1. Modeling Tree Growth Under Varying Silvicultural Prescriptions Leah Rathbun University of British Columbia Presented at Western Mensurationists 2010

2. Location Coastal Western Hemlock (CWH) BEC zone Temperatures - 5.2 to 10.5˚ C Second growth uneven- and even-aged multi- species stands regenerated naturally and from plantings. Western hemlock, Douglas-fir, western redcedar, red alder, Sitka spruce and yellow cedar

3. Box-Lucas Model Developed from Von Bertalanffy function Flexible model form

4. Database for Diameter Growth Permanent Sample Plot (PSP) data 1,455 untreated plots 0.008 to 0.806 ha 1932 to 2003 Varying intervals - 1 to 17 years, average of 5.0 years 13 to 11,750 live trees per hectare Site Index values from 6.2 to 52.8 m Average basal area per hectare value of 38.7 m 2 /ha

5. Parameter Prediction Approach Data was subset to obtain estimates for f 1 and f 2 for a species Subset defined from untreated data containing at least 4 measurement periods. Different combinations of predictor variables were used, based upon correlation values Linear, log-linear, and nonlinear equations AIC values were used to select model forms Box-Lucas model was refit using the resultant parameter estimates as starting values.

6. Variable Selection Tree size and stage of development, site productivity, and inter-tree competition were considered: dbh, height, and diameter increment Site index and growth effective age Curtis’ relative density and basal area per hectare Basal area of larger, stems per hectare, relative dbh, crown competition factor of larger

7. Selected Diameter Model Douglas fir: Cedar: Hemlock:

8. Untreated trees Douglas-fir Hemlock Cedar

9. Fertilization Effects 85 plots received fertilization Majority received one application of nitrogen ranging in concentration from 50 to 400 kg/ha A few plots additionally received ammonium phosphate.

10. Fertilization Effects All three parameters were modified individually Each possible combination of the three parameters were modified Akaike’s Information Criteria (AIC) values used to select final model

11. Fertilization Effects For Douglas fir and cedar: And for hemlock:

12. Fertilized Douglas-fir Hemlock Cedar

13. Thinning Effects 419 plots received a thinning event Average basal area cut was 8.2 m 2 /ha Average of 892 trees per hectare was removed Original model was fit using parameter estimates found from untreated data State variables changed immediately following a thin

14. Thinned Douglas-fir Hemlock Cedar

15. Fertilized and Thinned Effects 93 plots received a combination of a thinning followed by fertilization Fertilization was applied within the measurement period following thinning Fertilized model was fit using parameter estimates found from fertilized data State variables changed immediately following a thin

16. Fertilized & Thinned Douglas-fir Hemlock Cedar

17. Database for Height Growth 1,316 untreated plots 0.008 to 0.253 ha 1932 to 1996 Varying intervals - 1 to 30 years, average of 4.8 years 222 to 11,750 live trees per hectare Site Index values from 10.7 to 52.8 m Average basal area per hectare value of 38.1 m 2 /ha

18. Potential Height Model Data selection –Binning by dbh (90 th and 99 th percentiles) –Predicted values approach Box-Lucas model fit using dbh and a transformation of dbh in a linear model for f 1 and f 2 Predict 90 th and 99 th percent confidence interval, upper value Fit Box-Lucas model using dbh and a transformation of dbh in a linear model for f 1 and f 2

19. Potential Height Model Binning approach: - f 1 : dbh 0.5 for Douglas-fir and ln(dbh) for cedar and hemlock - f 2 : dbh 2 for Douglas-fir and cedar and ln(dbh) for hemlock Predicted values approach: - f 1 : dbh 2 for Douglas-fir and ln(dbh) for cedar and hemlock - f 2 : dbh 2 for Douglas-fir and cedar and ln(dbh) for hemlock

20. Potential height Douglas-fir Western hemlock Western redcedar

21. Douglas-fir Cedar Hemlock Average Height Model Growth Potential Dependent

22. Average Height Model Growth Potential Independent Douglas fir: Cedar: Hemlock:

23. Average height Douglas-fir Hemlock Cedar

24. Fertilization Effects 82 plots received fertilization All three parameters were modified individually Each possible combination of the three parameters were modified Akaike’s Information Criteria (AIC) values used to select final model

25. Fertilized Douglas-fir a)Low site quality, low density b)High site quality, low density c)High site quality, high density

26. Fertilized Hemlock a)Low site quality, low density b)Low site quality, high density c)High site quality, low density d)High site quality, high density

27. Thinning Effects 388 plots received a thinning event Average basal area cut was 7.6 m 2 /ha Average of 988 trees per hectare was removed Original model was fit using parameter estimates found from untreated data State variables changed immediately following a thin

28. Thinned Douglas-fir a)Low site quality, low density b)Low site quality, high density c)High site quality, low density d)High site quality, high density

29. Thinned Cedar a)Low site quality, low density b)High site quality, low density c)High site quality, high density

30. Thinned Hemlock a)Low site quality, low density b)High site quality, low density c)High site quality, high density

31. Fertilized and Thinned Effects 92 plots received a combination of a thinning followed by fertilization Fertilization was applied within the measurement period following thinning Fertilized model was fit using parameter estimates found from fertilized data State variables changed immediately following a thin

32. Fertilized & Thinned Douglas-fir a)Low site quality, low density b)Low site quality, high density c)High site quality, low density d)High site quality, high density

33. a)Low site quality, low density b)Low site quality, high density c)High site quality, low density d)High site quality, high density Fertilized & Thinned Hemlock

34. Conclusions Box-Lucas model works well Silvicultural treatments applied to managed stands, not experimentally designed study The adjustments added for fertilization worked well Modification of state variables only modeled the effects of thinning well for Douglas-fir Separate models are recommended for potential and average height

35. Acknowledgements Dr. Valerie Lemay Dr. Nick Smith Dr. Peter Marshall Dr. Lori Daniels Ken Epps and Island Timberlands FVS group at the U.S. Forest Service