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Regeneration imputation models for the ICHmw2 subzone in the vicinity of Nelson, BC Hassani, Badre Tameme 2002

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REGENERATION IMPUTATION MODELS FOR THE ICHmw2 SUBZONE IN THE VICINITY OF NELSON, BC. By B A D R E T A M E M E HASSANI B. F., Agricultural Technological Institute (ITA), Mostaganem, Algeria, 1986 M . Sc. Rural Planning in Relation to the Environment, International Center for Advanced Mediterranean Agronomic Studies (CIHEAM), Spain, 1997 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQIREMENT FOR THE DEGREE OF MASTER OF SCIENCE ' In T H E F A C U L T Y OF G R A D U A T E STUDIES F A C U L T Y OF FORESTRY DEPARTMENT OF FOREST RESOURCES M A N A G E M E N T We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June 2002 © Badre Tameme Hassani, 2002 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, 1 agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Ror^b JLsOxHrPM fr|a> The University of British Columbia Vancouver, Canada Date ^W, &Q,£^1) DE-6 (2788) Abstract Forests are dynamic systems, seldom in equilibrium. This is due, in part, to anthropogenic disturbances such as harvesting. Understanding the dynamics of complex stands has become a management priority and is the subject of a number of studies in northwestern North America. Understanding regeneration patterns in these stands is crucial, since future stands are determined by the way the regeneration is managed. The objective of this study was to explore and test the applicability of using imputation techniques rather than more traditional regression techniques for predicting regeneration in the complex mixed-species stands prevalent in the Interior Cedar-Hemlock moist warm subzone variant 2 (ICHmw2) in the vicinity of Nelson, BC. Two approaches were used: tabular imputation and most similar neighbour (MSN) imputation. The regeneration data collected during the 2000 field season and that collected during the 1998 field season are summarized. A series of tabular imputation and M S N imputation approaches are developed and their performances in predicting the regeneration are compared. The tabular approach depicted average regeneration by five site groups, two residual density classes, five time-since-disturbance classes, species, and height classes. The M S N approach made use of regeneration data of some plots (called reference plots) and a complete coverage of selected easy-to measure attributes for the entire data set (called reference and target plots) for its development. M S N imputation provided regeneration for the assumed missing regeneration data (target plots) by choosing a most similar plot from the reference plots to act as its surrogate. The most similar plot selection was based on a similarity measure that took into consideration the multivariate relationships between the two different sets of data. The full MSN imputation model (four height classes) was the best predictor for regeneration. Stand density indicators (basal area, number of residual trees per hectare, and crown competition factor) were the driving variables in the most similar neighbour selection process. When the number of match categories and the root mean square error (RJVISE) were used as comparison criteria, about 97.5% of the target plots were classified as being moderate to good. Perfect matches with high precision corresponded to those plots that had high number of cells with no regeneration (zero). The mismatch of basal area, trees per ha, crown competition factor, and seemingly, the presence/absence of advance regeneration seemed to be a major cause of poor predictions. A sensitivity analysis showed that Prognosis was mostly insensitive to regeneration predictions from both imputation models during the first 50 years of the projection. However, regeneration estimates were generally good. Also, with longer periods of simulation, it is likely that the model would be more sensitive, particularly to tabular predictions. As Prognosis80 grows stands based on the interaction among trees, a user can provide data either by using the selected most similar neighbour plot, or by using the means from the table that has the desired characteristics. As more data become available, these tables ii can be easily updated and the reliability of tables based on small sample size can be improved. There were not a lot of obvious trends apparent in the tabulated data. This may be due to the dominance of advance regeneration among the regeneration present. Advance regeneration would be more affected by the conditions that existed prior to the most recent disturbance than the conditions that exist today. Designing a sampling method that separates advance from subsequent regeneration will, without doubt, improve the results. iii Table of Contents Abstract ii Table of Contents iv List of Tables vi List of Figures xiii Acknowledgements xv 1. Introduction 1 2. Background 4 2.1 Study Sites 4 2.2 Regeneration 5 2.3 Imputation Methods 8 2.3.1 Tabular Imputation 9 2.3.2 Nearest Neighbor Method (NN) 9 2.3.3 Most Similar Neighbor Method (MSN) 9 2.3.4 K-Nearest Neighbor (K-NN) 10 2.3.5 Geostatistical Estimation (GS) 10 3. Methods 12 3.1 Sampling Procedures Used in 1998 12 3.2 Sampling Procedures Used in 2000 12 3.3 Analyses Procedures 14 3.3.1 Data Preparation and Summary 14 3.3.2 Tabular Imputation Models 15 3.3.3 The M S N Method 17 3.3.4 Comparison of the Two Approaches 19 3.3.5 Sensitivity of Prognosis80 to MSN and Tabular Regeneration Predictions.... 