Impact of plot size on the effect of competition in individual-tree models and their applications...

Impact of plot size on the effect of competition in individual-tree models and their applications

Jari Hynynen & Risto OjansuuFinnish Forest Research Institute,

Vantaa, Finland

Introduction• Description of competition has major impact on model

behavior• Correlation between observed competition and

increment are affected by sampling > plot size effect– statistical effect – sampling error

• when plot size in the modelling data differs from plot size in the simulation data

• correction method (Stage and Wykoff 1998)– coefficients of the structural model are corrected in

simulation according the plot size in the simulation data

– biological effect• plot size vs. size of competition zone• affects predicted stand dynamics• affects comparisons between the simulated development of

different treatment regimes

Goal

To empirically study the effect of alternative sample plot size on the description of competition

1) in growth model (model parameters)

2) in simulation results

in Norway spruce dominated stands based on an extensive data from inventory growth plots

Description of Competition

Overall stand density: Relative density factor: RDF

• describes the relative distance with respect to self-thinning line (Hynynen 1993)

• expressed by tree species

• calculated treewise

Dg

N self-thinning line:RDF=1.0

a stand withRDF=0.8

Competitive status of a tree:RDF of larger than subject tree:

RDFL

Modelling data

• an objective sample of Norway spruce stands: Repeatedly measured inventory growth plots – 337 stands

– 802 sample plots

– 9300 tree measurements

– one 5-year growth period from each stand were used

• 4550 growth observations Norway Spruce stands in INKA data

tally tree plots

stand

Experimental design

• Three systematically located sample plots within a stand– circular tally tree plots

(36 trees/plot on the average) including

sample tree plots

– smaller concentric sample tree plots (10 trees/plot on the average)

• Models were developed for trees on sample tree plots

Alternative sampling applied in the estimation of stand density variables

• Sample 1: RDF and RDFL calculated separately for each sample plot– 10 trees/sample– 116 m2 sample area

model Variant 1

Alternative sampling applied in the estimation of stand density variables

• Sample 2: RDF and RDFL calculated separately for each tally tree plot – 36 trees/sample– 331 m2 sample area

model Variant 2

Alternative sampling applied in the estimation of stand density variables

• Sample 3: RDF and RDFL calculated from pooled data of sample tree plots– 29 trees/sample– 337 m2 sample area

model Variant 3

Alternative sampling applied in the estimation of stand density variables

• Sample 4: RDF and RDFL calculated from pooled data of tally tree plots – 103 trees/sample– 964 m2 sample area

model Variant 4

Model development

• Individual-tree, distance-independent models were developed for– tree basal area growth– tree crown ratio

of Norway spruce trees• Models were developed for trees of sample

tree plots• Four model variants (Variants 1 to 4) were

fitted to data with four alternative values of competition variables obtained from four different sampling (Samples 1 to 4)

Model for tree basal area growth

where d = tree diameter at breast height, cmcr = tree crown ratioTS = temperature sum, dd.RDFL = relative density factor of trees larger than subject treeRDFNs RDFSp, RDFbl = relative density factor of Scots pine, Norway spruce,

and broad-leaved tree speciesHdom = stand dominant height, m

SI = site index of Norway spruce (index age 50 years), m

SC1, SC2, SC4 = categorical variable referring site types

u = random stand effectv = random sample plot effect

e = random effect of a tree

ln(ig)= a0+a1ln(d)+a2d2+a3(ln(d))2 +a4cr+a5cr(TS/1000)

+a6RDFL2 +a7(ln(RDFNs+1)+a8(ln(RDFSp+1)+a9(ln(RDFbl+1)

+a10(1/ln(Hdom)) + a11(1/Hdom2)

+ a12ln(SI) +a13SC1+a13SC1+a14SC2+a15SC4

+ u + v +e

tree dimensions

competition

stage of stand development

site

random parameters

Tree basal area growth model variants

Variant 1 Variant 2 Variant 3 Variant 4 Variable Parameter values Intercept -4.259 -3.411 -5.946 -5.699

ln(d) 0.665 0.720 0.672 0.738 d2 -0.0005 -0.0004 -0.0005 -0.0004

(ln(d)) 2 0.183 0.143 0.175 0.133 cr -0.678 -1.036 -0.696 -0.716

cr .(TS/1000) 1.916 2.101 1.923 1.911 (RDFL)2 -0.441 -0.938 -0.632 -1.095

ln(RDFNs +1) -0.434 -0.809 -0.991 -1.018 ln(RDFSp +1) -0.704 -0.555 -1.041 -0.972 ln(RDFDt +1) -0.444 -0.357 -0.916 -0.425 1/(ln(Hdom )) 6.622 5.718 7.682 6.184

1/Hdom2 -23.107 -20.922 -27.859 -22.904

ln(SI) 0.476 0.453 1.029 1.222 SC1 0.196 0.268 0.270 0.356 SC2 0.144 0.187 0.171 0.179 SC4 -0.029 -0.104 -0.135 -0.123

var(u) 0.09697 0.09380 0.09271 0.08976 var(v) 0.02573 0.02333 0.02163 0.02227 var(e) 0.2076 0.2048 0.2079 0.2055

