked, they should, if placed under good forest management, produce yields as good as or perhaps even better than those of the old furnace lands.

All-aged and understocked stands introduce perplexing variables which will require further study.

THE nELD TABLES

The yield values for fully stocked, even-aged, second-growth upland oak forests as determined in this study are summarized in table 2. Values are presented for even tens of site-quality index, with relative quality stated also. Site index is the height attained at an age of 50 years by the average dominant and codominant oak trees. Values for intermediate site indices can be obtained by interpolation from the tables or graphs.

The maximum mean annual growth of the merchantable stems on an average site is 47 cubic feet, or about 0.55 cord I?er acre. This is attained at about 50 years and continues at approximately the same rate up to 100 years. Although the rate is not high, it is fairly constant for this period of 50 years, or longer. Oak stands do not give heavy yields in comparison with softwoods, but their ability to maintain very nearly maximum growth for many years is.much in their favor.

oExcepting possIbly the poorer sites, where the percentage of seedlings is low.

YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 7

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TABLE 2.-Composite yield of second-growth upland oak (stand 0.6 inches d. b. h. and larger)-Continued

SITE INDEX 6O---AVERAGE SITE

Total Iheight. Averageaverage diameterBasal areaTreesAge (years) Idominant breast Entireper acre per acreand co­ high stem in-dominant side barkoak:

10________________ - -- --- --- -.-- ­20__________________ -- - --- -- --- ­30________________ -- - - - --- - -- - -­

- 40______________________________ 50________ -- - - ______ - ----- -- - -- ­60________________ --- -- - - -- ---- ­70____________ - - -____ - __- - --- -- ­SO______________________________ 90______________________________ 100_____________________________

Squarefeet CubicfeetInchesFeet NumberI

1.4 345

Yield per acre

Merchantable Inter-stem to a 4-inch nation-top outside al rulebark

Board Cubicfeet Cords feet

I

EntireScribner stem in-rule side bark

Board

Mean annual growth per acre

Merchan t a ble Inter-stem to a 4-inch nation-top outside al rulebark

Board feet Cubicfeet Cubicfeet .Cords feet

34 -_ ....

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q

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Z

26110___________ - - -- - ---- - - - ------ ­20_______________• ____-- - - ----- ­ 43

5630_________ - -- ---- -- - - - -------- ­6940________ --- - --- ---- - --- - - ---- ­

50____________ ------- - --- - ----- ­ 80 8960___________ - --- - ---- --------- ­9570____________ --- ------- - ----.- ­99SO________ ---- - - - - ---- ---- ----- ­

!l(L_____________ - - - -- - --- -- ---- ­ 103100_____________________________ 105

----_.-------- ­

17 30 41 51 60 67 71 75 77 79

4,060 1,945

965 611 482 390 326 292 268 248

41 68 84 93

100 108 115 123 130 138

_----­2.5 805 170

-­2.00 40 0.108

1,2654.0 10.35880 1,7255.3 1,580 18.59

6.3 2,165 2,230 26.24 2,590 2,800 32.947.2

8.0 2,970 3,290 38.71 8.S 3,325 3,730 43.88 9.4 3,655 4,120 48.47

10.1 3,970 4,480 52.71

850 3,200 6,300 9,700

12,800

50 500

1,400 3,150 5,650

42 43 43 43 42

29 40 45 47 47

.34

.46

.52

.55

.55

28 SO

126 162 183

2 12 28 52 81

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~ 15,650 18,300 20,900

8,350 11,050 13,700

42 41 40

47 46 45

.55

.54

.53

196 203 209

104 123 137

p2 t:1

SITE INDEX 7(}--GOOD SITE

10__________ - - -- -- - -- - - ----- -- -­ 21 43 1.63,140 410 10 0.12 41 1 0.0120______________________________ 8 _________ .2.91,500 7136 975 4.24360 150 49 18 .2130______________________________ 4.6 1,52548 743 88 1,270 1,75014.94 200 42Iii1 .50 58 740___________ - _____ - _____ - ----- ­ 472 6.0 2,07596 2,090 1,10060 24.59 5,500 52 52 .61 138 2850______________________________ 7.2 2,610374 10470 2,830 33.29 9,750 3,250 52 57 195.67 6560______________________________ 112 8.3 3,11578 304 3,4S0 13,900 6,70040.94 52 23258 .68 11270______________________________ 252 120 9.3 3,575 4,030 . 10,55083 47.41 17,700 51 25358 .68 151SO______________________________ 128 10.2 4,00087 224 4,510 21,200­ 14,10053.06 50 56 .66 265 17e90______________________________ 4,40090 207 136 11.0 4,960 24,500 17,200 4958.35 55 272 191.65100_____________________________ 92 192 143 11.7 4,780 5,400 63.53 27,650 19,900 48 .6454 276 199

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____ .lo. ____ 0.022490.24201.8 490442,435 18.3631 ----- ..---­57 60

3507.291,145 6203.4731,160 112 17.66565003,35019.881,6901,7955.390578 62215.77652,500 61 69

8,60030.712,6102,4406.999366 133275.8162 62

-40.59 6,65013,7503,4503,0858.3107290 189310.8Z6911,350 68

18,60048;944,1603,6909.5115235 227330.8015,900 60 67

23,10056.124,225 4,77010.7124196 246341.7959 58

19,70027,25062.824,725 5,34011.7132174 256344.776530,95069.065,200 5,87012.7 ~050140161 261344.7564562,10034,40075.066,3805,65013.6148148

10 TECHNICAL BULLETIN 560. U. S. DEPT. O~ AGRICULTURE

BASIC DATA

. Since permanent sample plots measured at intervals over a period of years were not available, it was necessary to use the temporary-plot method for determining yield. Its use assumes that contemporaneous measurement of several stands, on similar sites but of various a~es, gives the same results as successive measurements of an identical stand over a period of years. For the study 409 temporary plots were measured throughout the region (fig. 1). As stated before, fully stocked, even-aged stands were difficult to :find except in the vicinities of old iron furnaces. Nevertheless a fair geographic representation of most of the region was obtained.

PLOT SELECTION AND MEASUREMENT

The study plots were selected to meet the following requirements: (1) Thirty percent or more of the dominant stand composed of upland oak species; (2) fully stocked, as indicated by closed crown canopies (80 to 90 percent of complete closure) and the absence of very dense undergrowth; (3) even-aged; and (4) unifornily spaced tree stems. No distinct holes were permitted in the stand either on the plots or near their boundaries. In a few instances, where plots were estab­lished in stands containing recently killed chestnut trees, these trees were measured as if alive.

The field measurements were obtained by the standard methods set up by the committee on standardization appointed by the Society of American Foresters (28). Plot surveys were made with a staff com­pass and steel tape. The diameters of all trees 0.6 inch diameter breast high," and larger were measured with a diameter tape," Heights were measured with an Abney hand level, and ages were counted on cores obtained with a Swedish increment borer.

PRELIMINARY COMPUTATIONS

For each plot a tabulation of basal area, number of trees, and volume in each of four units (total cubic, merchantable cubic, Inter­national, and Scribner board feet) was made by species, crown class, and diameter breast high. These values were punched on cards so that the various sortings, countings, and summations necessary for the Yield analyses could be made on automatic machines. Volumes were obtained from tables," constructed for this purpose, which will be explained and presented later.

, Diameter breast high, 4.5 feet above average ground level. I On some plots, established in 1923, a 2.6-inch lower diameter limit was used. However, the errors in­

volved are relatively smaIl, as most of these plots are in the older age classes having few trees under 2.6inches diameter breast height. I The following tabulation shows the species for which the various volume tables were used. Only small

errors are likely to result from using substitute tables for species for which no tables are available, because the percentage of the stand volume involved Is very low, as shown in table 1. Even though the errors are smaIl, some of the selections are subject to criticism. For example, it would be more logical to use the redmaple volume table for such tolerant species as beech and sugar maple:

Volume table and other 8Peciu [or which table WII8 Ulled White oak AlI unknown species. Red oak Post oak, southern red oak, pin oak, black-Jack oak, and

other miscellaneous oak:species. Hickory - ------- . Ash. Virginia pine All pine, hemlock, and cedar. (For Scribner volumes, 88

percent ot the International volume was used.)YelIow poplar----------------- Aspen, basswood, cucumber, and sycamore.Red gum- ----------__~ Black gum.

YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 11

.

of

:;~~;;'i,~;Height curves for volume determination on each plot were made by '''8.. special process after careful analysis." The yield tables were ''',:constructed by Bruce's (3) and Reineke's (19) methods with some

odifications which are explained in the text to follow.

ELIMINATION OF PLOTS

Even though the sample stands used in this study were carefully selected as fully stocked, the difficulty met in finding such stands and the chance that an erratic one would be measured accidentally by one of the many field crews necessitated some statistical check on degree

stocking. Reineke (20) shows that the number of trees-average diameter relation, built up from a sample of an even-aged forest type, can be used as a standard for determining the density of stocking of individual stands. This use requires much less computational work than the usual basal area and number of trees tests because the dependent variable-average diameter takes care of the effect of both age and site. Also, Reineke shows graphically for a number of conifers, both in pure and mixed stands, that this relation is linear if expressed logarithmically. Application of this method to the oak­yield plot values was effected by computation of a logarithmic re­gression, log number of trees on log average diameter breast high. The resulting linear equation, representing the average relation for an of the yield plots, is-

Log number of trees=3.8638-1.4987 log average diameter breast high 11

By computing the residuals of log (number of trees) of the indi­vidual plots from the regression line, and grouping in terms of the standard error of regression, the grouping shown in table 3 was ob­tained. This shows no plot sufficiently erratic to warrant elimination, The one plot which is more than three times the standard error from the regression line is not beyond the realm of chance out of a total of 409 plots. Therefore, no plots were eliminated because of abnormal density.

It was, however, found necessary during the height-age analysis later described to eliminate five plots in the 80- and 90-year age classes. The samples of these two classes were found to be skewed; a large portion of the sample in each case was obtained in a single locality, Arbitrary limitation of the number of plots from anyone locality resulted in more nearly normal distributions in these classes.

10 In order to utilize the earlier measured field plots on which data for separate height-diameter curves for each major species had not been obtained, it was necessary to find some satisfactory method of assigning heights for volume computations. After the plots were sorted into 1o-footheight classes (probably averagedominant height), height-diameter em ves were plotted for the two numerically strongest age groups. The

• 60-, 70-,and 8O-foot height-dlameter curves for the 5O-yearclass were found practically to coincide with the corresponding curves for the 6O-yearclass. This test indicated no effect of age other than that already taken care of by dealing separately with each 1o-footheight class. To test the effect of species the 6O-foot heightclass was used. Separate height-diameter curves were constructed for each of the five major oak specles,white, black, scarlet, chestnut, and red. All of these curves followed the same trend; the greatest variation between the lowest and highest was but 5 feet. This indicated that species was of minor importance. A series of height-diameter curves, one for each lo-foot height group, was then plotted on one sheet. Prac­ticallyall of these merged into one curve a.t the lower end. Irregularities were ironed out and the final set of harmonized curves was made. This set of curves was tested graphically by plotting height-diameter curves from randomly pioked plots from several height classes. No bad discrepancies were detected, so these curves were considered su1Dcfently accurate for volume determinations. This analysis was made by Ray F. Bower at the Central States Forest ExPeriment Station in 1928.

11 Determined from average basal area. Blackcherry '.,. All cherry, beech sweet birch, elm, sugar maple, and

J-. miscellaneous otner species. Black walnut---,.,.~,.,.~_.:o:•.~:i~.._-------.-------- Butternut.

I

12 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE

TABLE 3.-D£stributiotJ, oj plots about regression line [or log (number oj tree8)~log (average d. b. h.) relation, by standard error groups

Standard error groups Distribution ot plots Standard error group~ Distribution of plots

+2 to +3_____________________ +1 to +2_____________________ oto +1. ______________________ oto -1.______________________ -1 to -2_____________________

Number 2

42 169 155 38

Percent 0.5

10.3 41. 3 37.9 9.3

-2 to -3 _____________________ -3 to -4_____________________

TotaL __________________

Number 2 ]- 409

5 2 --- ­o

Percent O.

-- ­100.

TABLE 4.-Average number oj years required Jor oak sprouts to reach breast height

Species Localities sampled

Sproutsmeasured

Average age at breast height

Species Localities sampled

Sproutsmeasured

--- ­Number

29 --~-

Average age at breast height

--- ­Years

3.1 ---~

1.7

White oak_________ Black oak. ________ Scarlet oak.; ______ Ohestnut oak, _____

Number 9

11 5 7

Number 315 140 358 16

Years 1.8 2.0 1.4 1.6

Post oak___________

Average.. ___

Number 1

-~--

YIELD ANALYSES

AGE OF STAND

The average age of the dominant and codominant trees was used as the stand age. This was obtained on each plot by averaging ring counts on 5 to 10 cores removed at breast height from as many dominant and codominant trees of the species prevailing. The resulting breast-height ages were corrected to total age by the addition of 2 years. This correction factor, which represents the average time required for the trees to reach breast height, was obtained from sprout analyses, the actual results of which are shown in table 4. Preliminary examination of the sprout measurements showed great variations in height at each age, which indicated both considerable variation in site from tree to tree and in vitality of the old root systems and stumps from which the sprouts originated. Assigning site values to individual sprouts would obviously involve so much speculation and error that no attempt was made to do it. The, general average for all sites was used instead. If stump ages are used, a correcti.on factor of 1 year is sufficient. The sample stands were considered even-aged if the ages of 'the individual trees of the dominant classes did not vary by more than 8 years.

,.. SITE INDEX

The height attained by the average dominant and codominant oak at the age of 50 years was used as the index of site quality. All oaks were grouped together in obtaining this height because species com­position changes with site and no one species Occurs invariably in the dominant stand on all sites. The diameter of this average tree Was obtained for each of the study plots in the customary way by averaging the basal areas of the dominant and codominant oaks and reading

The average relation between height and age for each 10-foot site index is presented in figure 2 and table 5. The site index of any stand

~ is obtained from this chart in the usual way by plotting the height of . U On a good many plots established during 1924, heights were measured on only two or three sample trees out of the dominant stand, so that it was impossible to construct hetght-dlameter curves directly.A careful analysis of the height-diameter relation and a special technique for the construction of the curves were worked out by B. Lucas at the Central States Forest Experiment Station in 1930. The average doml­nant height of each study plot was first computed by averaging the heights of all the trees measured. The plots were then combined by lo-foot average height groups, and height-diameter curves drawn for each group. .As much as 15 feet difference occurred between trees of the same diameter in different groupsThese groups were next subdivided by crown classesand new curves drawn. This time not much difference resulted between the dominant and codominant classesor between the intermediate and suppressed classesbut considerable difference was noted between the 2 groups. Comparlsons between species showed verylittle di1ference.' On the basis of these t1ndings 2 sets of harmonized curves were made for the various av­erage height groups, 1 for the dominant and codominant classes and 1for the intermediate and suppressed.With these harmonized curves 88 guides, the height-diameter curves tor individual plots were drawn by ,superimposing the actual height-diameter measurements for the plot, plotted on transparent graph paper,on the harmonized curve representing the same average height class. Since the harmonized curves were made for lo-foot average height classes only, interpolation was neressary when the average heJght of the plot was not an even lo-foot value. This was accomplished graphically by raJ...·sing.. or lowering the super­imposed sheet the required number ot units. Since the individual plots v~~g4P density, a shifting to left o~ right was then necessary to get the best fit to the plotte~ POints. Ifa.l?1b;~\"f~~low average derislty,the dJ&qleters tended to be somewhat larger for the same height,. andlf~., ... ::th6$'verage they would be;,¥6smaller. Th~ SBID.e procedure was used to obtain, both the dop}inantiD.'U.\mbdomhlant curves.

YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 10

the diameter equivalent from a table. The height was then read as usual from the height-diameter curve for the dominant stand."

120.----r -\I I III 1 I

I ­

I ­

J-

l-­

I ­

I­

o

...., »->

-

-

-

-1 I .I ,":l-..l. ~I I.! II ! II ! J I

20 30 40 SO 60 70 80 90 100 TOTAL AGE (YEARS)

FIGURE 2.-Height curves used for site classification.

14 TECHNICAL BULLETIN 560, U. B. DEPr. OF AGRICULTURE

the average dominant and codominant oak, as determined from meas­urements of the actual stand in question, over the age of the stand and reading the site index value from the curve passing nearest to this point. More exact readings can obviously be obtained byinterpolation.

TABLE 5.-Total height of average dominant and codominant oak

Total height by site index 1_ Total height by site index-

Total age (years) Total age (years) 40 50 60 70 80 40 50 60 70 80

- ­ - ­ - ­ - ­ - ­ --- ­Feet Feel Feel Feet Feet Feet Feet Feet Feet Feet10________________ 8 13 17 21 26 60________________ 45 56 67 78 8915________________ 12 18 24 29 35 65________________ 46 58 69 81 9220________________ 17 23 30 36 43 70________________ 48 60 71 83 9525________________

21 28 35 42 50 75_­ ______________ 49 61 73 85 9730________________ 25 33 41 48 56 SO ________________

50 62 75 87 9935________________ 29 38 46 54 63 85. _. _____________ 51 63 76 89 10140________________ 33 42 51 60 69 00________________ 52 64 77 00 10345________________ 37 46 56 65 75 95________________ 52 65 78 91 10450_______ . ________ 40 50 60 70 80 100_______________ 53 65 79 92 10555________________ 43 53 64 74 85

1 Total height of average dominant and codominant oak at 50 years.

DERIVATION OF THE SITE-INDEX CURVES

One of the most important problems involvedin the construction of yield tables from contemporaneous measurements of different stands, rather than from periodic remeasurements of identical stands, is that of assigning a site quality to those stands which are not of the reference age (in this case 50 years). The contemporaneous data may be used only on the assumption that the sample plot distributions throughout the range of site quality are approximately similar, in a geometric sense, for each age class. If so, an average curve of the dominant heights of all plots over age can be accepted as a satisfactory approximation of the dominant height-age curve for the average site. For the oak-Yield plots these heights are as given in column 2, table 6. The points representing plots on other than the average site are dis­tributed in the form of a comet-shaped belt widening with advancing age.

TABLE 6.-Location of site-classification curves

Height and Height by site index-standard devt-

Total age (yeats) ation of aver­age dominant 30 40 50 60 70 80 90oaks

-- ­ -- ­ -- ­ -- ­ -- ­ -- ­Feet Feel Feet Feet Feet Feet Feel Feet10___________________________ 18.1± 3.61 4.0 8.3 12.6 16.9 21. 2 25.6 29.920___________________________ 31.2± 5.32 10.4 16.8 23.1 29.5 35.8 42.2 48.530___: _______________________ 42.7± 6.42 17.6 25.3 32.9 40.6 48.3 56.0 63.e!lO ___________________________ 53.4± 7.42 24.4 33.3 42.1 51. 0 59.9 68.8 77.6

50_. _________________________ 62.7± 8.37 30.0 40.0 50.0 60.0 70.0 BO.O 90.000. ___________• ______________ 69.6± 9.23 33.5 44.6 55.6 66.6 77.6 88.7 99.770•• _________________________ 74.3± 9.83 35.9 47.7 59.4 71.2 82.9 94.6 106.3BO___________________________ 77.6±10~29 37.4 49.7 62.0 74.3 86.6 98.9 111.190___________________________ BO.3±10.62 38.8 51.5 64.2 76.9 89.5 102.3 114.9100. _______•_________________ 82. 5±10. 90 39.9 . 53.0 65.9 79.0 92.0 105.1 118.0

In most Yie~~tl?H,ll9ies recently made for second-growth stands the aver~e cury~~~s-'~~~it~ obtain, by anamorphosis, a senes of curves showing th~,.:ol\¥~~\~&fl.med at various ages on other than the average

YIELD, ETC., TABLES FOR EVEN-AGED UpLAND OAK FORESTS 15

site. These height curves are so spaced as to pass through the 40­foot, 50-foot, and successive 10-foot points on the 50-year ordinate, or reference age commonly used. The use of anamorphosis is a distinct step forward from the earlier technique of dividing the comet-shaped belt of points, by eye, into an arbitrary number of similar site-class belts, and of drawing, freehand, through the midzone of each a curve representative of height growth on that site. But the use of anamor­phosis assumes that the percentage relationship between heights on different sites at 50 years holds for all other ages. For example, if the height of the average dominant tree at 50 years on the poorest site is, as m the present case, about 60 percent of the height on the average site, an anamorphic curve for the poorest site would show a height

RD DEVIATION OFHEIGHT OFAVERAGE DOMINANTANDCODOMINANTOAK

'<: 15 C)

~ s ~ 10 ~ C

C 0:

5 C ~

<: ~

30 40 50 60 70 80 l::lU IVO

ONOFHEIGHTOFAVERAGE DOMINANTANDCODOMINANT OAK

/~ 2

~......--, ,/

\

~ -,"""'./'/

\

~

\

~

25 \\\

L..--1O

,

~

\\ \.\'1

-- ... V) o

10 20o CO 20<:

o i=: '::!: 15 0: ~ I.l.. o 10 h

~ o E 5

kI o Q oo

30 40 50 6010 20 TOTAL AGE {YEARS)

o

FIGURE 3.-Relation of standard deviation and coemclent of variation of height to age.

about 60 percent of that for the average site at 20 years or at any

other age.Actually, the percentage varies, particularly for the lesser ages. This will be seen from column 2 of table 6. The standard deviation from the height on the average site at 20 years, if multiplied by 3 and subtracted from the average (column 2), gives 15.2 feet as the height on the poorest site," which is less than 50 percent of the average. At 10 years the ratio has dropped to 40 percent. These percentage variations were found to be significantly correlated with age, as

shown in figure 3.14

11 If the 2O-year plots are distributed normally, in a statistical sense, about their mean, only lout of 370 plots would be more than three times the standard deviation from the aVerage;

it F. X. Schumacher originally suggested this test (5).kL:;:~~~,,":,.,;

---------------------

-------- -------- ---------------- -------- --------

------------------------ -------- ---------------- -------- ------ -- -------- ---------- ------ ------

16 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE

Since one percentage value was not applicable at all ages it was necessary to use varying percentages. This was accomplished by tcomputin~ the 10-foot height intervals on the 50-year ordinate (the classification age) in standard units (standard deviation) above or below the average curved value and applying these on each 10-year ordinate, converting back to actual height values by using the respec­tive standard unit equivalents and curved averages. The generalized equation for computing height of any site-index curve at any age is:

HA- l\H1.a=Ha-ua( ---;::;-J where H1.a=height of any site index 1 at any age a;

Ha=average height at any age a; HA=average height at any reference age A; ua=standard deviation of height about the average at any

age a; uA=standard deviation of height about the average at any

reference age A. The equation for these computations in the present study is:

62.7- 1\HI.a=Ha-ua ( 8.37 -J

where 62.7 = average height at the reference age, 50 years, from table 6, and 8.37 = standard deviation at the reference age, 50 years, from

table 6. Example: What is height of site-index curve 40 at 20 years? From

table 6 the average height at 20 years is found to be 31.2 feet and the standard deviation, 5.32 feet. Substituting these values in the equa­tion above and solving­

62.7- 40) H 40.20=31.2-5.32 ( 8.37 =31.2-14.4 =16.8

This method was used for computing the points in table 6 which were, in turn, plotted to form the customary set of site-index curves which have been presented in figure 2 and table 5. Determination of the site index of any stand can be made by use of the followingequation:

H - Ha)I=HA +UA ( U a

, where H=average dominant height of the stand in question, and the other terms are as defined above.

Example: What is the site index of a stand 40 years old with an average height of 48 feet? From table 6 the average height at 40 years is found to be 53.4 feet and the standard deviation is 7.42 feet. Sub­stituting and solving- . , .

1=62.7+8.37 (48~:~'3.4) =62.7-6.1 =56.6

"l ", •. ;,

~~;,.;J,.:

YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 17

PLOT DISTRIBUTION

Distribution of the sample stands by age and site index is shown in table 7. A good sample with respect to both site and age is indi­cated, though a weakness above 80 years is apparent. Considerable difficulty was experienced by the field parties in finding fully stocked plots in the older age classes.

TABLE 7.-Plot· distribution by age class and site index

Plot distribution by site index-Total age (years) Total

30--39 40-49 50-59 60-69 70--79 80--89 90--99

Num- Num- Num- Num- Num- Num- Nuan­ber ber berber ber ber ber10--19________________________________ 5 ________

20--29________________________________ 10 15 30 125 18 29 64

40-49 ___• ____________________________ 30--39________________________________ 1 25 1335 1 1 76

1 ---..._--­ 2 ________2 33 36 10 8450-59 ________________________________ 2 ________

60-69 ________________________________ 2 17 28 19 68 1 2 ________2 17 23 9 5470--79_______________•________________ 2 ________

80-89 ________________________________ 8 15 25--- .._--­ -----~--1 ________1 2---...--- ­90-99___. ____________________________ I ________ 1 --~-.-~ -- ­

TotaL___ .,___ •________ . _______ 2 12 128 183 171 7 404

NUMBER OF TREES

Yield data for the total stand were based on all trees 0.6 inch d. b. h. and over. The average curve of number of trees over age was plotted on semilogarithmic graph paper, in effect using -logarithm of number of trees over age. Use of this type of paper contracts the curve at the younger ages, where number of trees is great, making a decidedly less pronounced curve than on arithmetic paper and facilitating fitting the curve to the points." The series of curves for number of trees on different sites was obtained by a combination of mathematical and graphic methods of correlation. A multiple linear correlation between logarithm of number of trees, age, and site index was computed. The equation is:

Log (number of trees)=-0.01431 age-0.01113 site index+4.12427

This was modified by using Bruce and Reineke's (4) alinement-chart method to take care of the curvilinear relation between log (number of trees) and age. The net regression of log (number of trees) on site index showed no curvilinearity. The resulting values read from the modified alinement chart are shown in table 8 and pictured in figure 4.' The curves shown in this figure have the usual form, dropping rapidly in the younger age classes, then gradually flattening out. Thus, an average site has approximately 4,000 trees at 10 years of age, 1,000 at 30 years, and 500 at 50 years.

15It was found 8 good plan to replot this curve on arithmetic paper to be sure of a smooth trend.

115807°--31-----2

;,,;;.4 •.jf,,<

--

I

I~ ~~

(/;~-: /' ./ ./

~'/:/ '// -:

~~.>-:./

~~~'/

Ii~V fitV

10V 'f// ~

18 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS l~

~ITE INDEX ISO40' 80

70 ~ 140

60 ~

SO ~ 130 ii)

6,000 1----+4---+--t---t----t-~-t_-__t--_r--r_-1

40 120

50

"":'-...JIO5,OOO'-1\lT--t----+----+--t---l-_-+-_----l-_--J ....ct t&J

lij ~IOO

~ ~.

~4,0001:::) I

~ 90 Q.Iij ~=ffi

,

,~ lo.J 80

~ ~ "'(70

~ Q: 70~ 3,000 t­ " ~ ~ ~ 60~ -c" ..,J SO8~ ~ "'(.ll:l

40

30

20 ~

1010 20 30 40 50 60 70 80 90 100

TOTAL AGE (YEARS)

FIGURE 4.-Number of trees per acre shewing trends with age by site index. 0 0 10 20 30 40 50 60 70 80 90 100

TOTAL AGE (YEARS)TABLE S.-Total number of trees per acre 0.6 inch d. b. h. and larger

FIGURE 5.-Total basal area per acre for trees over 0.6 inch d. b. h. showing trend with age lly site index. Trees per acre by site index- Trees per acre by site index- STAND BASAL AREATotslage (years) I , IJ Total age (years) 1_----,,..-- --:--_--:-__ 40150160 70 80 4Q150160170180 The average relation between the total stand basal area (all trees

--'--'-_'__' 11 .__•__•__,__ '0.6 inch d. b. h. and over) and age for the various sites is shown in Num- Num- Num- Nuan- Num- Num- Num- Num- Num- Num­ figure 5.16 The values read from these curves are presented in table 9. ber ber ber ber ber

60 _ ber ber ber ber ber 15------ 4,710 3,660 2,825 2,170 1,675 10 ._ •••••• 6,850 5,295 4, 060 3,140 2,435 This analysis was accomplished graphically by a series of approxima­651 507 390 304 23565 _

590 457 353 274 21220__------- 3,260 2, 620 1,945 1,600 1,160 70 _ tions using the alinement-chart method."541 419 326 252 19625_- ---- 2, 235 1,730 1, 340 1,030 796 75 _30. 1,610 1,246 965 743 578 606 391 305 235 18280 _ 10 It is recognized that the straight-line relation above 40 years is not absolutely maintained and that35 1,245 967 744 578 447 483 375 292 224 17485 _ there should be 8 tendency for the curves to flatten out with advancing age. However, the data would40. 1,020 789 611 472 366 464 361 280 215 16890 _ not permit any but a straight line. It is believed that there may have been 8 tendency on the part of the 447 346 268 207 16145________________ 898 694 535 413 321 95 _ field crews to establish the boundaries of plots in the older stands tooclose to the trunks of the trees selected 428 332 2..~4 198 1M50________________ 802 ..623 482 374 290 100 _ and in this way Increase the basal ares. The difficulty of finding older stands probablY contributed to thisMo_______________ 724 1163 434 336 260 411 320 248 192 148

tendency. 17 See footnote on page 20.

------ ----------

------ ----------------- --------

.., ;,

20 TECHNICAL BULLETIN 560, U. S. DEPI' . OF AGRICULTURE

TABLE 9.-Total basal area per acre including all trees 0.6 inch d. b. h. and larger

2.­Basal area per acre by site index- Basal area per acre by site index-

Total afe Total age(years . (years)

40 50 60 70 80 40 50 60 70 80

Sq.ft.Sq.!t. Sq. ft. Sq.ft: Sq.!t. Sq.ft. Sq.ft. Sq.ft,Sq.!t. Sq.!t.10___________ 60___________3936 41 43 44 96 102 108 112 lIE15___________ 65___________49 53 56 58 60 99 112 12C106 1162(L __________ 70. _______ . __60 65 68 71. 73 102 120110. 115 12425______ • ____ 75___________69 74 78 80 83 105, 124113 119 12830________ •__ 80________ . __75 80 84 88 90 109 117 123 128 13235___________ 85. __________79 84 89 92 120'95 112 127 132 131140___________ 90 ___________82 88 93 96 99 124115 130 14013645______ •____ 95___________85 92 10096 103 127" 184119 139" 14460___________ 10(L. ________9589 104100 107 122 131 138 143 14855. __________ 92 99 104 . lOS III

DIAMETER OF THE AVERAGE TREE

Diameter of the tree of average basal area was obtained in the usual manner by dividing the stand basal area by the number of trees and reading the diameter equivalent from a basal-area table. The average relation with age and site was obtained in the same way from the average curves of basal area and number of trees.1S The average diameter equivalents were plotted and smoothed. The average relation with age and site is presentedin figure 6 and table 10;

40

10 20 30 40 50 60 70 80 90 TOTAL AGE (YEARS)

FIGURE 6.-Diameter of average tree at breast height showing trend with age by site imex.

17 The procedure followed in the basal area-age---site correlation was as follows: (1) A percentage aline­ment chart was made by Reineke's (19) method. (2) Age and site scales were adjusted simultaneously as explained by Reineke and Bruce (t1, pp. 11-14). (Old values of age and site used for both adjustments.) (3) With new 8jl;eand site values, new estimates of basal area were read. (4) With new basal area values both age and site axes were again tested and adjusted if necessary. Only site axis needed adjustment. (5) Basal area over age for site indices 40 and 80 were then read and plotted as a test to see if the relation was behaving normally. A constant percentage difference was noted between the two sites. (6) New estimates of basal area were read and the 'actual values were 'plotted over the estimated. The basal area axis was adjusted because the relation was not a 45° line. .(7) Another test of site index 40 and 80 was made followed by successive adjustments of site, age, and basal area until no further improvement was evident. It was found important to make the test curves of basal area over age after each change of the chart. Appli­cation of this method of analysis to these data was made by G. M. Jemison.

18 This is a digression from the standard method. The standard, direct correlation between average basal area, age, and siter_Ian average P,ereentage devlation twice as large and a standard error of estimatec

four times as large he method presented here (see table 32, p. (4). The difficulties encountered in this correlation rresults obtained led to the use of the less desirable method, which in this study gives closer the basic data.c. •

YIELD, :ETC., TABL:ES FOR EVEN-AGED UPLAND OAK FORESTS 21 TABLE lO.-Diameter of the average tree by age class and site index

Diameter at breast height by siteDiameter at breast height by site index-

index- Total ageTotal age (years)(years) 80706050408070605040

Incll~InchesInchesInchesInchesInches Inches Inches InchesInches 60___________ 9.8.37.26.15.210___________ 1.81.61.41.21.0 65___________ 10.8.87.66.55.515___• _______ 2.61.91.71.4 10.9.38.06.95.820___________ 70••_-------­~:t 3.42.52.21.8 75___________ ll.9.88.47.26.125___________ 4.43.83.22.8 SO ___________2.4 11.10.28.87.56.45.330___________ 4.64.03.42.9 12.85- __________ 10.69.17.86.76.2.5.435___________ 3.4 4.74.0 90___________ 12.1l.O9.48.16.940___________ 6.96.05.3 95___________4.53.8 13.11.49.88.47.17.645. __________ 6.65.84.94.2 13.100__________ 11.710.18.77.450___________ 8.37.26.35.34.555___________ 8.97.86.75.74.9

2 7 1 6

HEIGHT OF THE AVERAGE TREE

Height of the average tree (tree of average basal area) was deter­mined in the accustomed way by applying a percentage reduction factor to height values of the dominant stand. Figure 7 shows this percentage relation and table 11 present the final average values."

100

90

~80 I I I I II II I II-o~ 1- I I. I II:\: 10

o L.'_.....J__.J.-_-I--.....J-_...I.. ­

o I 2 3 4 5 6 7 8 9 10 II AVERAGE DIAMETER AT BREAST HEIGHT (INCHES)

FIGURll: 7.-Percentage relation between height of the average tree and height of the average dominant and codominant oak by average diameter.

TABLE n.-Total height of the average tree by age class and site index

Total height by site index-Total height by site index-

Total age (years) 'I'otal age (years) 70 8060504070 80605040

FeetFeetFeetFeet FeetFeetFeetFeetFeetFeet 817059493960_- __----- ------ ­211814II10______ ~- - ---' - -­ 7 847362514024' 65__-- -- ------ - -- ­29201515____-._ -- -- - ---- 10 75 8764534236 70_- ------ - ------ ­30251920. _____ -- -. - - ---- 14 78 906643 5425________________ 75__-- -------- ---­4236302418 92806880 ____________ ---­ 564442 4835282130___------------ ­ 948169574585. ___-------- ---­554732 4035____-- - -- -- -- --- 25 968370584690____- - - - ---. -- -. 52 6140_________ ------- 28 4436 9784715945. _______________ 95____-- --.- - ----- 46665740 4831 9986726050________________ 100___-------" ---- 477262524334 7666564655. ______ - -------- 37

10 Too much reliance must not be placed on this table, since lack of sufficient height measurements aeees­sitated obtaining the average heights in a rough graphical manner.

----------- ----------

YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 2322 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE

12. These curves show a remarkably steady increase in volume with advancing age, from the beginning, with practically no early 'stage of

YIELD IN CUBIC FEET

The total cubic volume analysis was done graphically by construc­ slow growth. This illustrates the early vigor of stands containingtion of a percentage alinement chart (19) which was then modified sprouts.slightly by adjustment of the site axis in the manner referred to under stand basal area. The relation between stand volume, age, and site, 6500

80is shown graphically in figure 8 and the values are tabulated in table 6,000 • .. ·\ .... 11~"'''''l'''''''''T'''''''1 I' T" .. , .. .. ".......,..,.,.........._.T ~r-',~, 6000

r--~I- IT·'· T'J 80

- / 5500

//v

/ / -:

/ / /

jV V /V1/ [/ /

/

/ / / /

/ V

IIV

/ V V

,/

./

/ IIV / '/V

lVI, //V -:V

IIV/V V !J/V /.

~~V

70'- /V B,5,000

~ 5000

i::' C,,)

iii

:V ­70 ~ . tJ

I::)

.~ -- -'-- / ./ ~4500 60 ~ ~ <.J

~ _ /V·i/"<- ~ "­.1::) \oJ~ 4,000 '?

III 60~ Q:: 4000 u:::) -c

~ '-- _'-- )/ 1/·;/'V ~ .> .;;, 0: 50~ 3500t.J

~ r-+--+--=--- L _ 1/,I//v .' ­-c 3.000 ~ 3000

..J~ . I /1/ 1./ " 7~ 50

\,J

0.. _' _ IA' / ...;·I/~ V ~ 40I " / '~ ~ ' /' . \,J 2500

~ -..I40:::) '1/ 1./ . V - ­ Q)..J

t.J

~. 7 /.' / '/ . .-L.----" ~ ~ 2.000 ~ 2000 I::) ~ r--'~~ A'~V/~I../."~ - ~ ~ ~ 1500II) J0U/V ' ­ ~

1,000 1000

~~l/ - ,OIl'

i...~ - - -'-

i

500V" I . ' ,: I I I I I I I -.jo «« I "I j I I I .1 .... f .•.• J... ,,1

0o /0 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 TOTAL. AGE. (YE.ARS) TOTAL AGE (YEARS)

FIGURE 8.-Yield per acre in cubic feet, excluding bark, showing trends with age by site index. FIGURE 9.-Yield per acre in cubic feet of merchantable stem, including bark (to a 4-inch top outside bark), showing trends with age by site index.

TABLE 12.-Yield per acre in cubic feet, excluding bark (all trees 0.6 inch d. b. h. and larger included) MERCHANTABLE CUBIC AND BOARD-FOOT YIELDS

Yields in merchantable cubic volume and board-foot volumes for both International and Scribner rules at various ages on different sites are presented in figures 9 and 10, and tables 13, 14, and 15. These were computed in the usual manner from the total cubic yield values, using the average ratios for the average diameter of each site-age class read from the curves shown in figure 11.

Yield per acre by site index- Yield per acre by site index-Total age Total age

(years) (years)40 50 60 70 80 40 50 60 70 80

Ou.ft, Cu. ft. co.«. Cu..ft; ou.«. Cu.[t. Cu.ft. cu.«. Cu.{t. oa.«.10___________ 60___. _______205 270 345 410 490 1,540 2,050 2,590, 3,115 3,69015___________ 65__________ .345 450 575 695 815 1,660 2,210 2,785 3,35020___________ 3,96070__________ .485 635 805 975 1,145 1,765 2,355 2,970 .3,575 4,22525___________ 75_______._._625 820 1,040 1,250 1,470 1,875 2,500 3,150 3,795 4,48030_________ .. 80__. _______ .755 1,000 1,265 1,7951,525 1,975 2,635 3,325 4,000 4,72535. __________ 85. _______. __900 1,180 1,495 1,800 2,120 2,075 2,770 3,490 4,205 4,97540_____. _____ 90_____._._._1,030 1,360 1,725 2,075 2,440 2,175 2,900 3,655 4,400 5,'20045. ____. ____ . 95___._ .. ____1,165 1,540 1,945 2,350 2,760 2,275 3,020 3,810 4,595 5,43050. _________ . 1,300 100._. _______1,720 2,165 2,610 3,085 2,375 3,140 3,970 4,780 5,65055... ______ ._ 1,420 1,895 2,385 2,870 3,400

--------- ----------

-------- ------ --- --- --------

24 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 25

35000I I I I I ,

i:' I I I I1~ >0000 I I 70

I i I

,i

/ ~/ I 17 I ............. CHANTABLE CUBIC FEET PER CUBIC FOOT'

1.2 '"Q i I I!250001 I I I 73 I

l.- 46 _~7 43 36 14 II 0 2I..J ~ 2 a .8~ ~ _ I)VV~ 4

Q..

~WOOO ~ I 0/1

~ ~~I ~ 15000 2 3 4 5 6 7 8 a 10 II 12 13 14~ 50 °0 ~ -..J

I I / /1' 7/ I 74 I........ 4 I

7~. ~ 10000<: '

40 6a i:: ~

50QO I I ·5:5K

::: () 4o o 10 20 30 40 50 60 70 ~80 90 100

TOTAL AGE (YEARS) ~ 3FIGURE 1O.-Yield per acre in board feet, International rule (lIS-inch kerf) (to a 5-inch top inside bark),

showing trends with age by site index.

TABLE 13.-Yield per acre in cubic feet of merchantable stem, including bark, to a it-inch top outside bark

00 2 3 4 5 6 7 8 9 10 II 12 13

ET PER CUBIC FOOT"I' 5

4

a 3

~ ~

2

TABLE 14.-Yield per acre in board feet, International rule, Ys-inch saw kerf, to a 5-inch top inside bark, including all trees\Qa,ving at least one 16-foot log

Total age (years) 1

Yield per acre by site index-Total age (years) 1

Yield per acre by site index­

40 50 GO 70 80 40 50

Bd·ft. 5,600 6,900 8,150 9,300

10,450 11,550 12,600 13,600 14,700

60

ns.«. 9,700

11,300 12,SOO 14,200 15,650 17,000 18,300 19,600 20,900

70

tu.«. 13,900 15,800 17,700 19,500 21,200 22,900 24,500 26,100 27,650

80

ns.«. 18,600 20,900 23,100 25,200 27,250 29,150 30,950 32,700 34,400

15________ 20________ 25________ 30________ 35________ 40________ 45________ 50________ 55_______ .

tu.«. 0 0 0

100 300 600 950

1,400 2,000

tu:«. 0 0 0

350 800

1,400 2,250 3,250 4,350

Bd·ft. 0 0

300 850

1,900 3,200 4,700 6,300 8,000

Bd·ft. 0

150 700

1,750 3,550 5,500 7,650 9,750

11,850

Bd·ft. 50

350 1,450 3,350 5,9.'50 8,600

11,200 13,750 16,250

60________ 65________ 70________ 75________ 80________ .85________ 90________ 95________ 100_______

ns.«. 2,700 3,450 4,250 5,100 5,900 6,750 7,600 8,350 9,200

00 2 3 4 5 6 7 8' 9 10 II 12 13 14

AVERAGE DIAMETER AT BREAST HEIGHT (INCHES)

FIGURE ll.-Merchantable cubic foot-total cubic foot and board foot-total cubic foot ratios for various average diameters.

I No trees containing a 16-foot log with a top diameter inside bark of 5.0 inches below 15-year class.

OARD FEET PER CUBIC FOOT.,.,. • _.~ ... ,--" I I_I'~_ ......

-II ~"""1

./ .s-

Y -6

14

"IV /

vi v

7i /

~ /

~ sz-W Yield per acre (merchantable) by Yield per acre (merchantable) bysite index-

Total age (years) Total age

(years)

site index­

40 50 60 70 80 40 50 60 70 80 _._--­

Gu.{t. Ou.ft. ce.«. ca:«. oa.«.10___________ co:«. co:«. co.«. Ou.ft, oe.«.60 ___________0 0 0 10 20 1,420 2, 080 2,800 15___________ 3,480 4,16065___________0 20 40 80 19020___________ 1,590 2,290 3,050 3,770 4,48070___________20 70 170 360 620 1,750 2,51025___________ 3,290 4,030 4,77075___________100 250 510 820 1,17030___________ 1,900 2.710 3,510' 4,280 5,06080 ___________270 540 880 1,270 1,69035___________ 2,050 2,900 3,730 4,510 5,34085___________480 820 1,240 1,690 2,160 2,20040___________ 3,070 3,920 4,740 5.600680 1,090 90_- _________1,580 2,090 2,610 2,33045___________ 3,230 4,120 4,960 5,870870 95___________1,350, 1,910 2,470 3,04050___________ 2,460 3,'380 4,300 5,180 6,130100__________1,060 1,600 2.230 2,830 3,45055___________ 2,590 3,520 4,480 , 5,400 6,3801,240 1,840 2, 520 3,180 3,820

------ -------------- --------

--- -- ---

27 26 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE

TABLE 15.-Yield per acre in board feet, Scribner rule, to an 8-inch top inside bark, including all trees having at least one 16-foot log

Yield per acre by site index- Yield per acre by site index-Total age Total age(years) 1 (years) 1

50

< 40

--60

---

80 40 50

---70

-­70 60 80

sa.«. ss.«. sa.«. Bd,ft. es.«. na.«. ea.«. ss.«. Ed. ft. tu.«.25_.. ______ 65_________ 13,70(0 150 1,700 4,3500 0 50 550 8,55030_________ 70_________ 15,90(0 50 200 500 2,350 5,650 10,5500 80075_________35_.. __. ___ 1,250 1,100 12,400 17,85<0 50 200 550 3,150 7,00040_________ 8050 150 2,500 _8,-350. .14,1001,100 19,7OC500 _________.,...!..-~5'O. J ..O.Oo....45_________ 85__.. _____100 4,300300 2,000 1,800 4,850 9,700 21,4OC900 15,70090_________50_._._._._ 150 6,6501,400 3,250 23,05(500 2,200 5,800 17,20011,05055_________ 95_________ 24,6()(250 750 2,150 4,950 9,000 2,700 6,700 12,350 18,60060_________ 100________400 1,100 6,700 11,3503,150 3,350 26,10(7,750 13,700 19,900

1 No trees containing a 16-foot log with a top diameter inside bark of 8.0 inches below 25-year class.

Average-diameter, number-of-trees, and basal-area values for the merchantable cubic- and board-foot stands are presented in tables 16-24. These were also computed from like values for the entire stand by using average ratios. Perfect checks between these tables are not expected, because of differences in weighting.

TABLE 16.-Average diameter at breast height of the merchantable cubic-foot stand, including all trees having any merchantable cubic volume (to a 4-inch top outside bark)

Average diameter at breast Average diameter at breast height by site index- height by site index-

Total age (years) Total age (years)

40 50 60 70 80 40 50 60 70 80

-­-­-­ -­-­-­-­In. In. In. In. In. In. In. In. In. In.10________________ 0.0 0.0 0.0 0.0 4.2 tiO___• ____________ 6.1 6.8 7~7 8.6 9.715________________ .0 4.2 4.3 4.4 4.5 65________________ 6.3 7.1 8:' 1 9.1 10. ~ 20________________ 4.3 4.4 4.5 4.7 5.0 70________________ 6.5 7.4 8.4 9.5 10.725________________ 4.5 4.7 4.8 5.1 5.5 75____ . __________ 6.8 7.7 8.7 9.9 11.230________________ 4.7 5.0 5.2 5.6 6.2 80. _______________ 7.0 7.9 9.1 10.3 11. 7 35__. _____________ 4.9 5.3 5.7 6.1 6.8 85________________ 7.2 8.2 9.4 10.7 12. ~ 40________________ 5.2 5.6 6.1 6.7 7.5 90________________ 7.4 8.5 9.7 11.0 12.745________________ 5.4 5.9 6.6 7.2 8.1 95________________ 7.6 8.7 10.0 11.4 13.1

50. _. _____________ 5.6 6.2 7.0 7.7 8.6 100_______________ 7.8 9.0 10.3 11.7 13.e55________________ 5.8 6.5 7.3 8.2 9.2

TABLE 17.-Number of trees per acre in merchantable cubic-foot stand, including all trees having any merchantable cubic volume (to a 4-inch top outside bark)

YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS

TABLE 18.-Basal area per acre in merchanioble cubic-foot stand, including all trees having any merchantable cubic volume (to a 4-inch top outside bark)

TABLE 19.-Average diameter at breast height of the International board foot stand, including all trees having at least one 16-foot log with a 5-inch top inside bark

Basal area per acre by site Basal area per acre by site index­ . index-

Total age (years) Total age (years)

40 50 60 70 80 40 50 60 70 80

-­-­-­-­ -­-­-­--Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft. Sq. ft.

10__-. __- -- ­ - - -- -­ 0.0 0.0 0.0 0.0 4.0 60_. _._. __________ 88.4 98.2 105.6 110.7 114. ~

15_____. ­ - --' - - - -­ .0 2.6 7.6 15.1 25.0 6.~ _______ - - - - - --.' 92.9 102.5 109.5 114.8 119.<

20•• ____ ---­ - -- --­ 5.8 16.8 26.3 37.5 51. 7 70_______ . ­ -- ­ - --­ 97.2 106.2 113.8 119.0 123. i

25_. -.__-- ­ -. - -- -­ 23.3 37.0 49.6 63.0 71. 2 75_______ .._______ 101.4 110.6 118.0 123.2 127.{

30. - -- --­ - - --- ­ - -­ 40.9 56.8 68.4 77.5 83.9 80________________ 105.4 114.3 122.0 127.3 131.4 35. _____________ ._ 55.3 68.4 79.1 86.1 91.1 85. _­ _____________ 109. 1 118.3 126.0 131. 3 135.!

40___. ___ · ________ 64.5 76.7 86.1 92.2 96.3 90_______ ._. __---. 112.8 122.2 130.0 135.5 139. j

45_. ______________ 71.7 83.3 91. 6 97.1 101.3 95________________ 116.3 126.0 134.0 139.4 143. j

50. _____________ ._ 77.7 88.9 96.3 101.9 106.1 100______ ---­ -. --­ 119.6 129.6 138.1 143.2 147.1 55________________ 83.2 93.8 101.0 106.2 110.3

;.I

Total age (years)

Average diameter at breast height by site index- Total age (years)

Average diameter at breast height by site index­

40 50 60 70 80 40 50 -­

In. 8.3 8.5 8.7 8.9 9.1 9.3 9.6 9.8

10.0

60 -­

In. 8.9 9.2 9.5 9.8

10.0 10.3 10.5 10.8 11.0

70 -­

In. 9.7

10.0 10.4 10.8 11. 1 11.4 11.7 12.0 12.3

80 -­

In. 10. Ii 11. 1 11. ~ 1U 12. ~ 12. j 13.] 13.1 13.1

15__-... -- -------­20____. ____ ------­25____----­ --.---­30_____. __._ -. ---­35_- -- -- ­ - - - -- ---­40. ______________ _" 45____- - - - - - - - - - -­50_­ -- --. - -- ­ ----­55. ___­ - - - - - --­ --­

In. 0.0 .0

7.0 7.1 7.2 7.3 7.5 7.6 7.7

-­In. 0.0 .0

7.1 7.2 7.4 7.5 7.7 7.9 8.1

-­In. 0.0 7.1 7.2 7.4 7.6 7.8 8.1 8.3 8.6

-­In. 0.0 7.1 7.3 7.6 7.9 8.2 8.5 8.9 9.3

In. 7.1 7.2 7.5 7.9 8.3 8.7 9.2 9.7

10.2

60____. ___________ 65______________ ._ 70____-- - - - - - - - - -­75____-. - --­ -.-­ -­80____________ ---­85______ . ______ . _90 ________________ 95__________ ­ ----­100_______________

In. 7.9 8.0 8.1 8.3 8.4 8.6 8.7 8.9 9.0

_

TABLE 20.-Number of trees per acre in International board foot stand, including all trees having at least one 16-foot log with a 5-inch top inside bark

Total age (years)

Trees per acre by site index-Total age (years)

Trees per acre by site index­

40 50 60 70 80 -­-­-­--

Num- Num- Num- Num- Num­bet bet bet ber ber 137 195 214 201 177 156 208 209 192 171 175 214 206 186 161 193 217 204 183 161 210 219 203 180 1~

224 220 202 178 15f 229 221 201 177 15: 232 221 I 200 175 14\ 234 222 199 173 14!

40 50 60 70 80

15__'_ ---- ­------­20_. __--­ - -------­25. ___-- -- -------­30____----­ ------­35__-- -----------­40____ ­ -- ­ - -.----­45______ ­ -- --­ - --­50_. __­ ___ ---­ ---­55____­- -­ - - - - - - --

Num­ber

0 0 3

17 34 53 74 95

117

--Num­

bet 0 0

14 36 64 91

117 143 169

--Num­

beT 0 6

28 64

103 139 174 202 213

--Num­

ber 0

17 53 96

140 171 192 205 205

--Num­

bet 5

32 82

133 178

187 191 190 186

60____---- -------­65____­ - - - - - - - - -.­70____________ . ___

75_­ -- ­ -- -- -.­ ---­80____-- ---------­85_____-.­ - ------­90________________ 95________ . _______ 100_____ . _________

TABLE 21.-Basal area per acre in International board foot stand, includin,g all trees having at least one 16-foot log with a 5-inch top inside bark

Trees per acre by site index- Trees per acre by site index-

Total age (years) Total age (years) 4040 50 60 70 80 60 70 8050

Num- Num- Num- Num- Num- Num- Num- Num- Num- Num­bet bet ber ber ber ber ber ber bet bet60________________10. _______________ 49 4570 0 0 403 333 2790 22515________________ 65________________25 153 435 377 3120 85 251 258 20770- _______________20________________ 82 176 253 414330 406 356 295 240 19225__• _____________ 75__. _____________327 402 453 454 401246 340 283 227 18180________________30____. ___________ 359 436 473 453 393410 330 273 218 17385________________35________________ 424 475 322 165460 416 358 384 264 21040___________ . ____ 90. _. _____________435 314 159456 467 370 313 377 255 20395________________45____. ___________ 154473 456 409 344 287 368 306 246 19650_______ . ________ 100_______________478 442 265 298 237383 322 362 190 15055________________ 472 425 244357 300

Basal area per acre by site index-Basal area per acre by site index-Total age (years) Total age (years) 80706050408070605040

ss.«.Sq.ft.Sq.[t. sc«ss.«.Sq. ft. Sq.ft,Sq.[t.sfl./t.Sq.ft. 108.599.988.670.544.960____-- - --- -- -- -.15________________ 1.80.00.00.00.0 114.2106.595.479.454.38.7 65___. - - -- -------­20____________ ---­ 4.61.6.0.0 70________________ 119.6112.6101.686.963.325.015.57.83.6.8 124.825____-- -----.---­ 117.9107.175____- ______ -.--­ 92.772.245.530.018.9 129.230____---- --.--- -- 4.5 9.6 80 ________________ 122.8112.398. 280.066.847.932.018.79.4 85_________ . ______ 134.235____--- - -- -----­ 127.7117.6103.586.679.064.546.127.814.9 90________________ 138.3132.040_. __--.-- -.- ---­ 122.7108.8 92.088.076.859.537.021.4 143.3136.545_. __---- - ------­ 127.8113.897.095__. _-.. _- -.-.- -­95.685.371.147.650______ -. --- - ---- 28.4 147.B140.3132.6119.1102.0100___- - -- --.- ---­102.355._. ______ • ______ 93180.859.236.8

------ --------

------ -- --

28 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 29

TABLE 22.-Average diameter at breast height of the Scribner board foot stand, in­cluding all trees having at least one l6-foot log with an 8-inch top inside bark TABLE 25.-Yield per acre of merchantable stem in cords, including bark, to a 4--inch

top outside bark

Total age (years)

A verage diameter at breast height by site index-

Total age(years)

A verage diameter at breast height by site index­

40 50 60 70 80 40 50

-­In.

11.0 11.1 11. 2 11. 3 11.4 11.5 11. 7 11.8

60

-­In.

II. 3 II. 4 11. 6 11. 7 11.9 12.1 12.3 12.5

70

- ­In.

11.8 12.1 12.3 12.5 12.8 13.0 13.3 13.5

80

-­In. 12.5 12.9 13.2 13.5 13.9 l4.2 14.5 14.9

25________________ 30________________ 35________________ 40. __________ • ____ 45_____________ ' __ 150. _______________ 55__. _____________ 60________________

In. 0.0 .0 .0

10.6 10.6 10.6 10.7 10.7

-­In. 0.0 .0

10.6 10.6 10.7 10.7 10.8 10.9

-­In. 0.0

10.6 10.7 10.7 10.8 10.9 11. 0 II. 2

- ­

In. 10.6 10.6 10.7 10.8 11.0 II. 2 11. 4 11. 6

- ­

In. 10.6 10.7 10.9 II. 1 II. 3 II. 6 11.9 12.2

65________________ 70________________ 75________________ 80 ______________._ 85________________ 90________________ 95________________ 100_______________

In. 10.8 10.8 10.9 10.9 II. 0 ILl II. 1 II. 2

7°1 I i I

Yield per acre of merchantable Yield per acre of merchantable

Total age stem by site index-

Total age stem by site index­

(years) (years)

40 50 60 70 80 40 50 60 70 80

-­--­-­--­ -­- ­ -­-­Cords Cords Cords Cord., Cords Cords Cords Cords Cords Cords10___________ 0.0 0.0 0.0 0.12 0.24 60___________ 16.71 24.47 32.94 40.94 48.9415___________ .0 .24 .47 .94 2.24 65___________ 18.71 26.94 35.88 44.35 52.7120___________ .24 .82 2.00 4.24 7.29 70___________ 20.59 29.53 38.71 47.41 56.1225___________ I. 18 2.94 6.00 9.65 13.76 75___________ 22.35 31. 88 41. 29 50.35 59.5330___________ 3.18 6.35 10.35 14.94 19.88 80___________ 24.12 34.12 43.88 53.06 62.8235___________ 5.65 9.65 14.59 19.88 25.41 85 ___________ 25.88 36.12 46.12 55.76 65.8840___________ 8.00 12.82 18.59 24.59 30.71 90___________ 27.41 38.00 48.47 58.35 69.0645. __________ 10.24 15.88 22.47 29.06 35.76 95___________ 28.94 39.36 50.59 60.94 72.12

50___________ 12.47 18.82 26.24 33.29 40.59 100__________ 30.47 41. 41 52.71 63.53 75.0655___________ 14.59 21. 65 29.65 37.41 44.94 TABLE 23.-Number of trees per acre in Scribner board foot stand, including all

trees having at least one l6-foot log with an 8-inch top inside bark

Trees per acre by site index- Trees per acre by site index-Total age Total age(years) (years)

40 50 60 70 80 40 50 GO 70 80

Num- Num- Num- Num- Num- Num- Num- Num- Num- Num­ber bet ber ber ber ber ber ber25__________ . ____ ber ber65_____• ________._0 0 0 2 530______.._________ 17 36 64 91 10770________________0 0 3 148 21 45 7435_______ •________ 100 11175______• _________0 2 8 15 26 27 5440________ . _______ 85 108 11480_______________ .2 6 14 23 40 34 64 9645.. _____________ 114 11885________________4 10 22 35 5850________________ 42 74 104 119 12090________________7 15 31 51 78 50 8355________________ 111 124 12195________________10 20 41 67 92 58 90 117 127 12260________.. ______ 100_______________13 23 53 80 101 66 102 124 129 122

TABLE 24.-Basal area per acre in Scribner board foot stand, including all trees having at least one l6-foot log with an 8-inch top inside bark

Basal area per acre by site Basal area per acre by siteindex- index-Total afe Total3ge

(years (years) 40 50 60 70 80 40 50 60 70 80

Sq·ft. Sq. ft. Sq,ft.sc« Sq.ft. Sq.ft. Sq,ft.25_________ •______ Sq. ft. Sq.{t.Sf/.ft.65________________0.0 0.0 0.0 1.0 2.5 10.5 23.630________________ 44.6 69.1 90.670. __________ ..____ .0 .0 1.7 3.6 8.2 13.6 30.435________________ 54.1 79.4 100.175________________.0 1.7 4.4 8.9 17.1 17.'5 37.3 63.2 88.9 108.640______________ ._ SO________________.2 3.3 8.3 14.9 28.3 21.9 44.6 71.8 97.145________________ 116.485________________1.7 5.6 12.9 23.0 41.3 26.8 51.9 80.0 105.1 123.450________________ 90________________3.6 8.6 19.0 34.6 54.8 32.0 59.5 88.1 112.5 130.055__• ____ . _______ 95__________ • _____5.3 12.6 26.0 46.0 68.0 37.8 67.5 96.1 119.3 136.060________ '-" ____ 100_. _____________7.6 17.4 35.2 ;9.657.8 43.9 75.9 103.6 126.0 141.9

YIELD IN CORDS

Satisfactory factors for converting solid wood volumes of oak trees of various diameters to stacked cords have not been determined. A recent study 20 in oak stands gives an average factor of 85 cubic feet of solid wood per cord. With this factor the merchantable cubic ;yield was converted to cords, as presented in table 25.

20 Made by the Allegheny Forest Experiment Station on the Black Rock Forest, Cornwall, N. Y.; basis. 23 piles of wood totaling 10 cords.

60, h' ~ l( 50 S:2 ~

i~1 7n 1==+1°6 1 ~ ~ I .A" I

.......,..... I

I ~ 30

I -------lso

(,!5

-J

~ I I I --140 ~ , 20 <:

~ 10

Y I I ~80

I/'I I I ---.., 70

0' I I I I o 20 40 eo eo

TOTAL AGE (YEARS)

FIGURE 12.-Mean annual growth per acre in cubic feet of entire stand excluding bark, showing trends with age by site index.

I

31 30 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE

MEAN ANNUAL GROWTH

The relations of mean annual growth, in the first four units, to, age and site are shown in figures 12, 13, and 14, and the tabular values, including those in cords, are presented in tables 26, 27, 28, 29, and 30. Culmination of growth in total cubic volume occurs at 50 years on all sites. This is the point at which the yearly growth reaches its maximum. The decline on both sides of the point is so gradual, however, that there is only 1 percent difference between the ages of 40 and 60 years. Culmination for the merchantable stand"

80

i:' ~ Ii:

I I~ ~ 60 ~

~ Q

J'\ IQ:

~ 40

:t:J.,: ~ o Q: ~

20 40 60

I II -I / /f I

20

I ~ 40" ~ <: <: ~ <:

~

80 100 TOTAL AGE (YEARS)

FIGURE 13.-Mean annual growth per acre in cubic feet of merchantable stand including bark, to a 4-inch top outside bark, showing trends with age by site index.

which is of more practical value, takes place at 55 years on the best sites, and at 90 years on the poorest. The trend here also is gradual after the point of culmination is reached, as shown in table 31, which expresses the mean annual growth as a percentage of the maximum for each site. This fact permits considerable leeway in determination of the rotation age when considering only the volume production. The growth rate is within 5 percent of the maximum for a period of approximately 50 years on any site, the best site arriving at this point at about 4:5 years and the poorest at 70 years.

/1 I I -----l80l

70

G5 C),

60 ~ ~ Ci)

50

YIELD, ETC., 'tABLES FOR EVEN-AGED UPLAND OAK FORESTS

400 I 1 I I

~

~ l(

~ 3:3 0 0 Q

~

~ Q

'" ll: \jj IQ.. 200

~ ~ '0

~ --J :§ <: . I<: 100

'" <: ~ ~

I

I i

Ir

'II

I Ir /7

/~ II

V

I \80

:=:J----- --------I

I =:j

rJ C)

~

~ (;)

00 20 60 80 tOO

TOTAL AGE (YEARS)

FIGURE H.-Mean annual growth per acre in board feet, International rule, ;{i-inch kerr to a 5-inch top, inside bark, showing trends with age by site index.

TABLE 26.-Mean annual growth per acre in cubic feet, entire stand, exclnding bark; all trees 0.6 inch d. b. h. and larger included

Total age (years)

Annual growth per acre by site index­

40 50 60 70 80

Total age (years)

Annual growth per acre by site index~

40 50 60 70 80

--­ --­ -­ --­ -­-­ --­ --­

10__.---- .. -­15. _____ - ---­20_­ __. ______ 25___________ 30___________ 35__­ ________ 40___________ 45___________ 50___________ 55.. _________

Cubic feet

20 23 24 25 25 26 26 26 26 26

Cubic feet

27 30 32 33 33 34 34 34 34 34

Cubic }eet

31 38 40 42 42 43 43 43 43 43

Cubic feet

41 4l\ 49 so 51 iii 52 52 52 52

Cubic feet

49 54 57 ii9 60 61 61 61 62 62

60 ___________ 65_________ -­70___________ 75___________ RO ___________ 8.5 ___________ 90___________ 95___________ 100__________

Cubic [eet

26 26 2ii 25 25 24 24 24 24

Cubic feet

34 34 34 33 33 33 32 32 31

Cubic feet

43 43 42 42 42 41 41 40 40

Cubic feet

52 52 51 iiI so 49 49 48 48

8 7 ,6

Cubic feet

6 6 6 6 5 5 5 5 5

--- --- --- --- --- ----- --- --- --- ----- --- ---

----

-------- --- --- ------ -- --- --- ------

--- --- --- --- --- -----

32 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE

TABLE 27.-Mean annual growth per acre in cubic feet, merchantable stand, including baric, to a ft.-inch top outside baric

- ----------------~

YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 33

TABLE 30.-Mean annual growth per acre of merchantable stem in cords,' including bark, to a ft.-inch top outside bark

Annual growth per acre, by siteAnnual growth per acre, by site index-index-

Total ageTotal age (years)(years)

70 8050 604070 806040 50 --~

Cords Cords CordsCords Cord'CordsCords CordsCords Cords 60 ___________10___________ 0.41 o..15 0.68 O.E ,2 0.02 0.280.00 0.010.00 0.00 65 ___________1.1___________ .41 .68 . f 1.55.15 .29.03 .06.00 .02 70 ___________20___________ .42 .68 . E o.29 .55.21 .36.10.01 .04 7.',___________ 25 ___________ .67.43 .55 .7 9.30.24 .39 .55.12.05 80 ___________30 ___________ .66.43 ./9..15 .66 .30.50.34.11 .21 8.1___________35 ___________ .66.42 ./ 8. .14 .30.42 .73.57.28.16 90 ___________40 ___________ .6.1.42 .54 .i.30.77.46 .tu.20 .32 9.1___________45___________ .64 ./.42 .53.79 .30.50 .65.23 .35 100__________50 _____• _____ .51.41 ./. I'll .53.30..12 .67.25 .38

55 ___________ .82.39 .54 .68.27

) Converting factor, 85 cubic feet per cord.

TABLE 31.-Percent of maximum mean annual growth per acre, at successive ages­merchantable stem, including bark, to a 4-inch top outside bark 1

Annual growth per acre by site

Total age (years)

40

Cubic feet

10_______• ___ 015___________ 020 ___________ 125___________ 4

30___________ 935___________ 1440___________ 1745___________ 1950___________ 2155___________ 23

index­

50 7050

Cubic Cubic Cubic feet feet feet

0 10 1 3 .1 4 8 18

10 20 3::1 18 29 42 23 4R35 27 40 52 30 42 55 32 45 57

4633 58

TABLE 28.-Mean annual growth

80

Cnbic feet

2 13 31 47 .16 sz 6.1 1i8 (\g 59

Annual growth per acre by site

Total age (years)

40

Cubic Jut60___________ 24

65___________ 2470____ . ______ 2.175___________ 2.180 __________ 21i85 __________ 2690___________ 2695___________ 26100__________ 21i

index­

.50 60

Cubic Cubic [eei feet

35 47 35 47

4736 47::Iii 4736

36 46 35 46 31i 45 35 45

70

Cubic feet

58 58 .58 57 51i 51i .15 56 54

per acre in board feet, International rule, ~~-inch saw kerf, to a 5-inch top inside bark, including all trees having at least one 16-foot log

) No trees containing- a 16-foot log with a top diameter inside bark of 5.0 inches below 15-year class.

TABLE 29.-Mean annual growth per acre in board feet, Scribner rule, to an 8-inch top inside bark, including all trees having at least one 16-foot log

Annual growth per acre by site Annual g-rowth per acre by site index- index-

Total age Total age(years) 1 (years) 1

50 60 7040 80 40 50 60 70 80 --~-

Board Board BoardBoard Board Board Board Board Board Boart feetfeet feet feet feet feet feet feet feet [eet15__________• 60 ___________30 0 0 4.1 tsz93 232 31o20___________ 65 ___________0 8 180 0 53 II)Ii ° 174 243 3222.1 ___________ 70_____ 0 0 12 28 58 61 116 183 2.13 :13 I)30___________ 75___________12 2R 58 1123 68 18912·1 260 3.335___________ 80___________5423 101 1709 74 196131 265 3440___________ 85 ____________13835 80 21515 2f,979 136 200 3445___________ 90 __. __ . ____ 842q950 10421 170 140 203 272 3450___________ 95 ___________28 65 126 195 275 88 143 206 275 3455_______. ___ 100_____36 79 215145 295 92 147 209 34276

Annual growth per acre by site Annual growth per acre by site index-­ index-

Total age Total age (years) ) (years) I

40 50 70 4060 80 50 60 70 80

BoardBoard Board Board Board BoardBoard Board Board Board feet feet feetfeet feet feet feetfeet feet feet25___________ 65__________fi0 0 0 2 S 26 67 132 21130___________ 70. __________0 70 2 17 11 31 81 151 22735__________ 75___________0 1 16 36 15 426 93 16:' 23840___________ 80___________281 1 12 62 18 50 104 24617645___________ 85___________442 7 9620 21 25257 114 18550. __________ 90 _________283 10 65 133 24 123 25664 HJl

55_____. _____ 95 __________14 395 90 1M 211 2,59130 19671100__________ 60 ________ 18 52 1127 189 34 78 137 199 261

1 No trees containing a 16-foot log with a top diameter inside bark of 8.0 inches below 25-year class.

80

Cubic feet

fig ss 5E 67 67 6f 5f 6f 64

40 50

--- ­

Percent 0 3

11 28 50 64 75 83

60 70

--- ­ --- ­

Percent Percent 0 2 6 9

17 31 43 57 62 72 74 83 85 90 89 I 95

10______________________________ -_ --. ___- -- ­ - -- ­ - ­ - -­15______________ • _____________ .___- -- - ­ -- - -- ­ - ---- ­ - -­20__________________________ . ________________________ 25___________________________________________________ aD__________________ • ________________________________ 35___________________________________________________ 40_______________________________ - _______ ­ - - - ­ - - - ­ - - -45_____________________________ ­ _- - ­ ___- -- - -- -. -- - -- ­

Percent 0 0 4

15 3.1 54 65 73

___________________________________________________.10 81 89 96 98 55_______________________________ - --_ -- ­ _-­ ---~--- -- ­ 88 92 98 100 60_______________ . __________ ------. ­ _________________ 92 97 100 100 65_________________ -­ ____-­ _._. - -- ­ - - --- ­ - ­ - ---- ­ --- ­ 92 97 100 100 70___________________________________________________ 75_____________________________ . ______________________ 80__• ________________________________________________ 85______________________ • _________ - -- ­ __­ - - ­ - ­ - -. - -- ­

90_________________________ ---_ --- ­ -_ - - ---- - ­ -- --- ­ -­9.1_________________ -­ ____- _-- ­ - - -- ­ - - -- - -- -. -- --- ­ - -­

96 96

100 100 100 100

100 100 100 100 100 100

100 100 100 98 98 96

100 98 97 97 95 95

100___________________________ ­ ____--­ - ----- ­ --- --- ­ 100 97 961 93]

Total age (years)

Maximum merchantable cubic feet per acre by site index­

80

Percent 3

19 45 68 81 90 94 99

100 100 100 100 99 97 97 96

1 94 94 93

I Heavy Jines enclose ages and sites between which stand may be cut and yet obtain within 5 percent of the maximum mean annual growth.

ACCURACY OF THE YIELD TABLES

Measures of the association of the various yield values with age and site, and the standard errors of estimate of the yield tables, are given in table 32. The percentage of variation accounted for, shown in column 3, indicates the part of the variation of the particular yield unit that is associated with age and site. The differences between these values and 100 percent are the percentages of variation not, accounted for. The difference between stand basal area and total volume with respect to percentage not accounted for is striking. Age and site account for 88 percent of the variation in volume and only 59 percent in basal area-a difference of 29 percent. Yet the stand­

115807°-37-3

34 TECHNICAL BULLETIN .560, U. S. DEPT. OF AGRICULTURE

ard errors of estimate show practically no difference in the reliability of estimating. The reason for this is the correlation between volume and height. Site index is based on height and height is one of the variables which determine volume. Higher correlations are expected since both the dependent and one of the independent variables contain height factors. This is true for all correlations with volume units.

TABLE 32.-Check of basic data against y1:eld tables

2 8 8

dVaria- Deviation Standar Corre- tion ac- Standard error error of

Yield table unit lation counted of estimate yield-index for Aver- Aggre- table

age gate reedings

-------

Percent Percent Percent Unit.~ Percent Percent Stand basal area _____________ square feet., . 0.769 59 11 +0.17 13.6 14.5 ±O.iNumber of trees ______________ logarithms__ .904 82 2,5 +. 07 .1292 25.7 ±l. ~ Average diameter _____________.___ inches __ .934 87 11 -.48 .78 l:t 6 ±.fAverage height; __________________feeL_ .96,5 93 6 -.28 4.0 8.2 ±.'Total volume________________ cubic feeL_ .9::16 88 12 -.32 321 16.2 ±.~Merchantable volume ___________ -_do. ___ .958 92 19 -.2.') 350 29.4 ±l.~International volume_________ .board feet __ .91)4 91 30 +1.04 1.807 47.4 ±2.~Scribner volume. __________ . ______ .do ____ .919 84 4.~ -2.8 1.516 68.8 ±3.4

In general the aggregate and average deviations and the standard errors compare favorably with those found in other yield studies. One must bear in mind, however, that these data cover a wide range of conditions as to location and species composition. Distinct differ­ences in geologic formation, residual soil, and climate occur over this vast region. As usual, the tables for merchantable cubic- and board­foot units have large errors of estimate and percentage deviations, because the decided influence of density on tree size is accentuated where tree size is the factor governing yield. McIntyre's studies in oak stands in Pennsylvania (15), which indicate an average of 5 per­cent more oak by basal area than the present study, show less scatter about the average.

USE OF TABLES FOR YIELD PREDICTION IN UNDERSTOCKED STANDS

Application of normal yield tables to understocked st'ands is at best an approximation, especially when dealing with mixed stands. The Yield table is a measure of the natural growing capacity of the best stocked stands, indicates what yields can be attained, and gives a goal to strive for and perhaps surpass under scientific management. Approximate yield predictions are usually obtained by correcting future tabular yield values by use of the present percentage relation between actual basal area, computed from a sample of the forest in question, and tabular basal area for the same age and site. Applica­tion of this percentage correction to tabular values at a future age gives a conservative estimate of yield, since understocked stands tend to approach normality with advancing age. For most practical pur­poses such predictions can be made for periods up to 20 years. Com­plete discussions of this general method of application can be found in a number of publications (7, 10, 14, 15,31) and in the standard texts on forest mensuration.

YIELD, ETC., TABLES FOR EVEN-AGED UPI1AND OAK FORESTS 35

EFFECT OF DENSITY AND SPECIES COMPOSITION ON YIELD

Table 32 indicates that 12 percent of the variation in total cubic volume yield is due to variables other than age and site. To deter­mine what part of this is due to stand density and what part to species composition, correlations were made between actual yield, in percent of the tabular, and these factors. The correlations obtained were as follows: Correlation between actual yield in percent of the tabular and- Correlation

(1) Density, deviation of actual from estimated log number of coefficient treea - _- - - - - - - - - - - - - - - - - - - - - - - - + O. 7180

(2) Basal area of white oak group in percent of the totaL_____ -.0829 (3) Basal area of black oak group in percent of the totaL_______ -.0684 (4) Basal area of other intolerant group in percent, of the total , , +.2992 (.5) Basal area of other tolerant group in percent of the totaL___ -.0462 (6) All five combined (multiple correlation) __- - - - - - - - - - - - - - - - - +. 7451

A correlation coefficient of 0.119 or larger is significant. Therefore only two of the gross correlations are significant, density being by far the most important. The multiple correlation with all five variables shows very little improvement over the gross correlation with density alone. The indications are, therefore, that density contributes about half (lOOXO. 718XO.718) of the variation from the tabular values and that species composition as expressed by these groups is of minor im­portance. It must be mentioned, however, that species composition probably affects yield more than these correlations show, but its effect is largely removed by the original correlation with site index. This is true because significant correlations occur between species composi­tion and site index. These will be shown later in the stand-table discussion.

CORRELATION OF TOTAL CUBIC VOLUME WITH AGE. SITE. AND DENSITY

A curvilinear multiple correlation of total cubic volume with age, site, and density was made by Bruce and Reineke's method (4) and a very satisfactory chart was obtained (fig. 15). The standard error of estimate was lowered 29 percent by including density, and a cor­responding improvement in correlation was achieved, as shown in table 33. Comparison of the two estimates of Yield is available in figure 16. In the younger age classes there is a greater range in yield with variation in site when density is considered as a variable than when it is omitted from consideration. This might indicate a defi­ciency of density classes among the younger ages in the sample used. Also, there is a tendency for the poorer sites to have higher Yields above 40 years. This indicates that the density of the older stands sampled on the poorer sites was lower than that of the rest of the stands sampled. In other words a correlation between density and site is indicated. This is borne out by the actual correlation coefficient of -0.1612, which is statistically significant.

36 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE

SITE INDEX DENSI"'"

100

1:""""20 A I 135

TOTAL AGE YEARS

100 -:+

90 -r­

80+

70+

60+

50+

STAND VOLUME

I CUBIC FEET

EXCLUDING BARK

7000

6000 I

,/SOoo

4000

I 3500

3000

Z500

zooo I l

'500

90

±

BO

70

60

t50

130 -}-+.15

125

~ 120J-...·10

~ ~ 115 "l; .... 110 +....05 ()

~ 105 "J

~ 100+ 0

~ ~ 95

<I) 90+--:05 tu "J ~ 85

40+ 10001

I

500 T

t 40

.\..

.... () 801:--10

l\: IlJ 75Cll ~ ::::J 70 i--:15 ~

3030 65

-.20

Age = Tota' age of stand In year-s Srtelndex = Total helghf" attained by average domlnan'" 60

and c odorrurrarrt oak at 50 years OenSlty = Deviation In logarithms of actual log number

of trees from average log. num ber of trees -.25 20 (Average log nu mber of trees - 3.6636 -1.4967 55

log average diamef"er breast high volume = Stand volume In cubic feet excluding b2!U"k,for

all trees 0.6 Inch diameter br-east high and Illirger A = Holding axls (age ...srre)

Basis - 404 sample plots from D.C.,lII.•Ga.,Ky.,Md,M!cr>. 50 ,.30 MO.,N.Y.,N,C.•Ohlo,Pa.,Tenn. t Va.,and W va. Standard error of estimate = 227cu. ft.(41.5%Of mean) Correlation Index = .969 Variance accounted for"" 94".

10

FIGURE 15.-Yield of upland oaks-curvilinear multiple correlation of stand volume with age, site index, ~nd density.

TABLE 33.-Comparison of yield correlations with and without density included as a variable

Total cubic volume yield correlated with-

Item Age and site Age, site index,

index and density

0.969 88

0.936Correlation index. __ - - - - -- _______ - - - - - - -- - -­94

Percent of variation accounted for - - - --- -- - -- -- - ---- == ==== ============= == Standard error of estimate:

2'l:l321 Percent. _________ -- -_ ------- --- ------------------------------­Cubic feet. __ . ___ - -- --. -- -- ------ - - - - - - -- - - -- - - - -- - --- - -- - - ----- - -- -­

11.516

YIELD, ETC. TABLES FOR EVEN-AGED UPLAND OAK FORESTS/ 37

Since density is measured by the number of trees present (fig. 17), the correlation between density and site indicates to some extent that the better sites have fewer numbers of trees for any given stand diameter than the poorer ones. On the other hand the correlation between volume and density is not significant (r=O.1028). Accord­ingly, if there are fewer trees but the same volume on the better sites for the same average diameter, it follows that there is probably less range in tree sizes.

6000

;::­~ ~ 5000

Iii::, ~

~ ~ 4000 <: Q::, .,J

~ ~ 3000

I!: CI)

/v ./[ ~ 140

! ! , ! ,

a 20 40 60 80 100 TOTAL AGE (V EARS)

CURVES OF" VOLUME FOR AGE AND SITE DISREGARDING DENSITY CURVES OF VOLUME FOR AGE AND SITE FOR AVERAGE DENSITY

WHEN DENSITY IS INCLUDED AS A VARIABLE

FIGURE l6.-Comparison between total cubic volume curves when correlated with age and site only and when density is Included.

A set of total cubic-volume values by age, site index, and density 21

classes are presented in table 34, as read from figure 15. One can readily see from this table that even though density was controlled in the field by selecting fully stocked stands as samples, the variations

21 Example of computation of density. If the number of trees in an upland oak forest stand is 500and their average diameter is 5.0 inches, what is the density of t.he stand? The logarithm of 5.0 is 0.6990. Substituting this value in the equation-average log (number of trees) =3.8638-1.4987 log (average diameter breast high) we get log (number of trees) =3.8638-1.4987 (0.6990) and solving=3.8638-1.0476=2.8162. The antilog of 2.8162=6M, or average number of trees for an average diameter of 5.0 inches, and 500 is 76 percent of 655. Therefore the density of the stand is 76. This can be computed graphically by direct reading from figure 19.

I ~ f.:: ~ 2000

~ o ~

~ ~ 1000

i;j ):

0'

~'~ ~ ;; 60 ~

...... I-­J"';'" 0)

__

_ _

----------- --------

---------------

---

38 TECHNICAL BULLETIN ,560. U. S. DEPT. OF AGRICULTURE

obtained are well worth considering, especially in scientific studies. It is entirely possible to include density 3,8 a variable in all of the yield tables, but this requires further analysis, which leads naturally towards application studies in understocked stands. These are planned in future work.

10.0 ~\9.0

B.O ~\\\

7.0 l\\\\\ \\\\~

6.0

\\\\~t\ \\~~

5.0

4.0

\ \\\l\\\\\ ~ - I-- ­\ \\\\\"0~ ­3.0 \ \\1\\\0~'0­

\ 1\\0~~ 2.0

~\~~ ~ ~t\ \

i ~~ w ~~OJ ~~~~ ~ 1.000 , \ \\r\\,\\\\[\~ 900 ,\ \ 1\\.\\~~\

\ ........ eoo

\. [\\\\.\.\:\,\\,w 100 It \ [\' ,\'\~'\~

\ ,~ 600 \\\l\\r\

\\\~ 0 ~ ~ 50

11. ~ ~ ~ ~4OQ W 0:: I­

300

\. \\ \\ \.\ ~\ l~

\\ \\:'\~~ \\ \ \ \\~~ ~

200 \ \ :~ l\~I\.

\ i\i\~~I\. '\ \ \

50

100

90

eo 70

60

\ ~~. \ \ \ 1\\\'\:1 \\ [\\ \ \ ­\. 1\.\\'­

\ \\. \\ ­\.

o o~ Oi':i o~

o~ o~ o(f o~

'q:

0 ....

~ o~ ~

40 3 4 5 6 7 8 9 10 15 20

AVERAGE DIAME.TER (INCHES)

FIGURE 17.-Stand density chart for upland oak.

YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 39

TABLE 34.-Yield per acre, excl1ldi.ng bark, by density classes, age, and site; all

Age (years)

0 010_____ - ---------------- ­ 262lli20 0 700 0 01Ii- ____ - - ---- - - - - - - - - - - -- - - - ­ 4liOaso(J 0 73 175 zso0 65020 __- - - .-------- - --- ­ .'i400 .'i 141 248 aso 440

R4225__- - - - --------- ---- ------ ­ 72022 17.'i :l0.'i 4U) .'i25 lil5

30 ____ --------- ­ 1,05090R182 il28 465 .'i87 700 800

1,27035__ - - - ------- ------ ­ 1,1207li3 885 995aas 490 63640 __- - - - ------- ­ l,4RO1,330940 1. 075 1,1904R5 045 R0545____ - - ----- - --- - ­ 1,7101,5401,125 1, 27.'i 1,4001i:\0 810 97050___ - - ----------- ­ 1,9201,740

775 955 1,140 1,300 l.4liO l,5!l0 55 ___ - - ---- ---- - --- ­ 2,100l,!l20

895 1.090 1,2RO 1,4fiO 1,620 1,760 2,2liO60 ____ - - -----.- ­ 2,0751,770 1,920

1.010 1,22;) 1,425 1.60065 ____ --'-- -------- ­ 2,4202,230

1,130 1.3.'iO I, .'i.'i0 1,740 1,920 2,060 70___ - - - .---- ­ 2,5liO2,31101,670 1,870 2,040 2,2001.23.1 1,460 2,117075__ - -- -- ----- ----- ­ 2.4752.100 2,3101,325 I, .'iliO 1,775 I. !l7080 _____________ 2,7802, MIO2,4201,420 I, sso 1,880 2,075 2,270

2,91085 __ -- - --------------- ­ 2,6902.370 2,5ilO1,500 1,7.'i0 l,97.'i 2,1RO90 _____ ---------------- ­ a.oas2, R20 2, ORO 2,290 2,475 2. fi:l5 I. soo I, R5095 ___ -- ------------- -_.­ 3,1502,925

1.075 1,9il5 2,175 2,3RO 2,575 2,730100_______________

FAIR SITE-INDEX 50

------ ­ I---T 10_________________ 15__________________

0 0

0 0

0 7

0 120

20 220

1O.'i 302

198 3!l0

soo 507

402 62~

20_______________ _ 0 sn IHO :102 402 495 595 710 84C 25----------------------- ­ 85 230 :lfi.'i 480 592 685 795 915 1,06f 30___________________ 35---------------- ­40_____________ _ __ 45 50____________ ,'!5__________________ 60 . 65---------------- ­70----------- ­75 80 85 90______ 95 100 .________

trees 0.6 inch d. b. h. and larger included

POOR SITE--INDEX 40

Yield per nero hy densit.y class 1

----------------~---~---~~-----

12011090 100sn GO 70 80 ~------- ------ --~. --- --- -- ­

Cu.hicOll.hicCubic Cnhic Cuhic.Cnhic Cuhic Cubic (r:r.tjeetfat [cet jeet jeet[eet [eet 0 7500 0 0

252 3\l8 543 002 785 885 1,000 1.150 1,30f 405 570 7\.'i 850 \l75 1,090 1,2201.:175 1,5:11 580 7;'0 910 1,000 1,200 1,32;' 1,470 i.sso l,8H 740 9201,1001,2601,4201,5401,690 1,875 2,06f 90.'i 1,110 1,300 1.470 1,630 1,770 1,9ilO 2.120 2,3H

1,0701,2801,480 i.ees 1,845 2,54(1,9802,1502.340 1,220 1,440 l,o,'iO 1.845 2.010 2,170 2,340 2,530 2,73( l,il4;, 1,.'i75 1,795 1,9802,180 2. 33.'i 2,500 2,6\l5 2,92(1 1.47!i 1,71.'! 1,945 2.148 2.335 2,490 2,060 2.870 3,10 1.fi1l0 1,841i 2,080 2.285 2.400 2,630 2,805 3,0.'iO 3,28 1,680 l,9!i0 2,18!i 2.400 2,59!i 2,7.'i5 2,935 3.1f>6 :1.41 1,790 2,OfiO 2,300 2.505 2,1i!l5 2.870 :I.OfiO 3.300 3,56' 1,895 2,160 2,410 2.610 2.Hl0 2.995 3.200 3,44fi 3,72 1.990 2.270 2.510 2,72.1 2,945 3,130 3,345 3,5\1.'i 3,89o2.090 2,3GO 2.610 2,H.10 3,O.'i0 3,240 3,4110 3.730 4,02

AVERAGE SITE-INDEX liO --------------------------~--_.._-----­

I{) __ - - - - ----------- ---- ----- ­ 2289,'i0I.'i____________________ --- ­4192RR140

40020 _____ - ---- ------- -­

1104305 79025 __ - - - --------- ­

47,'i 1l.15 6.'i0 R25

30____ - -------- ­990 ... _­35_ - --- --­ 1,220

1,230 1.0:1084040 _____

1.4301,020 1, 64.~

4.'i____ - --- -------- ­1,43.'i

1.8.'i5 1.21.'i50 _____ - - --- ..---- ..--- ----- ­

1. 6:10 1,5M 1,390Ii.'i __

2.0301,79,'i60 ___ - - ~ -==========-===---­ 2,19,)1.9501, eos

2, :~.'i0Ii.'i____ - - ----------- -------- ­I. R4.'i 2.110

2.4R570 ____ - ----- ----------- .. - ­

1,970 2.240 2, stn75 __ - - - ----------------- ­

2.01l,'i 2,3fiO 2,71080 ____ - - -------------.- ­

2.1\/0 2.46fi85 __ ------------------- ----­ 2.8402. 30.~ 2, ,'i85 2,410 2. li7.'i

90 ______ ------------------ ­2, !lliO

95- - -- - --------------- ­ 1.0702.49.1 2,785100 __-- - ..------------------- ­

1 Density is percentage of average number of trees,

3000

~"--

130

Cu.hic jeet

18o 3fJ.'i 57o 7i 5 9i 5

I,H o 1. 4, o 1,6( 1,9( o 2,1 °o2, ill 2,4, o 2,6' n 2,7 o 2, s o

°

a.o 3, I ° ° :1.2 5 il,4 o

1)40 050422 7.'i.'i

330245145 880fi::l5

flH,'i 540445340

l,I::1.'i85,'i 1..38.'i

748MHMO 1. 225

1,1l70 1,0809558,'i0728

1,478 l,92fi

1.3201,1801.07092R 1,740

2,210 I, .'i70 1,4251. aoo1.148

2,01.'i1,8401,67,'i1.540I, ::18O 2.4702,08,'i 2.27.1 2,720

1,92.11,77(,1,615 2••'i2ii

2.98.'i 2,33ii2,1702,0101.8::15

2.7fl.'i 2, \/75

2.5fili2. :1902.2402,050 3,2202,7M2.•'\80 2.42.)2.240 3,4203,170 3,63.'i

2,94,'i2,7502,M102,400 3,370 3,5S5

3.1302.9,'302.7.'i02.•'i6.'\ ;~, 8.')03,30S3.1002.9102, finO 4,0203. 72,,!3,4M 4,205

3.2403,04.'i2.820 3,8\/0

4,390 3,6003,3703,17.'i2,9.'i.'i

4,05.'! 4,580

3.7703,5303,3203.0110 4.2:15

4,77fi :1,9203,66.13,4S0:1,210

4.1004,0703,H203. ,'iROa.330

_______________________

40 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE

TABLE 34.-Yield per acre, excluding bark, by density classes, age, and site; all trees 0.6 inch d. b. h. and larger included-Continued

<lOOD SITE-INDEX 70

Yield per acre by density class 1

Age (years) 50 60 70 80 90 100 110 120 130

--­--­--­--­--­--­--­---Oubic Oubic Oubic Oubic Oubic Oubic Oubic Oubic Oubic feet feet feet feet feet feet feet feet feet10. _________________________ 30 179 310 420 532 622 728 850 98515_____. ____________________ 219 368 509 628 745 848 960 1,105 1,25520__________________________ 410 588 718 850 975 1,090 1,225 1,380 1,54525__________________________

598 765 925 1,075 1,220 1,350 1,480 1,655 1,83530__________________________ 700 970 1,155 1,320 1,475 1,610 1,770 1,945 2,13535. ____. ____________________ 975 1,180 1,380 1,555 1,730 1,875 2,030 2,225 2,42(J40__________________________ 1,210 1,430 1,645 1,830 2,005 2,160 2,335 2,525 2,72545_________. ________________ 1,415 1,650 1,880 2,080 2,270 2,42/i 2,595 2,795 3,02550__________________________ 1,640 1,000 2,135 2,335 2,530 2,680 2,870 3,000 3,34055__________________________ 1,845 2,105 2,350 2,550 .2,740 2,925 3,125 3,370 3,1J3060_. ________________________ 2,020 2,295 2,545 2,755 2,970 3,165 3,375 3,630 3,92565. _. _______________________ 2,175 2,450 2,695 2,930 3,170 3,360 3,580 3,870 4,181i70__________________________ 2,340 2,620 2,880 3,125 3,365 3,575 3,825 4,120 4,46075__________________________ 2,475 2,755 3,035 3,295 3,550 3,780 4,030 4,360 4,73080__________________________ 2,500 2,890 3,190 3,450 3,720 3,950 4,235 4,570 4,95085__________________________ 2,690 3,010 3,315 3,585 3,870 4,120 4,405 4,770 5,18090__________________________ 2,810 3,140 3,460 3,760 4,040 4,320 4,615 4,995 5,42095. _________________________ 2,940 3,270 3,605 3,925 4,225 4,505 4,825 5,225 5,OO/i100_________________________ 3,030 3,395 3,745 4,060 4,390 4,680 5,020 5,440 5,890

EXCELLENT SITE-INDEX 80

10.. ________________________ 58Q 1,360930 1,055 1,200830435 70'528815__________________________ 1,200 1,67e1,080 1,335 1,495482 642 800 94020__________________________ 1,9701,6201,190 1,345 1,470 1,7851,035885 86225__________________________ 2,28/i1,610 1,752 1,915 2,0001,277 1,4501,08089030____. _____________________ 2,050 2,215 2,405 2,6UI1,725 1,9101,120 1,340 1,54035__________________________ 2,9202,180 2,335 2,500 2,6001,9901,345 1,575 1,79540_. _____________________ . __ 2,645 3,040 3,2752,480 2,8252,3001,605 1,860 2,00045__• _______________________ 3,365 3,6253,1252,550 2,740 2,9202,1001,845 2,34850_. _. ______________________ 3,725 4,0203,230 3,4502,820 3,0352,360 2,6102,09055__________________________ 4,065 4,4103,325 3,530 3,7753,0802,310 2,8302, 58060____..____________________ 4,380 4,7604,0553,320 3,570 3,7953,0702,480 2,77065. _________________________ 4,690 5,0853,810 4,045 4,3353,5353,2602, 660 2,96070__________________________ 5,000 5,4204,325 4,6203,760 4,0503,4702,815 3,15575__. __. ____________________ 5,310 5,7504.,9004,290 4,5653,660 3,9702,985 3,325 80.;~ 5,130 5,555 6,0304,8003,825 4,160 4, 490 3,120 3,47585__________________________ 5,380 5,800 6,3254,700 5,0103,990 4,3503,250 3,62500____. _____________________ 6,1005,620 6,5904,915 5,2504,180 4,5403,400 3,78095. __. _. ____________________ 6,370 6,8505,8704,360 4,745 5, loW 5,4803,540 3,950100. ________________________ 6,600 7,1206,1204,530 4,930 5,340 5,6804,1003,670

1 Density is percentage of average number of trees.

THE STAND TABLES

Stand tables are essential for forest management, and it is today generally accepted that yield tables are not complete without them. Knowledge of the number of trees that may be expected in the various diameter classes is necessary for solving many problems in forest utilization and valuation. Because oak is used extensively for piece products, the yield of which depends on tree size, stand tables are especially important for the oak region.

It has been shown (2, 11, 16, 17, 23, 24, 25) that diameter distribu­tions of even-aged stands follow certain definite laws and have char­acteristic forms which are determined by certain computed values. Analyses of several oak stands brought out the fact that stands that contain a number of species having different growth characteristics and varying in their tolerance and their adaptability to the site have distributions with several modes. Obviously, such stands must be

YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 41

separated into their component parts and each analyzed separately, since no two stands have the same composition. Because it was im­practicable to analyze each species separately, some grouping was sought. Inspection of a number of stand tallies showed the white oaks to be somewhat smaller in size than the black oaks on the same area. The associated species also were found to fall, perhaps more pronouncedly, into two groups, one of small trees of tolerant species and the other of large trees of intolerant species. Four groups were, therefore, set up as follows: (1) The white oaks; (2) the black oaks; (3) the other intolerant species; and (4) the other tolerant species." A test showed the mean stand diameters (mean of the diameters) of these groups to be significantly different while each individual group seemed to be fairly homogeneous. The mean of the differences of the group means from the plot means (diameter) and their standard errors are given in table 35. They are all significant. Each group mean was also found to be very significantly different from each other ~roup mean, the ratios between the differences and their errors rang­mg from 18 to 108. Previous investigations (17, 24) show that cor­relation of the diameter distribution characteristics with mean stand diameter largely eliminates the effect of age and site, so stand analyses are generally based on mean diameter. Since these groups differ significantly in mean diameter, they are considered sufficiently dif­ferent to require separate analyses.

TABLE 35.-Mean differences between diameters of species groups and plot

Species group

Mean di1ference of diameters from those of

entire plot

Standard error of the dif­

ference

Ratios of mean dif­ference to its error

White oaks ___________ - --------------­ - ---------­ ----------­Black oaks ______ --­ -­ - -­ - - -­ -­ ---. - -. - - -­ --. - -- --­ -­ ---­ -­ -­Other intolerant species_______ ----­ -- ------­ ---------------­Other tolerant species ______________ . __________ c _____________

-0.0873 +.8594 -.5482

-1. 2778

±0.00819 ±.01244 ±.02396 ±.01548

11 69 23 83

The mathematical values which describe diameter distribution are: Number of trees, mean diameter, standard deviation about the mean, coefficient of asymmetry (skewness), and coefficient of excess (kur­tosis). The latter is of minor importance, is subject to considerable error, and to obtain it greatly increases the volume of computational work. Moreover, tables of Pearson's type III function (22), which disregards kurtosis, were available to simplify the computation of frequencies. The other values were, therefore, the only ones consid­ered. Charlier's types A and B curves have been used very conven­iently for diameter distribution analyses (16, 17, 23, 24, 25), again because available tables simplify fitting them. Pearson's type I curve was used in one instance (23), and was shown to fit exceedingly well but required a great amount of computational work. Pearson's. type III frequency was also tested in the latter case; it was found to fit very well in comparison with Charlier's curves .and has the ad­vantage of being more easily computed by direct reading of percentage

II The species grouping is as follows, employing the miscellaneous group composition given in table 1: White oaks: White, chestnut, and post oaks, and swamp oaks. Black oaks: Scarlet, black, red, southern red, pin, blackjack, and miscellaneous oaks. Other tolerant species: Black and red gums, beech, sugar and red maple, sweet birch, eastern hemlock, basswood, miscellaneous groups A and B, unknown, and dead trees. Other intolerant species: Chestnut, hickory, hickories, pines, ashes, cherries, yellow poplar, black locust, black walnut, sycamore, Iargetooth and other aspen, elm, eastern red cedar, butternut, and cucum­ber. '(See table 1 for scientific names of species and composition of miscellaneous groups.)

42 TECHNICAL BULLETIN 560, U. S. DEPI'. OF AGRICULTURE

frequencies from tables of areas. These tables were, therefore, used for fitting Pearson's type III curves to the first three of the above­mentioned four groups.

I ---,

I 4 'A I

I ~ r ­3 ~ "'2

~ 3Z ." ?- --~ 14z -

~ ~ 12!.......r; ~ (;)'1 -

I 1~I I ~ Il I I I ~ I ..L J '" ~O

7 e 9 10 II 12 13 14 IS ~ ~3 ~

~2 .....

~, .... (1)0

9 10 1\ 12 13 14 15

~ C7T'H Q:e

~.

ltl

5 .... I

I I~

4 V ~

~3 ~ ~2 ~

Q'I

'\, \

-" l.-"""""

.... ,, 'w

~O () 9 10 II 12 13 14 15

OTH 4::t

()

;::3 ~

~2

~, '" Qo

9 10 II IZ 13 14 15It COMPA

~5 ~ ~ ~4

fl)3 " z

°0 8 9 10 II IZ 13 14 15 MEAN DIAMETER OF SPECIES GROUP AT BREAST HEIGHT (INCHES)

FIGURE l8.-Relation between standard deviation of tree diameters and mean diameter by species groups.

c

~~. ~ W-­

ZI ...',

~ 33 30

~ ~\

----- ­ 1'1: 4 ..-~, ..

~ .4: I~ .u

35

~

YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 43

Standard deviation was computed for each 0.5 inch mean diameter (of species group) class separately for each of the four species groups. The average relations are shown in figure 18. The curves differ but appear to be quite satisfactory. .An exception is that for the "other tolerant" group, the shape of which indicates the presence of two universes of data. However, the relative importance of this group does not warrant further subdivision. Plotted values of skewness

I 1+3 I.-, I \ I I I \ \ \

.~ I i"'''It+ Z

...- ­26 9 '" ' 13 •I , - ,I< .. ilZ ~ :.0. _~ ~~ 26 Z' 2S':': 7 iL9 '!.. 9 J.-'. 3 3 ~

~ 2 Z, 10 Z~- 'i6"¥ 34 '5 ZO Z5 ~ "11130 .1'1- ~~ ';-g' z' .z ?t' "'r'1 J

~ 0 "> r- I I \ I I I

Io I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 MEAN DIAMETER OF SPECIES GROUP AT BREAST HEIGHT (INCHES)

• WJoIITE OAK AVERAGES _ BLACK OAK AVERAGES 2b NUMBER OF PL.OTS

FIGURE 19.-Rela.tion between skewness and mean diameter for the white and black oak:groups .

80

70

}::' 60

~

,, .:

• \ • 1 •1 ~OTHER~OLERANT , .. : I: : I(II ~ERCEIfI:)

• WEIGHTS IN NUMBER OF PL.OTS : 12 47 81 93 90 46 Z5 7

\ \ \

\

10

0 I I I ! I I I

~50 ~

CI)

~ 40

~ I.J.. o 30

~ ~ :::l20 ~

130 40 50 60 70 80 90 100

SITE: INDEX FIGURE 2O.-Computed and actual relation between percentage of number of trees by species groups and

site index.

------------

---------------

44 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE

in figure 19 show practically the same relation to mean diameter for both of the oak groups. The curve fitted to both of the oak groups averaged together was arbitrarily used for the other intolerant group also. Because skewness values as high as +3 were found in the other tolerant group the tables of Pearson's type III function could not be used. Average percentile curves were drawn for this group.

The percent number of trees in each species group changes with site, as shown in figure 20 and table 36. White oaks decrease and black oaks increase in number with increasing site quality, while the other two groups decrease slightly. These changes ill percentage composition are significant for the two oak groups but not for the others. Similar correlations between species composition and age showed no significance.

TABLE 36.-Percent of number of trees in each species group on different sites

Total number of trees by site index-Bpecies group

White oaks ____________________________________________________ Black oaks ____________________________________________________ Other intolerant species _______________________________________ Other tolerant species _________________________________________

Total____________________________________________________

40

Percent 59.3 14.7 14.5 11.5

100.0

50 60 70

Percent Percent Percent 42.053.5 47.8

20.9 27.0 33.2 14.2 13.9 13.6 11.4 11.3 11.2

100.0 100.0 100.0

80

Percent 36.3 39.3 13.3 11.1

180.9

V 2() ~

cY /V

lA? /

t4~ /

Y 77/

V 43

V ~3

45/V

V .~

V

A7 Mean Diameter - Mean or the Di~meters at Breast Height

r--­;;V AverageDiameter-Diameter of .theTree orAverage Basal Area

"

14

13

I~

Wi ~ o ~ 10

-::::.. \-. -~ 9

~ 1-: 8

~ ~7 ltl \-. ~ 6

~ t..::

~5 i::l 4 ~

~ ~ 3

2

00 I 2 3 4 5 6 7' 8 9 10 1/ 12 13 14

AVERAGE DIAMETER AT BREAST HEIGHT (INCHES)

FIGURB 21.-Relation between mean diameter and average diameter of the stand.

YIELD, ETC., TABLES FOR EVEN-AGED UPLAND OAK FORESTS 45

For stand analysis the mean diameter (mean of the diameters) of each species group was used as a basis, whereas for yield analysis average diameter of the stand (diameter of tree of average basal area) was used. Figure 21 shows the relation between mean and average diameter of the stand, and figure 22 the relation of each species group to the stand.

For each average stand diameter for each age and site, the mean diameter of each species group was read from the curves in figure 22. The corresponding cumulative frequencies, in percent, were read from

15 v 14

~ ~~13 1/.....0.3

~ ,V~'2 ~ Q) /'

~

\~I 6L.ACK OAKS ~ V/): /~I~

t> 10 ~ t->~ O'?--_4/ ~~9 ooeWHITE OAKS~V ...... ~)V ~ ./ ' ~8 '" c _"'0.5 /1/~-=

I' , ./!/~ /.~, ~ I-aoz+ I/C 7

~vlY'10V{OTHERt> INTOLER....NT~ '\\SPECiES....1/ ~

16/~6

I ,.pi V' ..ooc~ ,V~ ,I IC1 )(

I21/ 5 '" ~

~5 717 1:7 /

\ IV~ \ I?-...; ~IV '\10.3./~ ... ~ OTHER TOLER"'NT SPECIES~IZ'~~

~4

/ I'"" 3~3

s:::

~

~ ./.J~0

..... 6~2 WEIGHTS = NUMBER OF ~ ~ TREES IN THOUSANDS~

00 I 2 3 4 5 6 7 6 9 10 II 12 13 14 AVERAGE DIAMETER OF PLOT AT BREAST HEIGHT(INCHES)

FIGURB 22.-Relation between mean diameter of the species groups and average diameter of the plot.

the tables of Pearson's type III function (22), for each of the first three groups, standard deviation and skewness values having been obtained from the curves in figure 18 and curves similar to those in figure 19. The other tolerant group frequencies were read from the percentile curves. These cumulative frequencies 1Vere next converted to frequencies by successive subtractions. The final step was to apply these frequencies to the total number of trees in each species group-obtained by multiplying the total number of trees per acre (table 8) by the species group percentages (fig. 20). The completed tables are presented as table 37.

__ _

---------------------------------------------------------

-------------------------------------------------------------

----- ----- ----- ----- ---------- ----- ----- ----- ----- -----

------ ----- ----- ----- ----- ----- -----

--------------------- ------------------------------------ ----- ----- ----- ----- -----

__

TABLE 37.-Stand table--Distribution of trees by successive diameter classes, by species groups and age

BITE INDEX 4O-POOR BITE -,.

Ag6-andspeciesgroup

----------1 ,--,--,--'--'--1--1--'--1--'--'--1--,--,-------------­

Trees in each diameter class 1

£1 oS

\1!1\I\mlmll!llm!1111111s ~ .g ~ ~ ~ .g .g ~ ~ .g .g .g .g• C) C) C) .s C) C) C) oS oS S 9 ~ oS .s oS oS .s oS oS 0 ~ ~ ~ o ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:B .g.S ~

:B :B :B :B ~ :B :B :B .g .g .g .g.g .g .g .g oS .s.s.s.s.s.s .91 3 ~ ~ ~ ~ a ~ ~ ~ ~

10 ~ite osks, ~6 3::12 ~. -=:~~- -=:~~-I-=:~~- -=:~~-I-=:~~- -=:~~-l-=:~~- -=:~~-I-=:~~- -=:~~- -=:~~- -=:~~- -::~~- -=:~~ -I-~~·- -~~·-I-~~·- -~~·-I-~~·- -~~'-

TotaL -_______ 831 5,580 439 ­g= ~!~~f~::===:: M~ m~ ====== ======1====== ======1====== ======,====== ======1====== =========

20 years:WI Bla Otl Otl

'1

30Y~

Bb Otl Otl

'1

~ C<0-Ii~~::~~~:~ ::::{-i 1~ In ~ ij ~ LJ_ ~~~~~~ ~~~~:~ ~~:::~ ~:~~:: :~~~~~ ~~~:~~ ~~~:~~ ~~~~~~ ~~~~: ~:::~ ~~~~~ ~~ ~~: ~~:~~ ::~~~ rn c:l

TotaL______________ 8 104 216 253 212 134 60 23 10 1,020~_ ~ ======================= e

·~-~---'-'7!t>,~~~.~~~'?tl'

~w~r'~

liO years: 62 1 24 186White oaks I 1 14 2Ii 14:6 2 118102

I 151 __,, I__ ----I---~--I------I------I------I------I-----\-----\-----\-----\-----1-----1 4766711091119 312 12 26 8 5 1 ~ 116 ~ 1522 26 22g~~ fu~enmt_~~==== ----g­ ---i2­ 1 92 g140 13 ISOther tolerant________ 32--,--,__'__1_--._-'--'--'--'-_'--'__'__'--'--'--'--'--.--.-_.--.--.--,--TotaL______________ 3 ~ 121 1 160 172 133 86 43 18 8 ------ ------ ------1------ ------i-----. ------ ----- ----- ----- ----- ---.-- ----- 80216O~ ========= =====--========

C rg~~~~:~~~ ::::~: ---i ~ ~ ~ ~ ; 1 ~ J ~_ :~~~~~ ~~~:~~ ~~~~~~ ~~~~:~ ~~~:~~ ::~~~~ ~~:~~ :::~~ ~~~~~ ~::~~ ~~::~ ~~~~~ 1 ~

~ TotaL ~ --228681ti212612194-59ao15-7-==========-=======6M === === White ow____________ 13royears: I

TotaL______________ 1 11 '¥l = =

90 years: .White oW___________ 6

g~ fn~erant_~~=~== ----i- ----ir ---"5"Other tolerant._______ 5 11

TotaL______________ 1 8 21

6,800====== ====== ====== ====== ======\===== =====1==:== =====1===== ==::= 1, e C11

o ~

~ l1J

~ ~

~ o ~

=~=============::I

36 64 I 71 61 39 22 l 10 3 3 1 1

60 71 82 79 67 4:7 27 13 6 I 1 1 ======== =

16 32 4:8 63 4:11 32 18 10 3 3

~ 1t 1~ 1~ 1~ 1~ ~ i ----~- ----~- ----~- ~=====1t16 11 5 2 1 0 0

4:2 5ll 68 73 63 4:8 32 19 9 6 1 1

~ ~

1-3 ~

@ ~ C

i ~ b:I

4,062

~ l)'.l-1 -----1----- -----j----- ----- 321

~ t:d l?:l ;1 Z ~

I ~ ~ ----- ----- ----- ----- ----- ----- 4:83

=== ------ ----- ----- ----- ----- ----- ----- 265

====== ===== ===== ==~== ===== ===== ===== ~ ------ ----- ----- ----- ----- ----- ----- 111

1100lE~~::::~~ ::::~: ::::r ---+ ---~- 1 :1 1111__ J__J_---,_ ;;;;~: ;;;;~; :;;;~; ::::~~ :~:~~ ~::~: :~~:: :~::~ :~~:~ ~~~:: TotaL______________ 1 3 16 31 4:6 57 63 61 51 36 23 12 7 2 1 1 ----- ----- ----- -- --.-­

I

1

447 o ~ ~1 ~

4:11 ~ 1 Diameter classesare designated by midpoint values.

t1

------------------------------------------------ ---

---------------------------------------------------

TABLE 37.-Stand table-Distribution of trees by successive diameter classes, by species group8 and age-Continued ~ 00

SITE INDEX liO-FAIR SITE

32, 17 ,2 13

2 6 2

00

9

,48 27

1,

==1-

ss 87-----20

------ ------ ------ ------ ------ ------ ------ ----- ----- --.. -- ----- ----- -----______ 7 ----- ----- ----- 260 ----- ----- ----- 77 ----- ----- ----- 42

246

Trees in each diameter class

Age and species group il r1) ~.g

1,

~ r1) J j.g ~

r1) ~ ~ ~ gj

~ ~ r1) rn :Bgj

J ~ il

~ ~ ~ Q)

.S ~ il 1 il il 1 .g

~ .g .g .g .g

.S .s .S .S .S .s .S .S .S . ~ .S .S .S .S .S .S ..

~ .... ~ ~ ~ ~ ~ ~

.... ~

(

0 .... ~ CQ ..,. >Q cg ~ ex> Cl>

-- ---- ------.... .... ~ ~ ~ ~ Eo-- ------------------------------ -

10~: No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. N White oaks------------ 2li6 2,238 340 ---ii- ------ ------ ------ - .. ---- ------ ------ ------ ------ - ... _--- ------ ------ ------ ------ --..-- ----- ----- ----- --..-- -----Bl8Ck oaks____________ 89 819 188 Other intolerant_______ 83 671 98Other tolerant_________ 139 392 66

6 ______ -----... ------ ------ ------ ------ ------ -...---- ._----- ------ ------ ------ ------ ----- ----- ----- --..... - ----- --...------------ --17

--

1,

---- ------------------------------ -Total_______________ 566 4,020 6112 ------ --

5, ---- ----= ---------------------- ---- -

20 years: 27 472 639 243 M 13White oasa.,__________ ------ ------ ------ ------ ------ --_ .. -- ------ ------ ------ ---.. _- -----... ----- ----- ----- ----- ----- -----Bl8Ck oaks____________ 6 127 216 126 42 11

Other intolerant_______ 14 125 132 61 22 4 ______ -_ ..._-- ------ ------Other toleranL_______ 32 163 75 14 3 ______ ------ -- .. _-- ------ ------ --.. _-- ------ ------ ------ ------ ------ ------ ----- ----- --... -- ----- -------

------ ... ----- ------ ------ ------ ------ ------ ----- ----- ----- ----- ----- --..------------

78 --

-- ------------------------------ -TotaL ______________ 887 962 444 121 28 ---_ .. - ------ ------ ------ -_ ...--- ------ ------ ------ ------ -_ ...... _- -.. ---- ----- ----- -------= ------------------------------ -

30 years: 173 200 133 60 27 7 ______White oaks____________ 7 60 ------Bl8Ck oaks____________ ------ 5 36 73 73 44 18 8

3 -_ .. _...- ------ ------ -----.. ------ ------ ------ ---------- -----Other intolerant.______ 6 30 48 44 27 14 6 2 2 ______ ------ ------ ------ ..._---- ------ ...----- ------ ----- ----- -----Other tolerant_________ 8 69 so ______

----- ----- ----- 2, ----------

11 3 1 ------ ----- ------ ------ ------ ------ ------ ------ ------ ------ ----- ----- --------- ---- -------------------------------------- -Total __~ ____________ 20 164 307 328 236 110 so 17 6 ______ ------ -.. ---- ------ ------ ------ ----.. - ------ --.. -- ----- ----- ----- ----- -------= ---------------- = = -------------------- -

40 years:White oaks____________ Bl8Ck oaks____________ ------ 13 III 97 106 76 46 21 8 4 ______ -,----- ------ ------ ------ ------ ------ ----- ----- ----- ----- ----- --.--

------ ------ 16 8 5 2 1 ____________________________________ 3 17 36 43 35 20 8 3 ______ -._--- ------ ------ ------ ------ --...--- ----- ----- ----- ----- ----- -----Other intolerant_______ 3 11 21 2li 21 ------ ----- ----- ----- ----- ----l---Other tolerant_________ ______ 31 40 13 4 1 1 ______________________________________________________

~~~~~~ ~~~~~ ~I~~~~~ ~ ----- -.. -----------------------------------------Total_______________ 3 66 116 162 167 136 00 46 18 8 ____________________________________

=== = =====::t::=.====== ===

~

~ ~ b::l g ij Z 01 ~

~o

~ UJ

t::;1 l;l

~ o ~

> ~ Q q

~

~

.' "., "., ." _. _. \ .• _ .. _". ' ,'" ."', .'. ," ,'-, _ 'P."." . ., '. -,' '''' 0 • \ • . . ',' ,.' • . ",

't~''''' ~·.. i'~<"';Ni"" ~""":..;"~':"'h~"~,,,,.,, \ ;'~~"'\\ ~.i, ""I ~~~~,~. __\ ~1~~ ... 1.t;"l.;.,~l,:>"'~"'o!;\ ... ~'~~-""'";:...,,,-·~~·.~,:,"':~4 t\ ... J'~. J~""T .."< ,,; t .... d~..,." ... ~~'r,':. l' ,E"',-""~ I .... ,,'" ''''1'~4~-

.!.>:'

White oaks____________ 4 20 53 77 73 liS 30 13 7 3 • ------ ------ ----- ----- ----- ----- ----- ----- 333!ill years:Bl8Ck oaks------------ .:___ 1 6 14 26 31 25 16 8 3 1 ------ ------ ----- ----- ----- ----- ----- ----.: 130 ~ Other intolerant------- 2 6 14 18 17 13 8 6 3 2 1 ------ ------ ----- ----- ----- ----- ----- ----- 89

~ o::::~:::::::::---~- ~ : : ,,: ,,: ~ .: ---;~- ---;~- ----~- ----;- :::::: :::::: :::::: :::::: :::::: ::::: ::::: ::::: ::::: ::::: ::::: ;, 9

Q o

1-3t60 years:e~~~~~~~: ::::~: ::::~: ---;;- ~ 4 ij ; 11 ~ __J- ::::~: ;;;;~; ~~~~~~ ~~~~~~ ~~~~~~ :~~~~~ ~~~~: ~~~~~ :~~~: :~~~~ ::~:: ~~~~~ 1 ~

~ Ill' Total--------------- 1 13 33 55 72 87 84 70 48 2li 12 6 1 ------ ----- ----- ----- ----- ----- ----- 507 ~

UJ 70 YW~te oaks------------ 5 13 27 40 46 38 ==: 16 9 2 2 ------ ----- ----- ----- ----- ----- ----- 224

Black oaks------------ 1 3 5 10 16 17 15 10 6 4 2 ------ --.-- ----- ----- ----- ----- ----- 88 Other intolerant------- 1 2 5 8 10 10 9 6 4, 2 1 1 ------ ------ ----- ----- ----- ----- ----- ----- 59 ~ Other tolerant.-------- 4 11 15 10 4 2 1 1 0 ------ ------ ----- ----- ----- ----- ----- ----~ 48 ------ -------------------------------------------- l;l

Total_______________ 1 6 21 37 liO 69 66 60 49 33 20 9 6 2 ------ ----- ----- ----- ----- ----- ----- 419 ======= . == = ======= ~

White oaks____________ 2 8 18 30 37 36 28 20 12 6 2 2 ------ ----- ----- ----- ----- ----- ----- 20180 years:Black oaks____________ 1 2 6 10 13 14 13 8 5 3 2 ------ 1 ----. ----- ----- ----- ----- ----- 78 > Other intolerant------- 1 1 3 6 8 9 8 6 6 3 2 1 0 ------ ----- ----- ----- ----- ----- ----- li3 Other tolerant_________ 2 8 11 11 6 2 2 1 0 ------ ------ ----- ----- ----- ----- ----- ----- 43 ~

t::;1

Total_______________ 1 3 13 25 38 47 liS 54 47 37 27 16 7 6 2 ------ 1 ----- ----- ----- ----- ----- ----- 376 q========= ====-==== =. ====== ~ White oaks____________ 2 6 15 24 31 33 28 20 13 7 4 2 .-- ------ ----- ----- ----- ----- ----- ----- 18590 years:

Black oaks____________ 1 1 4 7 10 12 12 0 7 4 2 2 1 ----- ----- ----- ----- ----- ----- 72 ~ Other intolerant------- 1 2 4 6 8 8 7 5 3 2 1 1 1 ------ ----- ----- ----- ----- ----- ----- 40 t::;1Other tolerant--------- 1 6 8 10 7 4 2 1 1 0 ------ ------ ----- ----- ----- ----- ----- ----- 40 ---------------------------------------------------------- o

Total.______________ 2 10 18 32 40 47 49 44 36 27 17 12 7 2 2 1 ----- ----- ----- ----- ----- ----- 346

100,.,,,,, == === ========= ======= ~ White oaks-___________ 2 3 10 19 26 29 27 22 15 9 6 2 2 -_•• -- ----- ----- ----- ----- ----- ----- 171 Black oaks------------ 1 . 1 2 5 7 10 12 10 8 6 3 2 1 ----- -~ --- ----- ---.- ----- ----- 67 Other intolerant_______ 1 1 3 6 6 7 7 6 4 3 1 1 1 ------ ----- ----- ----- ----- ----- ----- 4li Other tolerant_________ 0 6 6 0 7 4 3 2 1 0 ------ ------ ----- ----- ----- ----- ----- ----- 37 ~

~ TotaL______________ 1 8 12 25 33 39 44 41 37 30 20 14 8 5 2 1 __•__ ----- ----- ----- ----- ----- 320 UJ

H: C-'

TABLE 37.-Stand table-Distribution of trees by successive diameter classes, by species groups and age--Continued

SITE INDEX 6O--AVERAGE SITE

Ageand speciesgroup

10 years:White oaks____________ Black oaks-----------­Other intolerant_______Other tolerant _________

Total___ •• __________

20years: White oaks____________Black oaks____________ Other intolerant_______ Other tolerant _________

TotaL __________ .._-­30 years:White oaks____________

Black oaks____________ Other intolerant______Other tolerant __-_____

TotaL ____ ••________

40 years:White oaks____________ Black oaks____________ Other intolerant_______ Other tolerant _________

Total _______________

.d

~ ~ m ~ ~

~ sc:> .S

~ ~ .d '5..,

l!a .S .S .S .S .S .S 0 ... e'1 Cl) "'" lQ CCl ~ 00

- ­ - ­ - ­ - ­ --'- ­ - ­ - ­No. No. No. No. No. No. No. No. No. 136 1,320 427 58 --­ ..-­ -----­ --_ ..-­ -----­

66 690 296 33 11 -----­ -----­ -----­ -----­51 372 124 17 -----­ -----­ -----­ -----­ -----­92 289 59 5 4 -----­ -----­ -----­ -----­- ­ - ­ --- ­ - ­ - ­ - ­ - ­ - ­

345 2,671 916 113 15 -----­ -----­ -----­ -----­- ­ - ­ --I - ­ - ­ =

19 242 363 214 74 18 ...----­ ...---­5 74 189 157 74 21 5 ------­ -----­

11 78 97 54 22 8 -----­ -----­ -----­24 126 57 11 2 -----­ -----­ -_ ..._-­ -----­

- ­ - ­ - ­ - ­ - ­ - ­ --- ­ - ­59 520 706 436 172 47 5 -----­ -----­- ­ - ­ - ­ - ­ - ­ = - ­

------­ 28 88 124 106 69 32 9 5

13 47 73 63 39 18 5 4 17 30 32 24 15 7 4 1 3 4li 44 12 4 1 -----­ -----­ -----­- ­ - ­ - ­ - ­ - ­ - ­ - ­ --- ­7 go 175 215 207 148 78 31 11

= - ­ - ­ - ­ - ­ - ­ = - ­ - ­..._---­ 3 17 47 67 64 47 26 12

2 7 20 33 39 31 20 2 7 13 17 16 13 8 5 2

-_ .._-­ 15 26 17 7 2 1 1 ---­ -­- ­ - ­ - ­ - ­ - ­ - ­ - ­ - ­

2 2.'i 58 88 110 112 95 63 34 == = - ­ - ­ ====

Trees in each diameter class

~ m

~ ~ ~ m J ~

.d '5 '5j o

.S .S .s. .S .S .S c>

0 ... e'1 Cl) ~ lQ :=l... ... ... ... ... - ­ - ­ - ­ - ­ - ­ - ­ - ­ - ­

No. No. No. No. No. No. No. No. -----­ -----­ -----­ -----­ -----­ -----­ -----­ ---- ..--- ..--­ -----­ -----­ -----­ -----­ -----­ -----­ --_..-­-----­ -----­ -----­ -----... -----­ -----­ -----­ ---_..------­ -----­ -----­ -----­ -----­ -----­ -----­ -----­-­- ­ - ­ - ­ - ­ - ­ --- ­-----­ -----­ -----­ -_.._-­ -----­ ...._--­ _.._--­ -----­

= = -----­ -----­ ---­ -­ ----- .. -----­ -----­ -----­ -----­-----­ -----­ -----­ -----­ -----­ -----­ -----­ -----­-----­ -----­ -----­ -----­ -----­ -----­ -----­ -----­-----­ -----­ -----­ ---_...... -----­ -----­ -----­ -----­-­- ­ - ­ - ­ --- ­ - ­ - ­--­ --­ -----­ -----­ --_ ..._­ -----­ -----­ ---­ -­ -----­

----3­ -----­ -----­ -----­ -----­ -----­ -----­ -----­-----­ ---_...- -----­ ----_.. -----­ -----­ -----­

-----­ ---- ..- -----­ -----­ -----­ -----­ -----­ ---_..------­ -----­ -----­ -----­ -----­ -----­ -----­ -----­- ­ - ­ - ­ - ­ - ­ --I-- ­

3 -----­ -----­ -----­ -----­ -- .._-- ---_..- -----­= = - ­ - ­ =

6 3 -----­ ---_ ..... -----­ -----­ -----­ -----­10 3 -----­ -----­ -----­ -----­ -----­ -----­2 -----­ -----­ -----­ -----­ -----­ -----­ -----­

-----­ -----­ -----­ -----­ -----­ -----­ ----_ .. -----­- ­ - ­ - ­ - ­ - ­ - ­ - ­~18 6 -----­

==:::::::ii::::=---­ - ­ - ­ - ­ - ­

J m '5 .S

~ ~... - ­ - ­No. No. ----­ ----­----­ ----­----­ ----­----­ ----­- ­ - ­----­ ----­

=

----­ ----­.._--­ ----­----­ ----­----­ ----­- ­ - ­----­ ----­

= ----­ --.-­.---­ --.-­----­ .---­----­ ----­- ­ - ­----­ ----­= ----­ ... - ....-----­ ---- ..----­ ----­----­ ----­--I-­

- ­ - ­

j c>... - ­No.

----­----­----­.---­- ­----­

----­----­----­----­- ­----­

----­--.-­----­----­- ­----­

----­----­----­----­- ­

=

~ .S ~ - ­No.

.....~------­----­----­- ­----­= ---_..-- ..-­----­----­- ­----­= ----­- ..--­----­----­- ­----:-­

----­----­----­----­- ­- ­

m j] ~ ~ - ­ - ­No. No.

----­- ..-- .. ----­----­ ----­----­ ----­- ­ - ­--.-­ ----­

----­ ----­----­ ----­----­ ----­_.._-­ ----­- ­ - ­----­ _...._­

== ----­ ----­---­ ... ----­----­ ----­----­ ----­- ­ - ­_..--­ ----­= ----­ ----­----­ ----­----­ ----­.---­ ----­- ­ - ­

- ­ - ­

-a "0 Eo! - ­

No. 1,941 1,096

5M 459 - ­

4,060 =

gOO 52li 270 220 - ­

1,945

461 261 134 109

- ­965

- ­292 165 ss 69

- ­611

=

50 years:White oaks____________ Bla.ckoaks Other intolerant_______Other tolerant_________

Total

90years:

----------- ­7

1 3 7

7 15

10 29 50

12 1 6

10 _

2 17 1====1==1==1===1==

o 6

White oaks____________ 1 3 6 10 15 19 21 18 14 9 7 3 1 1 - -- ----- 128 Black oaks____________ 1 1 3 6 9 11 12 11 8 6 3 1 1 73 Other intolerant ._____ 0 1 2 3 0 6 6 5 4 3 1 1 0 0 ------ ------ ----- ----- ----- ----- ----- ----- ~b Other tolerant_________ 2 5 6 6 4 3 2 1 1 0 ------ ------ ------ ------ ------ ----- ----- ----- ----- ----- ---- ­

Total_______________ 0 4 --W~"22~~____a4___a2~"22 19 11 ---; 4 1 1 ~ ---;j8 1="====1= = = 1==1 =1 ~

100 ~t:e oaks____________ 1 2 6 8 13 17 19 17 13 10 7 4 1 1 ----- .----- 119 Black oaks 1 2 4 6 9 9 10 9 7 5 3 2 0 ----- ----- ----- ----- 67Other intoler9.iit_~:~=~~ =~~~~===:::: ----il- ----2- 3 4 5 5 5 4 3 2 1 0 0 ----- ----- ----- .---- 34Other tolerant_________ 1 4 5 6 5 3 2 1 1 0 0 ----- ----- ----- 28

TotaL__________________________ 2 --8 --u18u----;';30-i'""'::-26"21---;:B 13 8 63 2 0 r.J..7-- ---248

---------------------------------------------------

------------------------------------------------------------

-----------------------------------------------------------

----------------------------------------------------------

TABLE 37.-Stand table---Distribution oj trees by successive diameter classes, by species groups and age--Continued ~

SITE INDEX 7o-GOOD BITE

Trees in each diameter class ~ o

~ .Ageand species group I 1 I .g I ~ I ~ I ~ I ~ I'~ I ~ I ~ I ~ I ~ I ~ I ~ I ~ I ~ I ~ I ~ I ~ I ~ I ~ I~ I~ I ~

~ .a .S .a .S .S .S .S .S .S ~ ~ ~ ~ .S ~ ~ .S .S ~ .a ~ .a ~ o .... ~ C') ... ao co t-­ 00 C> .... .... .... .... ~ .... .... ~ ~ .... ~ ~ ~ Eo! ~ ----------1--1--'--'--1--'--'--,--,--,--,--,--,--1--1--,--,--,--,--,--,--.--.- ­

bj q

White oaks____________ 66 765 409 7g _~~~_I_~~~_I_~~~_I_~~~_I_~~~_I_~~~_I_~~~_I_~~~_I_~~~_I_~~~_I_~~~_I_~~~_I_~~~_I_~~·_I_z.:.O:_I_z.:.~'_I_~~·_I_~~·_1-~~'-I f~i910 yoors: IN°'1 N°'1 No, INo. 10 1,042Blac): oaks____________ 42 542 375 73 4 .----_ 427Other intolerant_______ 30 235 132 26 3 352 ~ Other tolerant_________ 60 215 67 7 ~

TotaL. . .... 198 11,757 I 983 1851 17 ------ .:.:.=.:I-·----I.:.:.=.: ------ ------ ------ ------ ------ ------1------1------1----.1-----1-----1-----1-----1-- 13,140 Z Ot Q)

1=====i20 years: 1 I ~o

~~~g:::--:==~======= ----~- 19b ~~ t~g 11g~ :~ 1~ ====== ====== ====== ~===== ====== ====== ====== ======1======1======1=====1=====1=====1=====1=====1 ~~g ~g~~: ~~:E::::==== 1~ :~ ~~ i~ 2~ ~ ----~J===== ====== ====== ====== ====== ====== ====== ====== ====== ====== ===== ===== ===== ===== ===== ===== ~~ ~ TotaL .! 261 267 I 475/ 406\ 214 [ 87 1 25 1------/------1------1------1------[------1------1--- - --1---- --1- - - -- -1--- --1-- - --1--- -- 1- -- -- 1--- - - 1- --- - 11, 500 ======== ===::::::Z=Z:::=::C ==:=E:::: t:l t;J30YW~te oaks ------ 9 341 69 781. 59 3811 16 61 a [ ------ ------ - 1 1 -----1----- -----1----- ----- ----- 312Black oaks____________ 3 22 47 62 54 32 17 7 3 - - -- ----- -- -- _

101 ~ 83 o

I2;lg::~:::~::: :---;- : : .~ .~ .~ .2 <·I---~- ---~- ::::;: :::::: :::::: :::::: 1

:::::: :::::f:::: ::::: ::::: :::::\::::: ::::: ::::: 247

> 743

w~: '. 1

198 157 ~

m~=~~i::=====;=:==i= =:==~= -: ~f :~ ~ g! ~ ~f l' t ----~- ~~~~~~ ====== ====== ====== ====== ===== ===== ===== ===== ='==== =====1 1 53 ~ ~

Other tolerant ==_8_ ~~__7 3_1__1 1_ __0_============ ~ __ I==.::..:.:.::.=..=.:..:. ==.:..:.:..:.:.:..:.:..:.:.::..:.= 64

TotaL______________ 1 1 11 30 491 64 76 1 79 67 461 28 12 7 2 ------ --- ------11- - -- -- ----- ----- ----- ----- ----- ----- 472

1======z:::::::::::=======-==::::::=============== ~

.'lllll1lllilllJ••UI]lrlam.IJI•••IJilIL]Ulln'I'i ilTIF:.t:,C• .Lkbt· or:. ' ,JtttI !liteM ,.: $1£111.4 4 ~ 1~,II'. 'hi. LUll JU:,J

50 years:White oaks____________ 2 8 16 25 30 28 22 14 8 3 1 ----__ ----- ----- ----- ----- ----- ----- 157 ~Black oaks .__ 3 6 13 19 22 22 17 11 6 4 1 ----- ----- ----- ----- ----- ----- 124

OtherintoleranL_____ 0 1 3 6 8 9 8 6 5 3 2 0 ----- ----- ----- ----- ----- ----- 111 t;;l Other tolerant_________ 3 8 12 10 5 2 1 1 0 - ------ ----- ----- ----- .---- ----- ----- 42

~ TotaL._____________ 0 4 13 26 I~ 45 ~ 54 ~ 39 27 14 7 4 1 ------ ------ == ----- -----~ ----- -----~

t;J years:White oaks_.__________ 1 3 9 15 21 22 21 15 10 6 4 1 ----- ----- ----- ----- ----- ----- 128

Black oaks ._. 1 2 4, 8 12 16 18 15 11 7 4 2 1 -- ---.- ----- ----- ----- 101 ~ Other intolerant_______ 1 2 a. 5 7 7 6 4 3 2 1 0 0 ----- ----- ----- ----- ----- ----- 41 Other tolerant_________ 1 5 6 9 6 3 2· 1 1 0 ~ - ----- ----- ----- ----- ----- ----- 34

~ TotaL______________ 2 8 12 24 30 35 38 38 35 30 22 15 8 4 2 1 ----- ----- ----- ----- ----- 304 ____=1= =~.I==~I=_.....=I=____,=I_==\==,I="==I==~I===I~=__="I,=='==_<==I===i=:>o=,l==1==1==~

1 years: D:lWhite oaks___________ 1 2 5 10 14 \7 17 15 11 6 4 2 1 1 ----- ----- ---.- ----- ----- ----- 106 Black oaks____________ 1 2 4 7 10 12 13 13 9 7 3 2 1 ----- ----- ----- ----- ----- 84 Other intolerant.._____ 0 1 2 3 5 5 5 5 3 3 "1 1 0 0 ----- ----- ----- ----- ----- ----- 34 Other tolerant_________ 2 5 II 6 4 3 1 1 1 0 ------ ----- ----- ----- ----- ----- ----- 28 ~

TotaL_____________ 0 4 9 13 22 211 29 30 29 'J:1 20 18 11 8 4 2 1 ----- ----- ----- ----- -.--- 252 =-------=--=-------......---=--_._'~---------------- ~

Iyears:White oaks____________ 1 2 4 7 10 13 14 13 11 7 6 3 2 1 ----- ----- ----- ----- ----- ----- 94 Z Black oaks .____ 1 2 4 6 9 10 11 10 8 6 4 2 1 ----- ----- ----- ----- 74 Other intolerant_______ 0 1 2 4 4 5 4 4 3 2 1 1 0 ----- ----- ----- ----- ----- ----- 31 > Other tolerant.________ 1 3 4 II 4 3 2 2 1 0 0 0 ----- ----- ----- ----- --.-- ----- 211

~ TotaL______________ 2 6 10 16 19 23 24 25 24 19 18 14 10 7 4 2 1 ----- ----- ----- ----- 224

1=__-_--------1 ----=----=---------=----=-- q ) years:White oaks____________ 1 3 5 9 11 13 12 10 8 6 4 2 2 1 ----- ----- ----- ----- ----- 87

Black oaks .__ 1 1 a 4 7 8 10 10 8 7 5 3 1 1 ----- ----- ----- 69 Other intolerant .___ 0 1 2 3 4 4 4 3 3 2 1 1 0 ----- ----- ----- ----- ----- ----- 28 Other tolerant_________ 0 3 3 4 4 3 2 2 1 1 0 0 ----- ----- ----- ----- ----- 23 ~

--I----------------------------------------------------TotaL _.___________ 0 5 8 12 18 19 22 21 21 19 17 15 10 9 6 3 1 1 ----- ----- ----- W

JOyears: =----------------------=----=----------=--= ~ White oaks____________ 1 2 4 7 10 11 11 11 9 6 4 2 2 1 -- ----- ----- ----- ----- 81 Black oaks____________ 1 1 . 2 3 4 6 9 9 8 7 6 4 2 1 1 ----- ----- 64 ~

Other intolerant_______ 0 1 1 2 3 4 4 3 3 2 1 1 1 0 ----- ----- ----- ----- ----- 26 o Other tolerant_________ 0 2 3 3 3 3 2 2 1 1 1 0 • ----- ----- ----- ----- ----- 21 ~

TotaL ------O--4--6-9-1~18___w1Q1Q1817~ll-9---7-4---2---1---1-1==192 ~ D:l

c.n ~

------------------------------ -------- ------ ------ ------ ------ ----- ----- ----- ----------- -----

------ ------ ------ ------ ------ ------ ------ ------ ----- ----- ----- ----- ---------------------------------------------------------------------------------------------------

------ ------ ------ ------ ----- ----- -----______ ------ ------ ------ ------ ------ ------ ------ ----- ----- ----- ----- ----------- ------ ------ ------ ------ ------ ----- ----- ----- -----

------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ----- ----- ----- ----- ----- ----------- ------ ------ ------ -----

------ ------ ------ ------ ------ ------ ------ ----- ----- ----- ----- ----- ----------- ------------ ------ ------ ------ ------ ----- ----- ----- ----- -----

----------- ------ ----- ----------- ------ ----- ----------- ------ ----- -------------------------------- ----

----- ----- _____

-------------------------------------------------------

----------------------------------------------------

T.A.BLE 31.-Stand table-Distribution oj trees by succes8ive diameter classes, by species groups and age--Continued C1

'" " ,­

A.ge and species group -5 i.S ~~-5

- .S .S .El ~~ .... C"I cod "'" No.No. No. No.No.10 years: White oaks___________ 424 80 1832735

Black om____________ 411 115 2937829 3Other intolerant______ 20 162 113 26 3Other tolerant________ 159 59 1138

~ BITE INDEX 8O-EXCELLENT BITE

Trees in each diameter class ~

j i 18 i18:B:B ~ :Bi ~£ '5 ~ ~ -5'5 -5~ ~ ~ ~ -5-5 -5 j .S 3.S .S .S .S.El .S .S .S .El.S.El

0.S.S .S.El .... C"I 100;!:.... ........ ~:3 ~ --::l ~ ~ ~ ~00 ~100 co too co I------------ Eo!

ttl1\7'0. No. No. No. No. No.No. No. No. No. No.No. No. No. No. No. No. No.No.

.._-_ ... _.._--­ --- .._ ----_.. --_..._­ ......... oo..----­ --- ..-­ .. -----­_... _--­ _.._-­_... _-­ 95: ______ ..----- - ..-_ ..- ------ --- ..-- ------ ------ ------ ------ ------ ------ ----- ----- -----~

_...._-­______ ------ ------ ------ ------ ------ -_ ... _-- ------ - ...---- ------ -- .._-- ----- ----- ----- ----- ----- ----- 3~ ~ -_ .._-- -----­ ...._-- 271 1-3- ...- .._­Total- - _____________ 872 232 2,431 Z122 1,156 53

= c:.n20years: 0)4 ______White oaks___________ 38 110 126 844 38 17 42:---_ ...... ---_ ..­ .._--- ----­--- ..-- -----­ ...---­4 ..0Black oaks_____ •• _____ 128 128 14.9 64 3277 4lil...---­------ 2 ______Other intolera.nL _____ 5 41 1223 226 38 5 1~.._--- ----­..... ---­

--62 --

45 --

10 --

3 1 121 ~8 -_ ..--­Other tolersnt, - -----­6 ______Total _______________ ~302 238 128 5417 135 260 20 1,164--_ ..... ----­- .._--- ------ -----­ .._------- ----­----------------------------------------=

_----= ~

30 years: t?:lWhite om___________ 48 813 34 46 34 192 21141 2Black oaks ____________ 2 27 279 45 14 555 43 ~ 1 ______ 7~ ~ Other intolerant______ 1212 15 15 27 52 6 1 ______Other tolerant________

----14 --

24 --

16 6 2 1 6­--_ ..­----- ... -----­... _--- -----­ o----------------------------------------

fj~TotaL ______________ 22 19 751 74 00 105 97 68 372 671

~ =::III= 40 years: _____ 13:Wbiteoaks___________ ______ ______ 3 8 16 25 27 23 106 9 5 1 ______ -_ .......­ ----- ...._-- ----- ----- _____----3­ 1~Black oaks____________ ______ ______ ______ 1 4 9 17 25 27 25 17 10 6

_____ 41 c:Otberintolemnt______ 1 2 4 7 8 8 7 5 3 2 1 1 ______ -----r---­ _____ 41Otbertolerant________ ______ 4 9 12 8 4 2 1 0 0 __________________

3 3~

-------- eTotal_______________ 1 6 16 28 36 46 53 54 46 36 23 12 6 ============= =.=1== --------=1=

~

.111 n_,'II,-i'~I",I, UI'I••]IIII.LII.~J..t.UIfJ.tJ.J.;ltt,.UJ••,'OI•• 'IJ.l,IJI,l.Ilf'l.-III1,ll.IIIII.I,JlilJ.I~.,I,IJI-.,'"IIIll.lrlj[lll.JI.fJIJII :llUUrmll_

Whiteoaks----------- . 1 2 7 13 17 18 17 13 8 5 3 1 ------ ----- ----- ----- -_.-- ----- ----- 10550 years:Black oaks------------ 1 2 5 9 14 18 19 17 13 8 5 2 1 ----- ----- ----- ----- ----- ----- 114 a

Other intolerant- _____ 1 2 3 5 6 6 6 4 3 2 1 0 0 ------ ----- ----- ----- ---.- ----- ----- 39 Other tolerant-------- 0 5 6 8 ,6 3 2 1 1 0 ------ ------ ----- ----- ----- ----- ----- ----- 32 e;

TotaL 1 8 11 21 27 31 35 36 . 35 29 23 16 9 5 2 1 ----- ----- ----- ----- ----- ----- 290 = ======== ==-========== ~ c Whiteoaks___________ 1 2 4 7 10 13 13 12 9 6 4 2 1 1 ----- ----- ----- ----- ----- ----- 8560 years:Black oaks____________ 1 2 5 6 10 13 14 14 11 8 5 3 1 ----- ----- ----- ----- ----- 93 Other intolerant------ 0 1 2 3 4 5 5 4 3 ,2 1 1 0 0 ------ ----- ----- ----- ----- ----- ----- 31 Other tolerant__ 2 4 5 5 4 3 1 1 1 0 -:---- ------ ----- ----- ----- ----- ----- ----- 26 ~

TotaL______________ 0 4 8 12 17 21 26 24 26 25 21 19 13 9 6 3 1 ----- ----- ----- ----- ----- 235 f;j===== ===== = == ======~ rp.

White oaks___________ 1 3 5 7 9 11 10 9 6 4 3 2 1 ------ ----- ----- ----- ----- ----- ----- 7170 years: \

~~=~C:::: :::::: :::::: ----.- ----i- ----.- ----.- l l ~ : ~ 'g '~ '~ g.:': ----~- ---~- ---'- ..'. ::::: ::::: ::::: ~ ~ Other tolerant________ 1 3 3 4 3 3 2 2 1 0 0 0 ------ ----- ----- ----- ----- ----- ----- 22-------------------------------- ---'------------------- t?:l

80 y.::~tal---------------= , · - 8 12 \ 17 20 20 .18 17 14 8 5 a\1 1 == ----- :.:::::. ~15 20 11 196 Z

White oaks___________ 1 2 3 5 7 9 9 8 7 5 3 2 1 1 ----- ----- ----- ----- ----- ----- 63 Black oaks____________ 1 1 2 3 5 7 9 10 9 8 6 4 2 1 1 ----- ----- 69 Other intolerant._ 0 1 1 2 3 3 3 3 2 2 1 1 1 0 ------ ----- ----- ----- ----- ----- ----- 23 Other tolerant ., 0 2 3 3 3 a 2 1 1 1 0 0 ------ ----- ----- ----- ----- ----- ----- 19 ~

~ TotaL ~== --0 ---4 --6--8-1214161616U 15~12"--9- --7 -4- --2- --1- --1-====rn

00.-, = = = ===== ~=~=~~= o

~~_-_:::::::::::::::: :::::: :::::: ~ ~ ~ ~_ ~ ~ ~ ~ ~ ~ ~ : i l ---,- ---.- ---.- ---,- ---i- ::::: :: Other intolerant______ __ 0 1 1 2 2 3 3 3 2 2 1 1 0 0 ----- ----- ----- ----- ----- ----- 21 ~ Other tolerant -- __=___ 1 2 2 3 3 2 2 1 1 1 0 0 - ----- ----- ----- ----- ----- ----- 18

oTotal ====--0- --3--5- --7- --9----"l314151414141211ill --8- --5-3- --2---1- --1- ==---m 00 years: === =--====-- ' =====-- ~

White ossa, _ 1 1 2 4 5 6 7 7 6 5 4 2 2 1 1 0 ----- ----- ----- ----- 5~ ~ Black oaks____________ 1 1 2 4 5 7 8 7 6 6 4 3 2 1 1 58 o Other Intolerant , , 0 0 1 1 2 3 3 3 2 2 1 1 1 0 0 ----- ----- ----- ----- ----- ----- 20 Other toleranL_______ 1 2 2 2 2 2 1 1 1 1 1 0 0 ----- ----- ----- ----- ----- ----- 16 ~

TotaL____________ --_==--0 ---2 --4 --5- ---810~1212--"l312Ull--9 --7-7- --4- --3- --2- --1- --1-148 ~ rp.

CJl CJl

56 TECHNICAL BULLETIN 560, U. S. DEPT. OF AGRICULTURE

DISCUSSION AND APPLICATION OF STAND TABLES

The stand tables are based on the assumption that the Pearson type III function :fitsthe diameter distributions of these species groups. They are not expected to apply exactly to individual stands, but give an indication of the diameter range to be expected under natural conditions in extensive forest areas. Since the same percentage values apply on a particular site regardless of age, the same ratios actually found between the species groups in a given stand at the present time may be used at a future age. To predict the future stand the present ratios are computed, by sites, from the samples of the forest in question and then applied to the total number of trees estimated at the future age. To facilitate determination of these frequencies, table 38 is presented. It shows percentage values by mean diameter classes in each species group.follows:

The several steps in the computation are as

, (1) Estimating the future total number of trees and average diameter from the

yield tables. (2) Computing the future number of trees found in each species group from

the present ratios between species. (3) Reading the mean diameter of each species group from figure 22. (4) Interpolating the corresponding percentage frequencies from table 38. (5) Applying to the number of trees in each species group.

~

;::!

.~ e ~

~ ~ ~ ~

§ i; ;;:"

..c ee ~ ~

.b 'Q­~

.~ ~

~ .b

~

~ ~ e ~ ~

ee ~.t3 ~

~ ."

~ e ~

~... ." ~

~

~ e... ~

~ ~

§;

YIELD, ETC., TABLES .FOR EVEN-AGED UPLAND OAK FORESTS 57

~ -< 0 ~

S8

~

~O , 0

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TABLE 38.-Percentage distribution of trees "Jy diameter for various mean diameters in each species group-Continued c:.n

BLACK OAKS

Percent of trees by species group of mean diameter of-

Midpoint of diametel .! gj ~ ~ ~ :B 13 ~ ~ 13 ~ 18 ~ 18 ~ iB ~ gj ~ :3 '" gj

'5 .s:l .s:l .s:l l! '5 breast high class (inches) .s:l

~ ..l:l ..l:l 13 13 13 ] 13 .s:l .s:l 13 .s:l .s:l '5 0 0 0 0 0.s .s 0 0

0 0 0

oS .s .s .s .S .S a .S.s .S .s .S .s .s .S .S .S .s .s q d <;) q <;) <;) <;):3 ~ q 10 0 10 0 10 0 1Q 0 10 0 1Q 0 0 s ti ~ ;:!f :d ~

C'I ~ M M ... ... >Q wi <0 .0 r..: r..: a6 c:li-­-­-­-­-­-­-­-­-­-­-­-­-­-­-­-­-­-­-­-­-­0.25________________________ 9 4 1 1 ----7­ -----­ ..._---­ ------ -----­ .... _--­ ------ -----­ -----­ -_ ..._-­ -­ ..._-­ -----------­ -----­ -----­ ---­ ...--.. ---­ --_ ..-­ ---.. _­

L ____________________ . _____ 79 li2 30 16 3 1 ----S­ ------ ----i- ----i- ----i- -----­ ... _---­ -----­ -----­ --_ ..._­ -..... _-­ -----------­ -----­ -----­-----­~.._-_._ ..----.-------­----­ 12 36 43 38 29 19 11 3 ----2­ ---or -----­-----­ -----­ -..... _- ... -----­ -----­ -----­ -----­ --- .... ­3•••••••.• _•• _.___ •• _._____ • -----­ 7 20 29 34 32 26 19 12 8 4 3 1 ----i- ..._---­ -.... -... -­ -----­-----­ -----­ -----­-----­

4_____________ • _____________ ----­.. 1 5 12 20 26 30 29 24 18 13 9 6 4 3 1 ----i­ ...._---­ -----­ -----­ ------ -----­

5___________________________ ------ -----­ 1 3 8 13 19 24 27 25 22 17 13 10 7 3 2 ---or -----­ ------ ._---­

6___________________________ -..._--­ -----­ -----­ 1 2 5 9 14 19 23 24 23 20 17 13 7 4 2 1 -----­ ------ -----­7___________________________ -----­-----­ -----­ -----­ -----­ 2 3 6 10 14 18 21 21 20 18 13 8 5 3 1 1 --.._-­ -----­8___________________________

------ -----­ -----­ -----­ -----­-----.. 1 2 4 7 11 14 17 19 20 17 12 8 5 3 2 1 ----_ .. 9___________________________

------ .._---­ -----­ ----­.. -- .... _­ -----­ _.._--­ 1 1 3 5 8 11 14 17 18 16 12 8 5 3 2 1 10__________________________

----...- ------ .._---­ -----­ --.._-­ -----­ -----­ -----­ .._---­ 1 2 3 6 8 11 16 17 15 12 8 5 3 2 11. _________________________

----­..-----­ -----­ -.._--­ -----..

======1 ======

-----­-----­ -----­ -----­ 1 3 4 6 11 15 16 14 11 8 6 4 12__________________________

------ -----­ -----­ -.._--­ --...... - -----­-----­ --..._-­ -----­ -----­ 1 2 3 7 11 15 15 14 11 8 6 13__________________________

-----­ ----_ .. ----_ .. -----­ -- .._-­ ---.._­ -----­ .._---­ ---.._­ .._---­ -----­ -----­ -----­ 1 1 4 7 11 14 14 13 11 8 14__________________________

-----­--.._-­ -----­ -----­ -----­ -----­ --.._-­ -----­ .._---­ -----­ -----­ -----­ -----­ --.._-­ -- .._-­ 2 4 8 11 13 14 12 10 15__________________________

-----­ -_ .._-- .._---­ .._---­ -----­ .._---­ ----.... ----_ .. -----­ ...__ .._­ -.._--­ .._---­ ---.... ­ -----­ -----­ 1 2 4 8 11 13 13 12 16__________________________

---.... ­ --.._..- ----_ .. -----­ -----­ -----­ -----­ -----­ ---_ .... --.._-­ -----­ --.... _- .._.._-­ -_ .._-­ _.._--- -----­ 1 2 5 8 11 12 13 17__________________________ ------ ------ _.._- ..- -----.. -----­ ---_ .... -­ .._-­ .._---­ -----­ ..._---­ ----­.. -----­ -_ .._-- -_ .._-­ ------ -----­ ---- ... ­ 1 3 5 8 11 12 18__________________________

.... _--­ ...... _-­ ..__ .._­ -----­ -----­ -----­ --.._..- -----­-----­ "'---... ­ .... _--­ ...----­ ------ --_ .._­ -----­ .._-_ ..- --_ .... ­ --.._- .. 1 3 5 8 10 19__________________________

-­ .._-­ -----­ --_ .._­ -.... _-­ ..._---­ .._---­ ---­..- --_ .._.. -----­ -_ .._-­ ---_ ..- ---.._­ .._---- -_ .._-­ -----­ ----_ .. -----­ ..-..__ .. .._---­ 2 3 6 8 20__________________________

-----­---_ ..- -----­ -----­ .._---­ .._---­ -----­ ---------_ ..- ... _---­ -.._--­ --_ .._­ .._---­ -----­ ..-.._-­ -----­ -- ........ - -----­-----­ 1 2 3 6 21. _________________________

-----------­ -----­ -----­ -----­ -----­ .... _--­ --_ .._­ -----­ ----_ .. -----­ -----­ .._-- ..- -_ .._-- .... _--- .._..._-­ -----­ --.._-­ --------_ .._­ 1 2 4 22__________________________

-----­-----­ -----­ -.. _--­ -----­ -----­ .._-_ ..- -----­ -_ .... _­ ----... ­ - ..... _-­ ------ ---- .. ­ -­ .. --­ -----­ -_ .._..- -_ .._-­ ..-.._-­ .... _--­ -­ ..-_ .. -----­ 1 2 23.._________________________

-----­ -_ .._-­ --_ .... - -.._--­ -----­ -----­ -----­ -----­ --­ ....­ ... __ .... ­ -----­ -----­ -----­ -_ ...... - .._---­ -----­-----­ ----..- -----­-----­-----­ 1 1 24__________________________

-----­-----­ -.._--­ -..__ .... -----­ -.... _-­ .... _--­ -----­-...-.._­ -----­ -----­ ------ -_ ...... - --_ .._­ - .. _--- .._-_ ..- --_ .._- -----­ --- ..._­ ------ -----­ -----­ 1

OTHER INTOLERANT SPECIES

0.25________________________ 11 6 ------ - -_ .._- .._---­4 4 2 2 13 3 ----i- --_ .... - ----_ .. .._-_ ..- --_ ....-- ----- .._---- ----.. ­1. __________________________ 1

2 ----2­76 150 31 20 _.._--- -----------­14 7 5 4102___________________________ ------ ------ -_ .._-­

2 ----i- ----i- ----i­13 35 4 337 31 24 15 11 6 1 ..... _- -­19 8 _..._--- ----_ .. -----­3___________________________ ----_ .. ----i­4519 25 11 9 7 3 2 122 17 14 1 125 20------ 84___________________________ ----i- -_ .... -- -_ .... _­

_.._--­ 1 13 13 11 9 8 5 2 _...--­6___________________________

7 17 19 19 19 16 2 1 117 35___________________________ ------ ..1116 14 132 17 9 6 2 2 1 _..---- --_ .._­

7___________________________ 5 13 15 17 17 4 310----_ .. -----­

15 14 12 2 _........ - -_ ..... _­8_______________________ . ___

2 16 164 13 15 16 9 6 4 237 10------ ----_ ... ----..­15 15 1514 1410 12 11------ .... _--­ 4 6-..._-- .. 2 6 8 8 5 3 2 -_ ..... -... ..---_ ....._---­

1412 1411 14 13 10 4I 2 7 9 8 6 53 5------ ..----­ ----_ .. -----­D___________________________ --.. --- -----... 11 12 137 9 14 12--...... - -- ...--­ 1 2 2 4 55 10 8 610__________________________ ---_ ..- -----­

_.._--­ 4 9 10 12 122 6 7 11 61 1 3 9 8 -_ .._-- -----­------ .... _- ..­-.._--­----..­ll__________________________ 4 62 8 10 12 111 1 3 9-_ .._-­ 10-..... _-­------ ----..­ 7 ..----- ...----­

13_________________ . ________ 12_______________________ . __ -----­ -"-- ..­-_ .... _­ 1 2 21 3 10--_ ..-­ 5 8 11 10 8 14__________________________

9------ ------------ ----_ .. -----­_.... _-­_.._--­ 21 1 1 10 9_..---- ----_ .. ------ ..----- _...-.... ­ 3 5 9 108---.._­ ..... _-- -----­-.... _.... -- .... _­_..... _-­ 1 1 2 3 86 9 9--- .._­ ...... --­ 9 ..

_----- ..----­~ ----..­15__________________________

1 2 6 9 17__________________________ -----­

--- .._ 4 8 8--- .._­ ------ ------ ------ _.._--- -..._--­------ ------------ .. ------ -----­16__________________________ -----­ --_ .._.. .._---- _......... - .._---- -.._--- --..-..­_.... _-­ _.._--­ 1 2 4 6 8 --_ .._- -----­7--..--- ------------ -----­~---18________________________ ._ -----... _..---- --_ .._- ------------ ..----- -_ ..--- ------ .._--_ .. ------ ------ --..--- _.... _-- ......--- --_ .._- ------ 1 3 5 6 7 -- -----­_-_ .... _­ _.._--­ 1 2 6--_ .._­ 5.. _-_ .. -----.. ..... _--- _.._--­ 3.._---­ -.._--­ ---.._­ .----- --_ ..._­19__________________________

21 53----_ .. ------ ---_ .. ------ --_ ..... - ------ .._---- ------ -----­20__________________________ ------ ------ ------ ---_ ..- ------ ------ ...._---- -----­------ _.._--- ----_ .. ...-_ .._- ----------.... 1 2 4_.... --­ ------ -_ ..... ­------ ---.._­ ------ ----_ .. -----­---.._­------ ------ ..-..._-­21. _________________________ _....-.... 1 2 3------ .._---­ ---_ ..­ ---.._­ -_ .._-- ------ ------ -----.. ------ .._---­22__________________________ ------ ------------ ------ _.._--­ ------ -_ .....­

_.._-- .... _.._­ 2-_ .._-­ 1--_ ..-.. -----­ ----_ .. ---_ ..--_ .... - ------ ------ ------ -- ...--- ------ ------ --_ ...... - .. ------ ---_ ..- ----.­23__________________________ 1-_ .._-­ 1---.._..--.._-­.._---­ ------------ ------ -_ ..--- ----_... ------ -----­24__________________________ _-_ .._- .. 1_.._--­------ -_ .._-­ ..._-_ .. ------ ------ .... _--- ------ --_ .... ­----_ .. --..--- ---........----..------ ------ ------ ..._--­

OTHER TOLERANT SPECIES