19 4. Results 20 4.1 Summary of the Combined 1998 and 2000 Data 20 4.2 Regeneration Composition 21 4.3 Tabular Imputation 25 4.3.1 The Tabular Imputation Model 25 iv 4.3.2 Validation of the Tabular Imputation Model 31 4.3.3 Causes of Poor Regeneration Predictions for the Tabular Procedure 35 4.4 The M S N Models 37 4.4.1 Comparison of MSN Models 38 4.4.2 M S N Type 1 Model 39 4.4.2.1 Variable Validation 39 4.4.2.2 Frequency Selection of Target Plots 40 4.4.2.3 Performance of the MSN Type 1 Model 41 4.4.2.4 Causes of Extreme Regeneration Predictions 44 4.5 Comparison of Approaches 47 4.5 Sensitivity of Prognosis80 to MSN and Tabular Regeneration Predictions 48 5. Discussion 52 6. Conclusions 58 Literature Cited 59 Appendix I - Tabular Imputation Models 64 Appendix II- Validation Tables 79 Appendix III- Simple Correlations Between Auxiliary and Ground Variables for Runs 2 to 5 of MSN Type 1 94 Appendix IV- Canonical Coefficients for Runs 2 to 5 of MSN Type 1 Model 98 Appendix V- Tables of Validation Results For Runs 2 to 5 of MSN Type 1 100 Appendix VI- Scatter Plots of Regeneration Bias Versus Four Auxiliary Variables for MSN Type 1 and its Corresponding Tabular Imputation for Runs 2 to 5 104 Appendix VII- Comparison Between Auxiliary Variables of Outlier Target Plots and Their Most Similar Neighbour for Runs 2 to 5 112 Appendix VIII- Average Values of the Auxiliary Variables of Reference and Target Plot Outliers for Runs 2 to 5 114 List of Tables Table 1. Local and scientific names, and species codes for trees found in ICHmw2 4 Table 2. Ground inventory and plot information attributes used in the M S N analyses.... 18 Table 3. Number of plots in the combined 1998 and 2000 data set summarized by variable class 20 Table 4. Average regeneration per ha by species groups and by site preparation treatments 23 Table 5. Regeneration per ha by basal area, aspect, and slope classes 24 Table 6. Average regeneration per ha by time-since-disturbance class interval and site class for basal area class "Dense" (* indicates no plots) 25 Table 7. Average regeneration per ha by time-since-disturbance class interval and site class for basal area class "Open" (* indicates no plots) 25 Table 8. Average regeneration per ha by species and time-since-disturbance class for basal area category "Dense" and "Dry" sites 26 Table 9. Average regeneration per ha by species and time-since-disturbance class for basal area category "Open" and "Dry" sites 26 Table 10. Average regeneration per ha by species and time-since-disturbance class for basal area category "Dense" and "Slightly Dry" sites 27 Table 11. Average regeneration per ha by species and time-since-disturbance for basal area category "Open" and "Slightly Dry" sites 27 Table 12. Average regeneration per ha by species and time-since-disturbance class for basal area category "Dense" and "Mesic" site series 28 Table 13. Average regeneration per ha by species and time-since-disturbance class for basal area category "Open" and "Mesic" sites 28 Table 14. Average regeneration per ha by species and time-since-disturbance class for basal area category "Dense" and "Slightly Wet" sites 28 Table 15. Average regeneration per ha by species and time-since-disturbance class for basal area category "Open" and "Slightly Wet" sites 29 Table 16. Average regeneration per ha by species and time-since-disturbance class for basal area class "Dense" and " Wet" sites (* indicates no plots) 29 Table 17. Average regeneration per ha by species and time-since-disturbance class for basal area class "Open" and "Wet" sites (* indicates no plots) 29 Table 18. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Dry" sites 30 Table 19. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and "Dry" sites 31 Table 20. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Dry" sites 31 Table 21. Standard error of the mean regeneration per ha by height class, species for time-since-disturbance class 1, basal area class "Open" and "Dry" sites 32 Table 22. Regeneration per ha (SPH) with corresponding standard deviations (STD) and coefficients of variations (CV) for dense stands (* indicates no plots) 33 Table 23. Regeneration per ha (SPH) with corresponding standard deviations (STD) and coefficients of variations (CV) for open stands (* indicates no plots) 34 VI Table 24. Results of the comparison between true and tabular imputed regeneration per ha for the target plots using a combination of RMSE and match category for each of the five runs separately, and averaged over the five runs 35 Table 25. Results of the comparison between true and tabular imputed regeneration per ha for the target plots using a combination of the ratio of RMSE to the actual regeneration and plot match category 36 Table 26. Simple correlations between the auxiliary and ground variables used in M S N analysis of Run 1 (n = 265) 38 Table 27. Canonical coefficients weighted by canonical correlation for the 18 auxiliary variables for Run 1. (Bold numbers indicates relatively high coefficients) 39 Table 28. Bias, mean absolute deviation (MAD), and RMSE values for the three types of MSN for each of five runs and averaged over the five runs 39 Table 29. Average observed versus average predicted regeneration per ha for the 265 reference plots of Run 1 40 Table 30. Results of a comparison between true and most similar neighbour data for the target plots using a combination of RMSE and match category 41 Table 31. Classification results of the comparison between true and most similar neighbour data for the target plots using the combination of ratio of RMSE to the actual regeneration and plot match category 42 Table 32. Comparison between the auxiliary variables of the outlier target plots and most similar neighbour plots for Run 1 44 Table 33. Average values of the auxiliary variables of the reference and target (outliers) plots of Run 1 46 Table 34. Comparison between auxiliary variables values of the plots that had "poor match and high RMSE" with those of their selected most similar neighbour plots (shaded rows represent the selected most similar neighbour plots) 46 Table 35. Bias, mean absolute deviation (MAD), and RMSE values of Type 1 MSN and the corresponding tabular approach for each run and averaged over the five runs.. 47 Table 36. Bias, mean absolute deviation (MAD), and RMSE values for Type 2 MSN and the corresponding tabular approach for each run and averaged over the five runs.. 47 Table 37. Bias, mean absolute deviation (MAD), and RMSE values of Type 3 MSN and the corresponding tabular approach for each run and averaged over the five runs.. 48 Table 38. Summary of sensitivity analysis for the M S N Model 49 Table 39. Summary of sensitivity analysis for the Tabular Model 50 Table 1.1. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Slightly Dry" sites 64 Table 1.2. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and "Slightly Dry" sites 64 Table 1.3. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Mesic" sites 64 Table 1.4. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and "Mesic" sites 65 Table 1.5. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Slightly Wet" sites 65 Table 1.6. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and "Slightly Wet" sites 65 vii Table 1.7. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Dry" sites 66 Table 1.8. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Dry" sites 66 Table 1.9. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Slightly Dry" sites 66 Table 1.10. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Slightly Dry" sites 67 Table 1.11. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Mesic" sites 67 Table 1.12. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Mesic" sites 67 Table 1.13. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Slightly Wet" sites 68 Table 1.14. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Slightly Wet" sites 68 Table 1.15. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Wet" sites 68 Table 1.16. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Wet" sites 69 Table 1.17. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Dry" sites 69 Table 1.18. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Dry" sites 69 Table 1.19. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Slightly Dry" sites 70 Table 1.20. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Slightly Dry" sites 70 Table 1.21. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Mesic" sites 70 Table 1.22. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Mesic" sites 71 Table 1.23. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Slightly Wet" sites 71 Table 1.24. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Slightly Wet" sites 71 Table 1.25. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Wet" sites 72 Table 1.26. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Dry" sites 72 Table 1.27. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Dry" sites 72 Table 1.28. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Slightly Dry" sites 73 Table 1.29. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Slightly Dry" sites 73 V l l l Table 1.30. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Mesic" sites 73 Table 1.31. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Mesic" sites 74 Table 1.32. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Slightly Wet" sites 74 Table 1.33. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Slightly Wet" sites 74 Table 1.34. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Wet" sites 75 Table 1.35. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Wet" sites 75 Table 1.36. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Dry" sites 75 Table 1.37. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Dry" sites 76 Table 1.38. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Slightly Dry" sites 76 Table 1.39. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Slightly Dry" sites 76 Table 1.40. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Mesic" sites 77 Table 1.41. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Mesic" sites 77 Table 1.42. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Slightly Wet" sites 77 Table 1.43. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Slightly Wet" sites 78 Table 1.44. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Wet" sites 78 Table 1.45. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Wet" sites 78 Table ILL Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Slightly Dry" sites.. 79 Table II.2. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and "Slightly Dry" sites... 79 Table II.3. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Mesic" sites 79 Table II.4. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and "Mesic" sites 80 Table II. 5. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Slightly Wet" sites. 80 Table 11.6. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and "Slightly Wet" sites... 80 Table II.7. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Dry" sites 81 ix Table II. 8. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Dry" sites 81 Table II.9. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Slightly Dry" sites.. 81 Table 11.10. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Slightly Dry" sites. 82 Table II. 11. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Mesic" sites 82 Table 11.12. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Mesic" sites 82 Table 11.13. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Slightly Wet" sites. 83 Table 11.14. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Slightly Wet" sites. 83 Table 11.15. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Wet" sites 83 Table 11.16. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Wet" sites 84 Table 11.17. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Dry" sites 84 Table 11.18. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Dry" sites 84 Table 11.19. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Slightly Dry" sites. 85 Table 11.20. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Slightly Dry" sites. 85 Table 11.21. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Mesic" sites 85 Table 11.22. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Mesic" sites 86 Table 11.23. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Slightly Wet" sites. ...86 Table 11.24. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Slightly Wet" sites. 86 Table 11.25. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Wet" sites 87 Table 11.26. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Dry" sites 87 Table 11.27. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Dry" sites 87 Table 11.28. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Slightly Dry" sites. 88 Table 11.29. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Slightly Dry" sites. 88 Table 11.30. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Mesic" sites 88 Table 11.31. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Mesic" sites 89 Table 11.32. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Slightly Wet" sites. 89 Table 11.33. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Slightly Wet" sites. : : 89 Table 11.34. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Wet" sites 90 Table 11.35. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Wet" sites 90 Table 11.36. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Dry" sites 90 Table 11.37. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Dry" sites 91 Table 11.38. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Slightly Dry" sites. 91 Table 11.39. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Slightly Dry" sites. 91 Table 11.40. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Mesic" sites 92 Table 11.41. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Mesic" sites 92 Table 11.42. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Slightly Wet" sites. 92 Table 11.43. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Slightly Wet" sites. 93 Table 11.44. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Wet" sites 93 Table 11.45. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Wet" sites 93 xi Table III. 1. Simple correlations between the auxiliary and ground variables used in M S N analysis of Run 2 (n = 268) 94 Table III.2. Simple correlations between the auxiliary and ground variables used in M S N analysis of the Run 3 (n = 268) 95 Table 111.3. Simple correlations between the auxiliary and ground variables used in MSN analysis of Run 4 (n = 269) 96 Table III.4. Simple correlations between the auxiliary and ground variables used in MSN analysis of Run 5 (n = 262) 97 Table IV. 1. Canonical coefficients weighted by canonical correlation for the 18 auxiliary variables for Run 2. (Bold numbers indicates relatively high coefficients) 98 Table IV.2. Canonical coefficients weighted by canonical correlation for the 18 auxiliary variables for Run 3. (Bold numbers indicates relatively high coefficients) 98 Table IV.3. Canonical coefficients weighted by canonical correlation for the 18 auxiliary variables for Run 4. (Bold numbers indicates relatively high coefficients) 99 Table IV.4. Canonical coefficients weighted by canonical correlation for the 18 auxiliary variables for Run 5. (Bold numbers indicates relatively high coefficients) 99 Table V . l . Results of MSN validation of 16 ground and three selected auxiliary variables using reference observations (268 plots) of Run 2. RESID= Observed-Predicted. 100 Table V.2. Results of MSN validation of 16 ground and three selected auxiliary variables using reference observations (268 plots) of Run 3. RESID= Observed 101 Table V.3. Results of M S N validation of 16 ground and three selected auxiliary variables using reference observations (269 plots) of Run 4. RESID= Observed-Predicted 102 Table V.4. Results of MSN validation of 16 ground and three selected auxiliary variables using reference observations (262 plots) of Run 5. RESID= Observed-Predicted. 103 Table VII.l. Comparison between the auxiliary variables for the target plot outliers and most similar neighbour plots for MSN Run 2 (shaded rows represent the M S N plots) 112 Table VII.2. Comparison between the auxiliary variables of the target plot outliers and most similar neighbour plots for MSN Run 3 (shaded rows represent the MSN plots) 112 Table VII.3. Comparison between the auxiliary variables of the target plot outliers and most similar neighbour plots for MSN Run 4 (shaded rows represent the M S N plots) 113 Table VII.4. Comparison between the auxiliary variables of the target plot outliers and most similar neighbour plots for MSN Run 5 (shaded rows represent the M S N plots) 113 Table VIII. 1. Average values of the auxiliary variables of the reference and outlier target plots for M S N Run 2 114 Table VIII.2. Average values of the auxiliary variables of the reference and outlier target plots for MSN Run 3 114 Table VIII.3. Average values of the auxiliary variables of the reference and outlier target plots for M S N Run 4 115 Table VIII.4. Average values of the auxiliary variables of the reference and outlier target plots for M S N Run 5 115 X l l List of Figures Figure 1. Plot layout for sampling regeneration, small and large trees 14 Figure 2. Diameter distribution for all species combined 21 Figure 3. Average regeneration per ha by: a) site preparation, b) aspect, c) time-since-disturbance classes, and d) time-since-disturbance for species groups 22 Figure 4. Average regeneration per ha by years since disturbance and species groups for dense and open stands (dense stands: B A h a > 5m2; open stands <=5m2) 23 Figure 5. Scatter plot of the regeneration bias versus residual basal area of large trees, residual number of trees (TPH), crown competition factor (CCF), and aspect for 68 target plots in Run 1 of the Tabular model. Bias is observed minus predicted regeneration averaged over all plots 37 Figure 6. Observed and estimated regeneration of three plots illustrating three different criteria combinations. The black bar is the true regeneration of the target plot, and the white bar is the regeneration of the selected reference plot by M S N as the most similar neighbour (T: shade tolerant species, S: shade semi-tolerant species, I: shade intolerant species, and H: hardwood species. Numbers 1 to 4 refers to height classes) 43 Figure 7. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 68 target plots in Run 1 of the MSN model. Bias is observed minus predicted regeneration 45 Figure VI. 1. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 65 target plots in Run 2 of the MSN model. Bias is observed minus predicted regeneration 104 Figure VI.2. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 65 target plots in Run 3 of the MSN model. Bias is observed minus predicted regeneration 105 Figure VI.3. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 64 target plots in Run 4 of the MSN model. Bias is observed minus predicted regeneration 106 Figure VI.4. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 71 target plots in Run 5 of the MSN model. Bias is observed minus predicted regeneration 107 Figure VI.5. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 65 target plots in Run 2 of the tabular imputation model. Bias is observed minus predicted regeneration 108 Figure VI.6. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and X l l l aspect for 65 target plots in Run 3 of the tabular imputation model. Bias is observed minus predicted regeneration 109 Figure VI.7. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 64 target plots in Run 4 of the tabular imputation model. Bias is observed minus predicted regeneration 110 Figure VI. 8. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 64 target plots in Run 5 of the tabular imputation model. Bias is observed minus predicted regeneration I l l XIV Acknowledgements Funding for this project was provided by the Resource Inventory Branch, Research Branch, and Forest Practices Branch of the BC Ministry of Forests via FRBC funding. I gratefully acknowledge the support provided by Abdel-Azim Zumrawi, Research Branch; Barry Snowden, Forest Practices Branch; Ivan Istar and Richard E. Logan, Nelson Forest Region; Jim Annunziello, Kootenay Lake Forest District; Tom Johnston and Sandi Best, Arrow Forest District. I owe a special appreciation and would like to express many thanks to my supervisor, Dr. Peter Marshall, for his incredible support, guidance, and encouragement over the years. I am also grateful to my committee members, Dr. Valerie LeMay, Dr. Abdel-Azim Zumrawi, and Dr. Hailemariam Temesgen for their unlimited support and feedback, and for making my work enjoyable. My thanks are also to my friend and co-field crew member, Cornel Lencar, for his patience and guidance in the field. Finally, I would like to say to my family and friends: thank you very much for your support and encouragement. B T H June 2002 XV 1. Introduction Forests are dynamic systems and are seldom in equilibrium (Mitchell 1980). This is due to natural disturbances, anthropogenic disturbances, or a combination of these disturbance types. Current stand structure and species composition are the direct result of such disturbances and continue to be strongly influenced by them (McClure and Lee 1993). Changes in societies and their associated rural policies have always been a major factor that altered the pattern of disturbances (Oliver and Larson 1996). More is known about simple cohort stands than multi-cohort complex stands, probably because they are simple, have been considered as part of "secondary succession", and are usually managed by foresters (Oliver and Larson 1996). Traditional forest management practices, particularly clear-cutting, intensive site preparation and establishment of even-aged stands, are criticized of being unsustainable, compromising biodiversity and long-term productivity of worldwide forests (Lundqvist and Fridman 1996) and of Pacific Northwest forests in particular (Barg and Edmonds 1999; Greene 2000, Hof and Bevers 2000). Pacific Northwest forests are among the most complicated mixture of tree species on earth (Smith et al. 1996). Understanding the dynamics of these complex stands has recently become a priority and is the subject of a number of studies. Reasons for this include: they provide high aesthetic quality and wildlife habitat, they protect community watersheds, and they have a greater biological and structural diversity than most other temperate forests. In comparison with single-species stands, complex stands can provide a stable response to pest attacks, diseases and climate changes, and they can enhance long-term productivity (Cameron et al. 1997). Complex stands are created by minor disturbances and occur as mosaics of small single-cohorts, regularly distributed throughout the stand (Oliver and Larson 1996). Partial cutting is replacing clearcutting. Partial cutting is assumed to mimic small-scale natural disturbances and has created many multi-cohort stands in western conifer forests. Most successful silvicultural activities in these forests are conducted where site factors are restrictive enough that species composition can be kept under control (Smith et al. 1996) or focused towards only the most valuable commercial species, which tend to be relatively shade intolerant conifers. Forest management often involves a series of actions that change the course of secondary succession, and consequently affects future ecosystem development. Manipulation of regeneration constitutes a critical action for managers striving to predict and control secondary succession after harvesting. Regeneration in complex stands is extremely dynamic (Oliver and Larson 1996, Smith et al. 1996, Ek et al. 1997); however, the future stand is determined by the way the regeneration is managed. Smith and others (1996) stressed the importance of regeneration by the following statement: "physicians can bury their worst mistakes, but those of foresters can occupy the landscape in public view for 1 decades". By mistakes, they often refer to failures of silvicultural