1. Impact of plot size on the effect of competition in individual-tree models and their applications Jari Hynynen & Risto Ojansuu Finnish Forest Research Institute, Vantaa, Finland

2. 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

3. 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

4. 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 self-thinning line: RDF=1.0 a stand with RDF=0.8 Competitive status of a tree: RDF of larger than subject tree: RDFL

5. 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

6. 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

7. 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 m 2 sample area model Variant 1

8. 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 m 2 sample area model Variant 2

9. 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 m 2 sample area model Variant 3

10. 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 m 2 sample area model Variant 4

11. 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)

12. Model for tree basal area growth where d= tree diameter at breast height, cm cr= tree crown ratio TS= temperature sum, dd. RDFL= relative density factor of trees larger than subject tree RDF Ns RDF Sp, RDF bl = relative density factor of Scots pine, Norway spruce, and broad-leaved tree species H dom = stand dominant height, m SI= site index of Norway spruce (index age 50 years), m SC 1, SC 2, SC 4 = categorical variable referring site types u = random stand effect v= random sample plot effect e= random effect of a tree ln(ig)= a 0 +a 1 ln(d)+a 2 d 2 +a 3 (ln(d)) 2 +a 4 cr+a 5 cr(TS/1000) +a 6 RDFL 2 + a 7 (ln(RDF Ns +1)+a 8 (ln(RDF Sp +1)+a 9 (ln(RDF bl +1) +a 10 (1/ln(H dom )) + a 11 (1/H dom 2 ) + a 12 ln(SI) +a 13 SC 1 +a 13 SC 1 +a 14 SC 2 +a 15 SC 4 + u + v +e tree dimensions competition stage of stand development site random parameters

13. Tree basal area growth model variants 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

14. The effect of relative stand density (RDF) on tree basal area growth of largest tree in a stand (RDFL=0)

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

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

17. Model for tree crown ratio where d=tree diameter at breast height, cm cr= tree crown ratio TS= temperature sum, dd. RDF= relative stand density factor (incl. all tree species) H dom = stand dominant height, m SI= site index of Norway spruce, m TH 0-5 = categorical variable referring recent thinning (< 5 years ago) cr = 1-e -f(x), in which f(x)=(a 1 -a 11 TH 0-5 ). ( H dom ) -a2. d a3. exp(-a 4 RDF). TS a5. SI a6

18. Variants of the model for tree crown ratio

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

20. 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

21. 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 m 2 –established in 1961 –37-year observation period (1961- 1988) –8 measurements One unthinned and one repeatedly thinned sample plot were chosen for simulation study

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

23. Predicted and observed yield of stand basal area in unthinned sample plot of Norway spruce

24. Simulated and observed development of stand basal area in repeatedly thinned sample plot of Norway spruce

25. Predicted and observed yield of stand basal area in thinned sample plot of Norway spruce

26. Relative difference between the predicted yields of thinned and unthinned sample plots

27. 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)

28. 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

29. 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

30. 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