N-tree-distance sampling in riparian forests of western Oregon: a simulation study

1. N-tree-distance sampling in riparian forests of western Oregon: a simulation study Z. Haxton, T. Marquardt and H. Temesgen College of Forestry Oregon State University Western Forest Mensurationists’ Meeting Missoula, Montana June 21, 2010

2. Outline • Challenges in sampling riparian areas • N-tree distance sampling overview • Objectives • Methods • Results • Conclusions

3. Riparian area challenges • High within-stand variation. • Alternating conifer-hardwood patches. • Edge effects.

4. USFS crews told to switch prisms to get 7 in-trees every time (Bell 1994). Wensel et al. 1980

5. N-tree-distance sampling

6. N-tree-distance sampling

7. N-tree-distance sampling

8. Advantages • The same number of trees is measured at every sample point, leading to potential gains in field efficiency. • Can be more efficient for estimating density of rare objects (e.g. snags; Kenning et al. 2005).

9. Disadvantages • Requires accurate horizontal distance measurements. • Determining which trees are the nearest n to a sample point is not necessarily a trivial undertaking. • Practical, universally design-unbiased estimators are currently not available.

10. N-tree-distance sampling

11. N-tree-distance sampling

12. N-tree-distance sampling

13. Estimators • Operational forest inventory using n-tree distance sampling is currently being explored in Germany (Nothdurft et al. 2010). • The development and testing of new estimators is currently an area of active research. • Many estimators have been developed in the last 20 years, but not all are necessarily easy to understand and implement.

14. Objectives • Compare the statistical performance of selected n-tree-distance sampling estimators for estimating stem density and basal area of headwater riparian forests of western Oregon. • Compare the statistical performance of the estimators to that of fixed plot sampling and variable plot sampling for estimating density and basal area, respectively.

15. Methods From Cissel et al. (2006)

16. Methods From Cissel et al. (2006)

17. Methods From Marquardt (2010)

18. Methods • Monte Carlo simulation programmed in VBA • Procedure: • Randomly locate four sample points. • See what trees would be captured using fixed plot, variable plot and n-tree distance sampling at each point. • Estimate stem density and basal area with each method. • Repeat 2,000 times! • Values of n from 2 to 10 explored • Variable plot BAF and fixed plot radius were scaled to capture an average of n trees per sample point.

19. Methods where Ŷi = estimated value for a given repetition Yi = known true value Relative bias Relative RMSE

20. Results – density bias

21. Results – basal area bias

22. Results – density RRMSE

23. Results – basal area RRMSE

24. Results – density RRMSE

25. Results – basal area RRMSE

26. Conclusions • Results should be extrapolated with caution. • No statistical advantage to n-tree distance sampling. Density » fixed plots best. Basal area » variable plots best. • Moore estimator had lowest overall bias, Kleinn-Vilcko estimator had a less skewed distribution of estimates. • An n of 6 may be most appropriate for n-tree distance sampling. • There may be an application for these estimators as long as the population is not too clumped.

27. References Bell, J. (1994). Is it true that… maintaining a constant tree count in VP gives better answers? Available online at http://www.proaxis.com/~johnbell/newsindex/isittruethat.htm; last accessed June 8, 2010. Cissel, J., P. Anderson, et al. (2006). BLM Density Management and Riparian Buffer Study: establishment report and study plan, U.S. Geological Survey. Scientific Investigations Report 2006-5087. Kenning, R. S., M. J. Ducey, J. C. Brissette and J. H. Gove. (2005). Field efficiency and bias of snag inventory methods. Canadian Journal of Forest Research 35:2900-2910. Kleinn, C. and F. Vilcko (2006). A new empirical approach for estimation in k-tree sampling. Forest Ecology and Management. 237(1-3):522-533. Lessard, V., D. Reed and N. Monkevich (1994). Comparing n-tree distance sampling with point and plot sampling in northern Michigan forest types. Northern Journal of Applied Forestry 11(1): 12-16. Lynch, T. B. and R. Rusydi (1999). Distance sampling for forest inventory in Indonesian teak plantations. Forest Ecology and Management 113(2-3):215-221. Marquardt, T., H. Temesgen and P. Anderson (2010). Accuracy and suitability of selected sampling methods within conifer dominated riparian zones. Forest Ecology and Management. 260(3):313-320. Moore, P. G. (1954). Spacing in plant populations. Ecology 35(2): 222-227. Nothdurft, A., J. Saborowski, R. Nuske and D. Stoyan (2010). Density estimation based on k-tree sampling and point pattern reconstruction. Canadian Journal of Forest Research 40(5):953-967. Prodan, M. (1968). Punkstichprobe für die Forsteinrichtung (in German). Forst. und Holzwirt 23(11):225-226 (not directly examined by author, citation via Lynch and Rusydi 1999). Wensel, L. C., J. Levitan and K. Barber (1980). Selection of basal area factor in point sampling. J. For. 78(2):83-84. Yamada, I. and P. A. Rogerson (2003). An empirical comparison of edge effect correction methods applied to K-function analysis. Geographical Analysis 35(2): 97-109.

28. The estimators Uncorrected Prodan Moore Kleinn-Vilcko where m = number of sample points n = number of trees at each sample point Ai = plot area of the ith plot in ha = π(ri2)/10,000 ri = radius of the ith plot in m dn = distance to the nth tree dn+1 = distance to the n+1th tree

29. From Yamada et al. (2008)