The effect of relative stand density (RDF) on tree basal area growth of largest tree

in a stand (RDFL=0)

0

10

20

30

40

50

60

70

80

90

100

0 0.2 0.4 0.6 0.8 1RDF

Variant 1

Variant 2

Variant 3

Variant 4

basal area growth, cm²

Model

The effect of relative tree size (RDFL) on tree basal area growth in a stand with

high relative density

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1RDFL

Variant 1

Variant 2

Variant 3

Variant 4

basal area growth, cm²

RDF=1 Model

The effect of relative tree size (RDFL) on tree basal area growth in a stand with

moderate relative density

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1RDFL

Variant 1

Variant 2

Variant 3

Variant 4

basal area growth, cm²

RDF=0.5 Model

Model for tree crown ratio

where d =tree diameter at breast height, cmcr = tree crown ratioTS = temperature sum, dd.RDF = relative stand density factor (incl. all tree species)

Hdom = stand dominant height, m

SI = site index of Norway spruce, m

TH0-5 = categorical variable referring recent thinning (< 5 years ago)

cr = 1-e-f(x),

in which

f(x)=(a1-a11TH0-5).( Hdom)-a2 .da3 .exp(-a4RDF).TSa5 .SIa6

Variants of the model for tree crown ratio

Variant 1 Variant 2 Variant 3 Variant 4 Parameter Value

a1 a2 a3 a4 a5 a6 a11

1.426 0.589 0.269 0.491 -0.195 0.417 0.016

1.413 0.531 0.239 0.698 -0.336 0.454 0.063

0.550 0.564 0.272 0.648 -0.205 0.743 0.021

0.527 0.539 0.254 0.649 -0.237 0.770 0.028

RMSE 0.0999 0.0948 0.0992 0.0980

Predicted, mean

0.753 0.753 0.753 0.753

The effect of relative stand density on the predicted tree crown ratio

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1RDF

Variant 1

Variant 2

Variant 3

Variant 4

crown ratio

Model

Simulation study

1. Model variants were added to Motti-simulator– stand simulator based on individual tree growth models

– stand-level analysis tool for assessing the effects of alternative management practices

2. The development of sample plots of a thinning trial were predicted with the model variants

3. The simulation results were analyzed by – comparing the results of model variants

– comparing the simulation results with measured stand development

in stands with different management schedule

Simulation data

• Repeatedly measured spacing trial for Norway spruce located in southern Finland– independent– subjectively chosen– treatments:

• four thinning intensities: 0,10,25,40 % of stand basal area removed

• three replicates

– plot size 1000 m2

– established in 1961– 37-year observation period (1961- 1988)– 8 measurements

• One unthinned and one repeatedly thinned sample plot were chosen for simulation study

Simulated and observed development of stand basal area in unthinned sample plot of Norway spruce

0

10

20

30

40

50

60

40 45 50 55 60 65 70 75 80stand age, years

Variant 1Variant 2Variant 3Variant 4Observed

stand basal area,

m2ha-1

Model

Predicted and observed yield of stand basal area in unthinned sample plot of

Norway spruce

0

10

20

30

40

50

60

70

Variant 1 Variant 2 Variant 3 Variant 4 Observed

MortalityThinning removalGrowing stock

basal area,

m2ha-1

Simulated and observed development of stand basal area in repeatedly

thinned sample plot of Norway spruce

0

5

10

15

20

25

30

35

40

40 45 50 55 60 65 70 75 80stand age, years

Variant 1Variant 2Variant 3Variant 4Observed

stand basal area,

m2ha-1

Model

Predicted and observed yield of stand basal area in thinned sample plot of

Norway spruce

0

10

20

30

40

50

60

70

Variant 1 Variant 2 Variant 3 Variant 4 Observed

MortalityThining removalGrowing stock

basal area,

m2ha-1

Relative difference between the predicted yields of thinned and

unthinned sample plots

-5

0

5

10

15

Variant 1 Variant 2 Variant 3 Variant 4 Observed

%

Conclusions (1/4)

1) Model parameters

• Competition effect is clearly affected by sample (and plot) size

• Overall stand density:– increase in sample size increased the the effect of

overall stand density

• Competitive status of a tree: – the effect increased with increasing plot size

• sampling area cannot compensate the small plot size: Variants 2 and 4 (large plots) more sensitive to RDFL than Variants 1 and 3 (small plots)

Conclusions (2/4)

2) Simulation results• in unthinned stand:

– notable differences in the predicted total yield between model variants

• highest level of mortality predicted with model variant 1

– largest overprediction of total yield obtained with model variant 1 (based on small plots)

• in thinned stand– no major differences in the predictions between model

variants

– all the models ended up in a slight overprediction

Conclusions (3/4)

2) Simulation results (... continued)

• Differences between the predicted development of different treatment regimes affected by model variant– include biological and statistical effects

– affect the conclusions that are drawn from the comparison of alternative management regimes

• referring growth and yield

• the value of harvestable wood

• the profitability of forest management

Conclusions (4/4)

3) Biological plot size effect

• Has major impact on the description of stand dynamics

• Sample tree plots of this study were too small for reliable description of the effective competition zone

• The impact remains small if spacing and size distribution is controlled by thinnings