treatments applied during stand establishment. The proportion of forest stands managed as uneven-aged is low and poses a major problem and challenge for modelling the development of these stands (Mielikainen 1996). Natural regeneration is considered as the best indicator of the sustainability of uneven-aged forests (Guldin and Baker 1998). Complex stands have complex structures and species composition and rarely have uniform regeneration patterns (Oliver and Larson 1996). An understanding of regeneration patterns in complex stands is lacking, in part, because of the emphasis in recent decades on pure single-species stands (Oliver and Larson 1996, Smith et al. 1996). Mixed species stands can be more productive than pure stands (Smith et al. 1996). Slow rates of natural regeneration following clearcut harvesting combined with legislated reforestation deadlines have steered silvicultural practices in BC towards plantations over natural regeneration (Eastham and M l 1999). However, even in planted areas, natural regeneration contributes to overall stocking, enhance species diversity, and improves the spatial structure of the stands. Current changes in harvest practices stress the use of natural regeneration opportunities in restocking harvest areas. In temperate forests, the time scales involved in forest dynamics greatly exceed human life spans. Modelling is a means to overcome this problem. Several models have been developed to predict the course of secondary succession following different silvicultural treatments or natural disturbances in complex stands; however, few of them have been dedicated to predicting the consequences of timber harvest on the establishment of regeneration. Ek and others (1997) speculated that imprecision in estimating post-harvest conditions has prevented the widespread development of regeneration models. Boisvenue (1999) calibrated the regeneration establishment component of the Prognosis80 model1 for Interior Cedar Hemlock moist warm zone variant 2 (ICHmw2) stands following partial cutting. Her results were not satisfactory; accurate prediction of regeneration proved difficult for a range of situations. Model calibration and testing suffered from a shortage of data. Shortage of data has often been a constraint in forest modelling (e.g., Favrichon 1998, Guldin and Lorimer 1985). The high cost and time required to collect detailed data limit the size of sample that is feasible. Imputation techniques have shown several advantages over classical estimation methods in different studies (e.g., Moeur et al. 1995, Moeur and Stage 1995, Ek et al. 1997, Haara et al. 1997, Van Deusen 1997, Maltamo and Kangas 1998, Moeur and Hershey 1998, Moeur 2000, Temesgen and LeMay 2000b). It is hoped that this approach will make better use of limited data to predict regeneration. 1 Prognosis30 is a growth and yield model for simple and complex forest stands. It is an adaptation of the U.S. Forest Service model now called Forest Vegetation Simulator (FVS) developed in North Idaho in the early 1970s as Prognosis (Stage 1973). 2 The purpose of this study is to test imputation techniques for predicting regeneration in the complex mixed-species stands prevalent in the moist warm variant of the Interior Cedar-hemlock zone (ICHmw2) subzone variant in the vicinity of Nelson, BC. Data collected by Boisvenue (1999) were used, augmented by additional data collected in the 2000 field season. Boisvenue's data were collected primarily from partially cut stands, with a wide-range of retention levels. The 2000 data were collected from "open" stands (i.e., <20 % crown closure), since these conditions were not well represented in her data. The specific objectives of this research were to: (i) explore the applicability of using imputation techniques to predict regeneration and (ii) present the results of the selected models. The remainder of this thesis is divided into five chapters. Chapter 2 provides some background on the study area and details of some forestry applications of imputation techniques. Chapter 3 describes the methods used to collect the 1998 and 2000 field data, and the analytical methods employed. Chapter 4 summarizes the data collected and presents results from the tabular imputation and most similar neighbour techniques. Chapter 5 contains a discussion of the results obtained in this study. Chapter 6 provides recommendations for additional studies and conclusions. 3 2. Background 2.1 Study Sites Study sites are located in the Columbia-Shuswap moist warm variant of the Interior Cedar-hemlock zone (ICHmw2). The Interior Cedar-Hemlock (ICH) biogeoclimatic (BEC) zone is the largest and the most productive zone in the interior of BC (Meidinger and Pojar 1991, Delong 1997). It is also one of the largest biogeoclimatic zones in the Nelson Forest Region, where it is found at lower to middle elevations (Braumandl and Curran 1992, Cameron 1997). The zone extends south into eastern Washington, