Agricultural Meteorology, 17(1976) 161--183 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

A S I M U L A T I O N M O D E L OF S E A S O N A L C H A N G E S IN THE V A L U E OF C A T T L E D U N G AS A F O O D R E S O U R C E F O R AN I N S E C T

PETER SANDS and R. D. HUGHES

Division of Computing Research, and Division of Entomology; Commonwealth Scientific and Industrial Research Organisation, Canberra, A. C.T. 2601, (Australia)

(Received October 15, 1975; accepted June 3, 1976)

ABSTRACT

Sands, P. and Hughes, R. D., 1976. A simulation model of seasonal changes in the value of cattle dung as a food resource for an insect. Agric. Mete orol., 17:161--183.

In the Canberra region the larvae of the Australian bushfly feed in cattle dung, and the quality of this dung is an important determinant of the population dynamics of the insect. A measure of this quality is provided by the mean mass of puparia reared under standard conditions in the laboratory. This paper presents a simulation model by means of which this measure and its seasonal variation can be predicted from standard observations of rainfall, temperature and 09h00-humidity. The model is based on the growth index of Fitzpatrick and Nix, but incorporates a simple model for the phenological changes occur- ring in the pasture from which the dung derived. The model successfully simulates the masses of pupae reared in dung derived from a number of distinct pastures within 200 km of Canberra throughout the seasons 1970--71, 1971--72 and 1972--73.

INTRODUCTION

The eco logy of the Austral ian bushf ly (Musca vetustissima, Walker), an i m p o r t a n t nuisance pest of man and s tock animals, has been s tudied exten- sively (Hughes, 1970; Greenham, 1972; Hughes et al., 1972; Hughes and Nicholas, 1974). The results o f these studies are being welded into a simula- t ion mode l o f the popu la t ion dynamics of the fly. The principal breeding med ium of bushf ly larvae in the s tudy region is cur ren t ly cat t le dung, the character is t ics o f which are i m p o r t a n t variables in the model . Greenham (1972) has shown tha t egg to adul t survival and the u l t imate size of flies s t rongly depend on the t ex tu re o f dung, and on its water and n i t rogen con- tent . In this way, survival and those popu la t i on variables which depend on fly size (e.g. f ecund i ty ) may vary up to three-fold in a typical season. Clearly a measure o f individual size is a critical variable in the dynamics o f bushf ly popula t ions . Accord ing ly , this paper presents a s imulat ion mode l with which such a measure o f size can be pred ic ted using as mode l inputs on ly readi ly available meteoro log ica l data.

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A suitable measure of size is the mean mass of individual pupae and their puparia. This mass, henceforth termed the pupal-mass, depends largely on the competit ion between larvae for the dung and on its nutritive value. The latter varies somewhat between samples from different individual cattle, and from distinct pasture types, but most importantly, it varies continuously for a given herd feeding on the same pasture (Greenham, 1972). Greenham con- cluded that the nutritive value of cattle dung varied with the species composi- tion of the pasture, and with the growth and maturi ty of the herbage. While a predictive model of bushily parameters could be based on physico-chemical analyses of dung samples, these analyses are neither readily available for any wide range of sites, nor easily obtained. As daily weather records are available for sites over the whole geographic range of the bushfly, Greenham's (1972) suggestion that bushily parameters might be derived from a general model of pasture growth based on climatic data alone was followed; indeed, with con- siderable success.

In the experiments upon which the model is based, the larvae were reared at various densities (larvae per litre of dung) under controlled environmental conditions. This paper is thus concerned with the joint effects of both dung quality and larval density on the pupal-mass. It was found (p. 164) that for a given density the pupal-mass can be considered as a function of a single vari- able, i.e., an index of dung quality.

Following Greenham's suggestion, the relative growth index of Fitzpatrick and Nix (1970) was chosen as the basis for establishing a suitable predictor of dung quality, but alone it proved inadequate. The predictive value of the growth index varied seasonally with the growth and maturi ty of the pastures. Accordingly, the growth index was modified (p. 172) by multiplicitive factors depending on the phenology of the plant and reflecting these changes. This dung quality index furnished a good fit to the observed pupal-masses.

Data corresponding to three sites and two seasons (i.e., six combinations) were available. As the relative growth index would be expected to vary in absolute terms between the different pasture types involved, the model was built on the basis of two sets from one site. Only minor readjustments of the parameters were required to obtain a fit for a further two sets of data. A fifth set was adequately simulated after allowing for the fact that it was a pasture of a very different character from the others, namely an unimproved pasture of poor native grasses. However, although the start and end of the sixth site-season were well simulated there appeared no way of reconciling a major medium-term discrepancy for it to be compatible with the others. Finally, further sets of data for the native pasture, collected previously for a different purpose, provided independent tests of the model. Simulations of these data were also satisfactory.

EXPERIMENTAL METHODS AND RESULTS

Ten-litre samples of freshly dropped cattle dung were collected weekly at

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each of three sites over the period September to March in the seasons 1971-- 72 and 1972--73. One site was near Canberra, another at Jugiong 100 km to the northwest , and the third at Bombala, 200 km to the south. The site near Canberra was at Gungahlin in 1971--72, but was changed to Uriarra the fol- lowing year. The Gungahlin site was a neglected pasture of a mixture of most- ly native grasses. All o ther sites had mixtures of legumes and grasses, usually improved by the annual application of fertilizer.

At each site a small herd of cattle grazed cont inuously on that pasture alone. The only except ion was at Uriarra in 1972--73, when for a period towards the end of a drought f rom 72360 to 73035, no herbage was present and hand feeding with hay was necessary. (Throughout this paper dates are given as the year and day of year; thus 72360 is Dec. 25, 1972.) The progress to matur i ty of the pastures and their subsequent senescence were judged very crudely f rom estimated peak flowering and, in seasons when regrowth was meagre or delayed, by the final breakdown of the senescing herbage. The estimated d a t e s o f p e a k f l o w e r i n g were:

Jug.

1971--72 71334 1972--73 72312

Gun./Uri. Bom.

71333 71363 72328 72347

In 1972--73 the est imated dates of the complet ion of senescence were 72363 at Jugiong and 73018 at Bombala.

The bulk samples of dung were held at 4°C before use. Although the dung was fresh, contaminat ions by field flies sometimes occurred, as indicated by the transmission of a disease to larvae reared in dung collected at Bombala on 71315. One-litre subsamples of dung from each site were set up each week in individual open sandboxes. To one subsample from each site 200 newly hatched larvae were transferred. To other similar sets of sub- samples larvae were added at 630 and 2000 larvae per litre in 1971--72, and at 1000 larvae/1 in 1972--73. The large number of larvae required were hatched from eggs laid in the laboratory on dung from a Canberra dairy farm. This dung was the source of a microsporidian disease which may have affected larvae reared in the dung f rom all sites f rom 72020 to 72060.

The dung pads formed f rom the subsamples and containing larvae were held in an insectary under similar drying condit ions at 27°C until the prepupal larvae emerged to pupate in the sand. When all pupae had formed, they were sieved f rom the sand, counted, cleaned and weighed in bulk. The average mass of the individual puparia and the enclosed pupae (i.e., the pupal-mass) in each subsample was then calculated.

The dates of collection of the original dung samples and the average pupal- mass for each larval density are shown for each site and season in Table I. Seven-day hygrothermographs recorded the climatic environment of the pas- ture f rom which each dung sample was derived and daily rainfall was recorded by the proper ty owners. On the basis of these data and the method of

164

pp. 170--172 below, the Fitzpatrick--Nix growth index was calculated and is also tabulated in Table I.

To facilitate the discussion of the construction of the pupal-mass model, data for Jugiong in 1972--73 are shown in Fig.1. It is evident that there is a general association between pupal-mass and the nitrogen content of the dung. This association guided the development of the model.

THE EXISTENCE OF A SINGLE MEASURE OF DUNG QUALITY; DEPENDENCE OF PUPAL-MASS ON LARVAL DENSITY AND DUNG QUALITY

The pupal-mass for 200 tarvae/litre is plotted in Fig.2 successively as a funct ion of the corresponding pupal-mass for each of 630, 1000 and 2000 larvae/1. These plots suggest that the pupal-mass is a function of larval den- sity (L) and one other parameter (q}. Since the point-to-point variation is that between dung samples, q is an index of the nutritive value of cattle dung to bushfly larvae. It is this quanti ty to which the term "dung qual i ty" refers.

If L, and L2 are distinct densities, Fig.2 suggests that for masses up to about 13 mg:

M ( L 1 ) = b M ( L 2 ) (1)

where b is a constant depending on LI and L2. The biological basis of eq.1 is that differences in the pupal-mass of larvae reared in distinct samples of the same dung are due to the larvae growing at different rates as a result of com- petition. The values of b obtained from each of Fig.2 are:

(a) b = 2.5; (b) b = 2.0; (c) b = 1.5.

The existence of a genetic upper limit to the pupal-mass is evident in the data only at low larval densities, hence the definition of q will be based on the observed pupal-masses of larvae reared at 2000 larvae/1. The dung quality index q is defined to be proportional to the amount by which the pupal-mass, M20o0, of larvae reared at 2000 larvae/1 exceeds the minimum pupal-mass, m0, for viability at this density. Formally:

M2ooo = mo + sq = s (q + qo) (2)

where s defines the scale of q a n d qo = tools. Since the climatic conditions during these experiments included a drought, it is assumed the correspond- ing observed pupal-masses were close to the minimum for pupal viability. Hence from Table I, rn0 = 1.8. The maximum M~000 was about 14 mg; whence s = 6 assigns to q the range 0 < q < 2; with q0 = 0.3.

From eqs. 1 and 2 the pupal-mass M for any density L, is:

M ( L , q ) ~ - s ( L } ( q + q o ) ( f o r M < 13mg) (3)

where M depends on L solely through s (L) . From eqs. 1 and 3, b = s ( L ~ ) / s ( L 2 ) .

165

20-

1S-

10-

5-

'X ~ JUGIONG 1972- 73

Mean mass of puparia (mg) A "/ reared at 200 larvae/litre l /

• V / reared at 1000 ' ~Jxlarvae/litre \ . . , . / ~ /

-n /i~;\ ^ Total Nitroge ' du g \ / /~, '~__.z \(parts per 1000 dry wt.) ~.- X / - - - /

~ V ~

250 300 350 034 I

084

Fig.1. The data for Jugiong 1972--73. Pupal-masses are given for both 200 and 1000 larvae/1. Also included are: the results of ni t rogen analyses (using the methods of Green- ham, 1972) for whole dung and for the < 100 p fraction available to the larvae; the growth index; and the observed pasture status.

166

'FABLE I

Average pupa l -masses obse rved when d i f fe ren t dens i t ies of bush f ly larvae were reared f rom dun g co l lec ted on the dates ind ica ted over two years at three sites

Day Average mass Growth Day Average mass G row th n u m b e r of pupar ia , index n u m b e r of pupar ia , index

larvae/l : × ] 00 larvae/l: × 100

200 630 2000 200 1000

Jugiong Jugiong

71257 14 14 8 15 72257 18 10 30 265 16 17 t 3 32 263 20 16 20 272 13 13 12 30 270 19 16 37 279 17 16 13 30 277 18 10 39 286 16 16 14 28 284 18 14 42 293 16 15 12 25 291 18 15 30 300 18 16 13 32 298 16 8 63 307 17 16 12 30 305 19 11 57 314 17 15 10 60 312 16 11 61 321 17 16 10 87 319 16 7 54 328 18 17 14 57 326 14 6 51 335 18 16 10 69 333 11 5 48 342 17 15 9 92 340 11 5 41 349 17 16 8 75 347 NA N A 30 356 NA NA NA 65 354 NA N A 20 363 14 13 8 94 361 10 5 16

7 2 0 0 5 15 13 8 77 73004 5 3 1() 012 16 14 9 89 011 5 3 7 019 18 16 11 91 018 4 2 14 026 14 14 8 79 025 6 3 8 033 14 12 8 69 032 NA NA 10 040 16 11 8 54 039 7 3 26 047 14 9 5 70 046 10 6 27 054 13 10 5 55 053 15 10 42 061 12 9 4 50 060 17 10 35 068 14 9 NA 46 067 12 7 30 075 12 7 NA 37 074 7 4 29 082 6 6 3 31

Bombala Bombala

72257 10 6 17 7 1 2 6 6 5 4 2 4 263 13 5 14

273 5 3 2 10 270 13 6 26 280 11 6 3 21 277 14 6 14 287 11 7 3 23 284 15 8 23 294 10 7 4 19 291 10 4 13 301 12 8 4 15 298 10 5 25 308 11 6 3 14 305 10 4 21 315 11 5 4 29 312 16 9 38 322 13 11 5 49 319 18 11 44 329 16 12 7 37 326 10 5 32 336 14 11 5 40 333 19 14 32

167

Day n u m b e r

Average mass of pupar ia , larvae/1 :

200 630 2000

G r o w t h index x 100

Day n u m b e r

Average mass of pupar ia , larvae/l:

200 1000

G r o w t h index x 100

343 350 357 364

720 0 6 013 020 027 034 041 048 055 062 O69 076 O83

Gungahlin

71 2 5 6

267 274 281 288 295 302 309 316 323 330 337 344 351 358 365

72007 014 021 028 035 042 049 056 O63 070 077 084

15 10 6 10 12 6 NA NA NA 11 7 5 13 10 5 14 9 6 15 11 6 13 11 6 11 10 6 12 9 5 12 6 4 10 8 5 16 12 6 NA NA NA 19 NA NA 16 12 7

7 4 2

8 5 2 6 5 3

11 7 4 11 8 4 15 8 4 13 10 5 14 9 5 13 9 6 14 10 5 14 12 5 15 12 6 14 9 5 13 11 6 NA NA NA 11 9 6 13 10 5 14 10 6 13 9 4 11 8 4 13 9 4 11 9 4

9 5 2 9 7 4 8 8 4

13 NA NA 11 8 NA 11 7 4

46 42 3O 39 49 62 75 69 8O 61 9O 8O 75 67 56 56

10

45 37 3O 53 38 48 66 78 78 57 87 92 78 96 92 80 94 88 75 67 55 73 57 79 52 55 42

340 347 354 361

73004 011 018 025 032 039 046 053 060 067 074

Uriarra

72257 263 270 277 284 291 298 305 312 319 326 333 340 347 354 361

73004 011 018 025 O32 039 046 053 060 067 074

18 NA NA 12 10 10

8 7 6 7

11 11 13 16 17

18 16 18 19 17 18 18 19 18 17 16 14 10 NA NA

7

8 9 7

10 11 16 18 19 18 19 18

10 NA NA

5 5 4 4 4 3 4 6 5 7

10 14

11 13 14 14 13 13 13 14 13 11

9 8 5

NA NA

4

4 3 5 6 5

11 13 14 13 16 11

35 32 27 18 11

8 9 7

20 35 30 59 53 63 60

23 35 30 26 31 40 55 62 66 52 55 44 36 26 16 12

7 16 26 10 37 75 81 83 75 67 53

1 6~

With s(2000) = 6, the other s(L) follow from the above values for 5:

L 200 630 1000 2000

s(L) 15 10 7.5 6

The final mass of a larva is proportional to its growth rate, which is propor- tional to the amount of nutr ient per larva and hence to 1/L. Thus it might be expected that s(L) is proportional to 1/L. However, when L is large this relation fails since the very small larvae fail to produce puparia.

20 M2oo

15 . , , . ,

lo 2

5. (a)

E g

20 M200

~s I ..:..

(N

.... ~ .... Ib .... i~ .... 2'0 M2ooo

.... ~ .... Ib .... ~ .... 2'o Mlooo

20-

15-

10 ~

M2oo

(c)

. . . . ~ . . . . ~b . . . . i~ . . . . 2b

/%4630

Mean moss (rag)

Fig.2. The re la t ionships be tween pupal-masses a t 200 larvae/l o f dung wi th pupal masses at th ree o t h e r densit ies, 630, 1000 and 2000 larvae/l. Crosses d i f ferent ia te the data for Jugiong 1971- -72 because i t is felt tha t the pupal masses for 200 and 2000 larvae/1 are no t se l f -consis tent for tha t site-season.

169

For pupar ia , then , s (L ) t ends to a non-ze ro l imit as L increases. The values o f s (L) are f i t t ed by:

s (L) = s* + ae -XL (4)

where s* = 5.5, a = 13 .45 and ?~ = 0 .00174 . Eqs.3 and 4 were used wi th the pupa l -masses fo r L = 1000 and L = 2000

to associa te a dung qua l i ty index q wi th each sample o f dung and in Fig.3 the

M 20-

15-

10-

u u 200

x u u

u ~ f . . ~ * u 630 x x x

x x o x o

x o o Xo o u o o

x x~ 0 1000

2000

i q • ~ ~!o l!S 2.o

Fig.3. The da ta po in t s are the obse rved pupal masses at 200 larvae/l p lo t t ed against dung qual i ty , q, in fe r red f rom pupa l masses for 2000 and 1000 larvae/1. Data for Jug iong 1971- - 72 are again d i f f e r en t i a t ed as open circles (see cap t i on for Fig.2), and da ta o b t a i n e d at 1000 larvae/l when the pupa l mass at t h a t dens i ty exceeded 13 mg are ind ica ted by LJ. The curves give the pupal masses at 200, 630, 1000 and 2000 larvae/1 d e t e r m i n e d f rom eq.5.

pupa l -mass a t a dens i ty o f 200 larvae/1 is p l o t t e d as a f u n c t i o n o f the q so de t e rmined . A l t h o u g h q is de f ined in t e r m s o f the pupa l -mass for L = 2000, values of q in fe r red f r o m eq.3 us ing the pupa l -masses a t 1000 larvae/1 will n o t be s ignif icant ly in e r ro r p rov i ded M ~ 13 mg; for those wi th L = 1000 and M > 13 mg, q is l ikely to have been u n d e r e s t i m a t e d . The p o i n t p lo t in Fig.3 suggests t ha t the genera l i sa t ion o f eq .3 is:

M(q, L ) = M * [1 - e -q (a +/3~)] (5)

t 7 0

where ei = s ( L ) (q + qo), s (L ) , q and q0 are as before, M* is the limit to the pupal-mass and a and i~ are two constants. An appropriate value for M* is 19.5, and a and ~ were determined so that with L = 200, M = 4.5 at q = 0, and M = 16.5 at q = 1, viz a = 0.047, ~ = 0.0025. Eq.5 was used to plot oil Fig.3 curves for the pupal-mass as a funct ion of q for each of L = 200, 630, 1000 and 2000. Finally, these curves were used to produce on Fig.2 curves for the pupal-mass at L = 200 as functions of the pupal-masses at L = 630, 1000 and 2000 larvae/1.

It has been established that dung quality can be represented by a single variable, q, such that the pupal-mass M, as a funct ion of q and the larval density L, is given by eqs.4 and 5. The remainder of this paper, in particular the section on pupal-mass model, is devoted to determining the dependence of q on the climatic variables.

COMPUTATION OF THE FITZPATRICK--NIX GROWTH INDEX

The dung quality index q is based on a general climatic model of pasture growth (Fi tzpatr ick and Nix, 1970) and this section presents those results necessary to const ruct their model given daffy maximum and minimum tem- peratures, 09h00 relative humidity, and rainfall.

The Fitzpatrick--Nix growth index, G, an estimate of the ratio of the rate of pasture growth obta ined under a given set of environmental condit ions to the op t imum rate of growth, is assumed to be proport ional to the three func- tions fT, fI, and fw, each of which varies f rom 1 under optimal condit ions down to 0:

G = f w f l f w (6)

The growth response of the pasture to temperature is measured by fT, a func- t ion only of mean tempera ture T; the response to radiation is measured by fI and to soil water by fw.

Our model calculates a growth index representative of the growth condi- tions experienced over a period of several days, N say, and T is the N-day average of the daily maximum and minimum temperatures. The funct ion fT (Table II) was derived f rom data in Fi tzpatr ick and Nix (1970, f ig. l .6) , but modified in the vicinity of the 5°C threshold. Values of fI for the Canberra region are given in Table III (H. Nix, personal communicat ion) .

The soil water response is the ratio of actual to potential evaporation f rom the pasture and its calculation necessitates the use of simple models to pre- dict the pan evaporat ion (Ep) and the soil moisture (W). Pan evaporat ion (in mm) is inferred f rom the meteorological data using relations due to Fitz- patrick (1963, eqs.3, 4, 6):

Ep = N e l + N e : [p(Ta) - 0.01 H p(T)]

T a = k T m [1 + logl0(d/12)]

k = max (0.9, min {1.0, ( T * / T m * ) + 0.06} } (7)

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where el = 0.84, e2 = 0 .247, p(T) is the s a tu r a t i on v a p o u r pressure ( m b a r ) o f air a t T°C, d is t he n u m b e r o f hour s f r o m sunrise to sunset , H is the N - d a y mean 0 9 h 0 0 relat ive h u m i d i t y , T and T* are r espec t ive ly the N-day m e a n and long t e r m annua l m e a n t e m p e r a t u r e s , and Tm and Tin* are s imilar ly de f ined for m a x i m u m t e m p e r a t u r e s . The n o t a t i o n y = min{ }, or y = m a x { }, implies t h a t y is assigned the value of the smallest , or largest, q u a n t i t y , respec- t ively, o f the list b e t w e e n the { }.

The v a p o u r pressure in mil l ibars is given by:

p(T) = 6 .11e ( ° ° 7 1 6 T - 0"000226T2) (0 ~ T < 50) (8)

and d is r e la ted to the day o f the yea r D by:

d = 7 .64 acos ( - t an6 t anA) (9)

A = 0.4 sin [ ~ ( D - 81 ) / 183 ] J

TABLE II

The Fitzpatrick--Nix thermal index, fT, for temperate grasses and legumes, with a modi- fied 5°C threshold

Mean fT Mean fT Mean temp. temp. temp (°C) (°C) (°C)

fw

0 0 16 0.89 28 0.61 4 0 18 0.96 32 0.15 6 0.04 20 1.00 34 0.04 8 0.15 22 1.00 36 0

13 0.67 24 0.94 40 0

TABLE III

The Fitzpatrick--Nix light index, fI, applicable to the Canberra region

Day fl Day fl of of year year

1 0.96 190 0.64 36 0.94 275 0.89 85 0.85 303 0.93

149 0.65 365 0.96 169 0.62

where A is the dec l ina t ion of the sun and 5 the l a t i tude of the site. The f irst o f eqs.9 is f r o m S m a r t (1962) ; the second is empir ica l .

The ca lcu la t ion o f the soil wa t e r c o n t e n t W at the end of the N - d a y pe r iod is based on the m ode l s o f McAlpine (1970) and Clark and Dal lwi tz (1974 ,

172

model B) and is derived from the water content W at the beginning of the N-day period, the rainfall R during the period, and the estimated total pan evaporation Ep, using the equations:

w = rain{W*, W_ + R}

E = min{w, max {0, r(Ep- Eo)(w/W*) + rE()} }

W = w - E

(10)

(Ii)

(12)

where W*, (the maximum capacity of the soil for water), r and E0 are con- stants. Clark and Dallwitz {1974, Table 12) give values of W*, r and Eo for the Canberra region: W* = 124.1 mm, r = 0.718 and e0 = -0 .714 mm. In terms of this water balance model, the moisture index fw is:

f w = E / r E p ( 13 )

An initial value of W for the Gungahtin and Uriarra sites was taken from the Canberra values in Clark and Dallwitz (1974, f ig . l l}; objective guesses were made for the remaining sites. However, due to the negative feedback inher- ent in eqs.lO--12 the water balance model is remarkably insensitive to inac- curacies in the initial values chosen for the soil water. Whereas the water balance model works adequately over short-time periods, the pan evaporation approximation is reliable only over periods of a week or more. The growth indices which appear on Figs.1 and 5--7 were computed using the results of this section with N = 7, i.e. over weekly periods.

DUNG QUALITY AND THE GROWTH INDEX; THE NATURE OF DUNG

The observed pupal-masses for a density L = 200 were used to estimate from Fig. 3 values of q for each dung sample. Since dung dropped at a given time was derived from the pasture a few days earlier, it is appropriate to relate the dung quality on day D to pasture conditions on day D - S D . The data in Table I suggested that ~D may be as high as 7 days (which is not inconsistent with the physiology of cattle}, and this value was adopted.

The inferred values of q were plotted as a funct ion of the associated growth index G and it was clear that no single-valued function of G alone could fit these data. Bearing in mind Greenham's (1972) suggestion that the nutritive value of dung depended on the maturi ty of the herbage on which the cattle fed, it was then assumed that:

q(D} = g , G { D - 5D) (14}

where g, depends on the phenology of the pasture. This raises the question as to how dung quality may be related biologically to the growth index, and how this relation may be affected by pasture phenology.

Greenham's (1972) work strongly implicates the nitrogen content of dung as a major factor in its favourability for bushily larvae. The bulk of the nitrogen in the dung has its origin in the nitrogen content of pasture plants.

173

Since fresh growth is particularly rich in ni trogenous materials a relation is likely between their quant i ty and the rate of plant growth, which in turn is limited by the growth index. However, the phenology of the plant also limits the rate of growth, and this is reflected in the changing nitrogen con ten t of the plant as it matures and senesces (Butler and Bailey, 1973). Nitrogen rises to its highest levels in the early growth stages, falls rapidly during flowering, and then more slowly during senescence. If the dung quality index is largely determined by dung nitrogen, eq.14 is reasonable only if g l is a funct ion of the phenological state of the pasture with a form resembling the dependence of plant nitrogen con ten t on phenology.

To explore these relations a simple model of the phenological changes in a pasture is needed•

A SIMPLE PASTURE GROWTH MODEL

The development of a perennial pasture passes through a sequence of phases, each phase delimited by an event. Starting in winter, the phases are dormancy, vegetative growth and senescence; the events are opening (O), flowering (F), death (D) and regrowth (R). As plants f rom two successive growth phases can be present in a pasture at one time, the two are regarded as separate components of the pasture. The five possible states S (= 0, 1 • . . 4 ) of a pasture and the number of components associated with each state

TABLE IV

States of a pasture and the number of components*

S Components Description

0 0 1 1 2 1 3 2 4 0

winter dormant vegetative growth alone senescing growth alone senescing pasture with regrowth drought dormant

*For explanation see text.

are as given in Table IV. A change in the state of a pasture is called a transi- tion, and a transition can only be caused by an event; possible transitions are given in Table V.

Opening and regrowth are certainly governed by the prevailing weather conditions. In the late winter near Canberra short periods when condit ions are marginal for growth are interspersed by periods too cold to allow it. The pastures do not seem to respond immediately to such stimuli, but do so once the favourable growth conditions are consistent. In our data favourable growth condit ions persisted once the growth index, G, reached 0.1 for the

] 74

first t ime in spring. This cond i t i on was thus used to def ine opening . R e g r o w i h of a senescing pas tu re s eem ed to need more s t imu la t ion and it was assumed to occu r when the 10-day runn ing average of G exceeded 0.2. Phenologica l changes in pas tures are d e t e r m i n e d by the a c c u m u l a t i o n o f day degrees ,b above a t e m p e r a t u r e t h re sho ld fo r pas tu re d e v e l o p m e n t of T* (= 5°C). Flow- er ing (F) c o r r e s p o n d s to a phys io logica l age (1) o f (Df, d e a t h (D) to (Pd. As no rel iable obse rva t ions o f the dea th o f pas tures were available, the cons t r a in t (D d = 2q)f is i m p o s e d t h r o u g h o u t this paper . In the in teres ts o f s impl ic i ty , it is

TABLE V

Possible transitions in pastures; the entries in this table are the state (S) into which a pas- ture in the indicated initial state goes consequent upon each of the events: opening (O), flowering (F), regrowth (R), death (D) and the onset of winter dormancy (W) (impossible transitions are indicated by a dash)

Initial Events: states(S) O F R D W

0 1 - - - 0 1 - 2 . . . . . 0 2 -- - 3 0 0 3 - 2 . . . . 0 4 . . . . . . 0

a s sumed t h a t all pheno log ica l events o c c u r a t def in i te ages. The ca lcu la ted even t - t imes fo r var ious values o f q~f are t a b u l a t e d in Tab le VI, a long wi th those field obse rva t ions available. These suggest q~f varies b e t w e e n 800 and 900. The la t t e r value p r o v e d overal l to give the best s imula t ion of the pupa l -masses and has been used e x c e p t where o the rwise s ta ted . Winter d o r m a n c y sets in at mid-year .

The m o d e l o f pas tu re g r o w t h is r equ i red to furn ish the pas tu re s ta te and ages. Given the s ta te and q) at the end o f one t ime interval the p r o c e d u r e to f ind the c o r r e s p o n d i n g values at the end of the n e x t t i m e interval is: (i) e s t ima te the g r o w t h index a t the end of th is interval; (ii) e s t ima te the increase in q) f r o m the daily m a x i m a and m i n i m a over this interval ; (iii) d e t e r m i n e if any events occur red ; and (iv} m a k e any necessary change in pas ture s ta tus using Tab le V.

THE PUPAL-MASS MODEL

The fo l lowing de r iva t ion o f t h e pupa l -mass m o d e l was based largely on the da t a o f Jug iong 1 9 7 2 - - 7 3 alone, and when the bes t had been d o n e wi th this s i te-season, a r e f i n e m e n t to the s t ruc tu re o f the m o d e l was m a d e by consider- ing Jug iong 1971- -72 : Pas ture p h e n o l o g y was d e t e r m i n e d using the resul ts o f the prev ious sec t ion .

F r o m the o b s e r v e d pupa l -masses fo r 200 larvae/1 a t Jug iong in 1 9 7 2 - - 7 3 ,

TA

BL

E V

I

Ob

serv

ed d

ates

of

even

ts i

n t

he

pa

stu

res

co

mp

are

d w

ith

th

e d

ates

pre

dic

ted

wh

en

usi

ng

dif

fere

nt

val

ues

of

the

ph

eno

log

ical

pa

ram

ete

r,

(|)f

(day

-deg

rees

ab

ov

e 5

°C b

etw

ee

n o

pe

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g a

nd

flo

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ing

)

Sea

son

S

ite

Dat

es e

ve

nts

o

bse

rved

F D

19

71

--2

Ju

gio

ng

7

13

34

--

1

97

2--

3

Jug

ion

g

72

31

2

72

36

3

19

71

--2

G

un

ga

hli

n

71

33

3

19

72

--3

U

riar

ra

72

32

8

--

19

71

--2

B

om

bal

a 7

13

63

--

1

97

2--

3

Bo

mb

ala

7

23

47

7

30

18

Pre

dic

ted

dat

es o

f p

ast

ure

ev

en

ts w

he

n:

• f=

8

00

¢|

)r =

90

0

~f=

1

00

0

O

F D

R

71

25

2

71

33

7

72

02

6

71

34

3

72

19

8

72

31

2

72

36

1

72

31

9

71

25

6

71

34

2

72

03

0

71

34

3

72

24

0

72

32

3

73

00

2

72

32

4

71

27

7

71

35

8

72

05

3

72

00

3

72

25

0

72

34

3

73

02

4

72

36

3

O

F D

R

O

F

D

R

71

25

2

71

34

3

72

03

7

71

34

4

72

19

8

72

32

1

73

00

4

72

32

2

71

25

6

71

35

0

72

04

5

71

35

2

72

24

0

72

33

1

73

01

2

72

33

2

71

27

7

71

36

3

72

06

8

72

00

3

72

25

0

72

35

0

73

03

3

72

36

3

71

25

2

71

35

2

72

05

9

71

36

5

72

19

8

72

32

9

73

01

6

72

33

9

71

25

6

71

35

6

72

06

1

71

36

3

72

24

0

72

33

8

73

02

2

73

04

2

71

27

7

72

00

6

72

08

8

72

01

3

72

25

0

72

35

5

73

04

7

72

36

3

Ev

ents

: O

= o

pen

ing

; F

= f

low

erin

g;

D =

de

ath

; R

= r

egro

wth

.

17t;

values o f q appropr ia te to each dung sample were inferred f rom Fig.;L t{efer- ring to eq.14, the rat io o f each inferred q to the cor responding g rowth index, taking a c c o u n t o f the delay 5D, is the value gl required to r ep roduce the observed mass. Let ~ be the f ract ional physiological age relative to f lowering:

= 4)/<i>r ( 1 5 )

so tha t ~ = 1 at f lower ing and ~ = ~d = (l)d/OPf at death. The es t imated values of gl are p lo t t ed as a f u n c t i o n of O in Fig.4a. Data for those dates where there

o u

-o E

J=

(D

o

21 3 ~. . , 2

2

(21

. . . . . . . . . . • A2L 0s ~0 1~ ~0

OJ5 1,0 1-5 2.0

Phys io log ico t age re la t i ve t o t i m e o f f l o w e r i n g ( j ' )

Fig.4. a. Growth index scalar gl(qb) as a function of physiological age (dp), estimated from pupal-masses for Jugiong 1972--73, 1 = spring growth; 2 = midsummer regrowth; 3 = late summer regrowth; (2) indicates data when regrowth and senescent pastures overlapped considerably. b. Growth index scalar as used in the model: (1) is for Improved pastures and (2) is for the native grass pastures, i.e.. Gungahlin.

are c o n c u r r e n t vegetat ive and senescent c o m p o n e n t s in a pasture (i.e., whose state S = 3) have been o m i t t e d since then ¢ is n o t un ique ly def ined (see the next paragraph) . Also o m i t t e d are two points early in the season where gj was anoma lous ly high. The resemblance o f this curve to those for the n i t rogen c o n t e n t o f pasture plants as shown in Butler and Bailey (1973) is gratifying.

Scaling G with a func t ion of ~ raises the ques t ion o f what to do when the

177

pas ture s ta te c o r r e s p o n d s to S = 3, since d is t inc t dung qual i t ies qv and qs will be o b t a i n e d fo r the vege ta t ive and senescen t c o m p o n e n t s , respec t ive ly . The ca t t le have access to b o t h c o m p o n e n t s and the dung p r o d u c e d will be an aver- age, in some sense, o f t h a t a p p r o p r i a t e to each c o m p o n e n t a lone. I f ¢v and ¢s are the f rac t iona l ages of the vege ta t ive and senescen t c o m p o n e n t s , it is sug- gested tha t :

q = aqv + (1 - a)qs (16)

where 0 < a < i and qv = g~(¢v) G and qs = g , (~s )G are c o m p u t e d f r o m the pas tu re s ta te and g rowt h index on day D - S D . The choice o f a is guided by the fol lowing: (i) w h e n Cv is small, the senescen t c o m p o n e n t cons t i t u t e s an u n a v o i d a b l y large f r ac t i on of the ca t t l e ' s diet ; (ii) as dea th is a p p r o a c h e d

TABLE VII

Values of gl((~) as they are related to ¢ in curves (1) and (2) of Fig.4

¢ Curve of gl(~b)

(I) (2)

0.0 3.40 0.80 0.2 3.35 1.35 0.4 3.10 1.55 0.6 2.50 1.45 0.8 1.70 1.20 1.0 1.00 0.75 1.2 0.60 0.50 1.4 0.45 0.4O 1.6 0.40 0.32 1.8 0.35 0.25 2.0 0.30 0.18

(i.e., ~s -~ Cd), the die t b e c o m e s exclus ively vege ta t ive g rowth ; and (iii) the f u r t h e r advanced senescence is at r eg rowth , the qu icker vege ta t ive g rowth d o m i n a t e s the diet. The s imples t sui table choice is:

= Cv/[~bv + (~bd - Cs)] = ~bv/(~bd - ~bso) (17)

where %0 is the age o f the senescent c o m p o n e n t at r egrowth . As requi red: 0 < a < l .

At this s tage the m o d e l was appl ied to all s i te-seasons. With the e x c e p t i o n of Gungahl in 1 9 7 1 - - 7 2 (which is cons ide red in detai l in the Discussion) the resul ts were encouraging , a l t hough the pupa l -masses dur ing the ear ly stages of vege ta t ive g rowth were general ly ove re s t ima ted . Accord ing ly , gl(¢) was scaled d o w n to the values given in Tab le VII , c o l u m n 1, and p l o t t e d as curve (1) in Fig.4b.

The re r e m a i n e d an o v e r e s t i m a t i o n of the pupa l -mass dur ing per iods of high g rowth index (G > 0.75) , seen a t Jug iong in 1971- -72 . When the g rowth index

178

is high, pasture growth is likely to be rapid and as such may be nitrogen lim- ited. Granted this, the actual dung quality should be less than that indicated by the model hitherto developed. This possibility is modelled by rewriting eq.14 (for qv and qs) as:

q = gl(O) g~(o, G ) G (118)

where g1(0) is as before and g: takes account of any relative reduction in the assimilated nitrogen in times of potentially rapid growth. As such g2 has the value 1 when G is small and decreases monotonically as G tends to unity. The dependence of g2 on the age ¢ of the pasture is biologically necessary since nitrogen deficiencies are not manifest in ptant growth much beyond flower- ing. The form adopted for g: is:

g:(0, G) = 1 - k(0)G n (19)

k(0) =g0max{0, min{1, (1 + 50-0) /250 } }

where go is a constant, n a small positive integer and 0 < 50 < 1. As before, 0 and G are appropriate to the pasture and growth index on day D - 5D. On the basis of Jugiong 1971--72, the following choice was made: n = 4, 50 = 0.2 and go = 0.4. The introduction of the factor g: implies the existence of an optimal growth index for dung quality; in this case, the opt imum growth index is 0.76.

This completes the construction of the pupal-mass model. It comprises: (i) the Fitzpatrick--Nix growth index, eqs.6--13, and Tables II and III; (ii) the pasture growth model of p. 173; (iii) the relationship between dung quality and growth index, eqs.16--19 and Table VII, column 1; and (iv) the depend- ence of the pupal-mass on larval density and dung quality, eqs. 4 and 5.

Fig. 5 compares the observed pupal-masses for all site-seasons with those obtained using this pupal-mass model. The growth indices were calculated at 7-day intervals and the pasture model was run on a daily basis. When needed, daily values of growth indices were obtained by linear interpolation between the weekly values.

DISCUSSION OF THE SIMULATIONS FOR ALL SITE-SEASONS

It is apparent from Fig.5 that with the exception of Gungahlin 1971 72, the simulations reproduce well the magnitudes and trends of the observed data although some anomalies are apparent: During the period 72020--72060 the larvae were affected by a microsporidian disease, and the observed de- clines in pupal-mass may reflect this infection rather than an actual decline in dung quality. The late-season recovery at Uriarra in 1972--73 is about 10 days late, but towards the end of the drought (72360--73035) the pasture was virtually bare of grass and the cattle were hand fed with hay, thus break- ing the link between pasture and dung quality.

Fig.5 also includes the simulated pupal-masses for a rearing density of

]79

E

>

o

c~

"6

o

L

o

(3.

-6 :3

E

O E

20-

15-

10-

5-

0-

15

10-

5-

\ \

\ \

i

O , I ' I ' " ' ' I ~ i

2 0 -

\I ', \

l O - I~ ~ ' - I I ~ - ~ \ \ h' I J . ..... ! \ \ f l "

/ !

":'~" :i~"', ~ ~ . ~::~'~'~'~" ~'~{'t~"-~-~ ~'~, ~'.. ~, ."":~ .......

n ~ - I ~ ~ ~ i i I i i I 1 ] i i

'250 3()0 350 I 030 080 300 350 I 030 080 1971-72 1072-73

Doy numbers

Fig.5. Compar i sons be tween s imulated . . . . and observed pupal-masses at all sites and seasons at a densi ty or 200 larvae/l, to~ether with es t imates or growth index and pasture s ta tus (see Fig . l ) . At Uriarra in 1972--73 the triangles indicate where dung was derived from hand-fed cattle.

180

1000 larvae/ l a t Jug iong 1972- -73 . With the e x c e p t i o n of ear ly in spring, thv fi t is sa t i s fac tory . In general , for all s i te-seasons, the s imula t ion at all densi t ies were o f c o m p a r a b l e qua l i ty to those a t 200 larvae/1.

The t i m i n g o f t r ends in the pupa l -masses depends on the t rends in the g r o w t h index and on the t iming o f var ious events in the d e v e l o p m e n t of the pas ture . T rends in G, gove rned by the c l imat ic variables , are b e y o n d the m o d e l l e r ' s con t ro l . However , the day degrees to f lower ing and dea th can be

E ._o L- 0 O. "-s Q,.

0

- 0

" 0 C:

"6

0 i::

15-1 / \

10-

5-

0 -

x

c

.4=

O

Q

I ! t 1 I

250 300 350 l 030 080 1971--72

Day numbers

Fig.6. Simulation for Gungahlin 1971--7 2 presented as in Fig.5 but using as gl(~b) cur~e (2) in Fig.4 b.

used to exerc ise con t ro l ove r the d e v e l o p m e n t of the pas ture . Hence , (P f (wi th dP d = 2q~f) was var ied in an a t t e m p t to i m p r o v e the s imula t ion . No improve - m e n t was o b t a i n e d fo r a n y si te in 1971- -72 . Fo r all sites in 1 9 7 2 - - 7 3 4~f = 1000 gave an i m p r o v e d f i t in the ear ly pa r t o f the season bu t a worse f i t to the la te-season recovery . The converse was t rue fo r (Pf = 800. The original

181

choice of 900 is thus a compromise. The time of initiation of spring growth was varied by changing the growth index needed to initiate growth from

15- GUNGAHLIN 1970--71

E o

O O_ o_

-6

c

o

E g ID

10-

5 - /" / ' / . /

I

\ \ larvae reared v ' \ at 400/litre \

\ \ / ~ J

", / \ larvae reared \ \ ,.4 /' '/ al 200/litre

\ A , , ,

" O

c

O

O

1970--71 Day numbers

Fig.7. S imulat ions for Gungahlin 1970- -71 at two larval densities presented as in Fig.6.

0.1 to 0.15. With the exception of Jugiong 1972--1973, this had no effect on the simulations. However, in Jugiong 1972--73, an improvement of the fit between 72270 and the New Year was observed. At this site-season there was

a short-lived rise in the growth index around 72200 followed by a prolonged cool and dry spell until 72240. The improved fit was a consequence of the initiation of spring growth being delayed until 72240.

The pasture of Gungahlin differed from the others in that it was an un- improved mixture of native grasses. This may afford an explanation of the pronounced discrepancy evident in Fig.5 between the simulated and observed pupal-masses for this site. in order to investigate this possibility, simple changes in the function g,(0) were made and the resulting simulation is shown as Fig.6. This improvement involved first scaling g,(¢} by 0.6 and then a fur- ther decrease for small o and an increase for ~5 > 1; see curve (2), Fig.4b and Table VII, column 2. The fit so obtained is the best that could be done whilst maintaining a form for g,(¢) consistent with that for other site seasons and with our belief that it in some way represents the nitrogen content of the plants.

These changes in gd¢) can be explained on the basis that native grasses generally provide less nitrogen in a form accessible to the larvae. Further, either the conditions required to break winter dormancy show a wide varia- tion between the many species present or less nitrogen is available to the native species early in the vegetative phase than later. With regard to the latter, it is characteristic of many unimproved pastures that the nitrogen available to the plants increases during the early stage of the season.

In order to investigate the possibility that the parameters determining the timing of events in the development of the Gungahlin pasture differ from those assumed at other sites, changes in apt and the growth index necessary to initiate spring growth were made. The latter had only an insig- nificant effect since the increase in Decreasing q,f to 800 improved the slight deterioration on prior dates. of the pupal-masses around 71320

G in early spring was quite sudden. fit beyond 71350, but brought about a However, the pronounced overestimation remained. This could only be removed by

further changes in g, (0}, with ~f = 8 0 0 ; these were deemed unacceptable since the observed peaks at 71338 and 72015 were no longer simulated.

After the work hitherto described had been completed, two further sets of data which included the pupal-masses on a number of dates during the season were found. These data related to the Gungahlin pasture during the 1970--71 season. The parameters used to simulate these data were those appropriate to the simulation shown in Fig.6, and the results for densities of 200 larvae/1 and 400 larvae/1 axe plotted in Fig.7. From day 70360 onwards the simulation is good. The trough in the observed masses at day 71100 is anomalous: few pupae were produced.

CONCLUSION

The model presented here performs welt and is biologically acceptable. Only minor modifications of parameters governing pasture phenolog-g and

183

the nutrient status of grass types seem sufficient to allow the application of the model to simulate changes in the quality of cattle dung obtained from the range of pastures around Canberra. The simulation of dung quality in widely different areas, such as in the subtropical zone, may require further modifications besides those inherent in the Fi tzpatr ick-Nix growth index as applicable there.

REFERENCES

Butler, G. W. and Bailey, R. W. (Editors), 1973. Chemistry and Biochemistry of Herbage. Academic Press, London, Vol. I, 639 pp.

Clark, L. R. and Dallwitz, M. J., 1974. On the relative abundance of some Australian psyllidae that coexist on Eucalyptus blakelyi. Aust. J. Zool., 22: 387--415.

Fitzpatrick, E. A., 1963. Estimates of pan evaporation from mean maximum temperature and vapour pressure. J. Appl. Meteorol., 2: 780--792.

Fitzpatrick, E. A. and Nix, H. A., 1970. The climatic factor in grassland ecology. In: R. M. Moore (Editor), Australian Grasslands. Australian National University Press, Canberra, pp. 455.

Greenham, P. M., 1972. The effects of the variability of cattle dung on the multiplication of the bushily (Musca vetustissima Walk.). J. Anim. Ecol., 41: 153--165.

Hughes, R. D., 1970. The seasonal distribution of bushily (Musca vetustissima Walker) in south-east Australia. J. Anita. Ecol., 39: 691--706.

Hughes, R. D. and Nicholas, W. L., 1974. The spring migration of the bushfly (Musca vetustissima Walk.): evidence of displacement provided by natural population mark- ers including parasitism. J. Anim. Ecol., 43: 411--428.

Hughes, R. D., Greenham, P. M., Tyndale-Biscoe, M. and Walker, J. M., 1972. A synopsis of observations on the biology of the Australian bushily (Musca vetustissima Walker). J. Aust. Ent. Soc., 11: 311--331.

McAlpine, J. R., 1970. Estimating pasture growth periods and droughts from simple water balance models. Proc. Int. Grassland Congr., 1 l th . University of Queensland Press, Brisbane, pp. 484--487.

Smart, W. M., 1962. Textbook on Spherical Astronomy. Cambridge University Press, Cambridge.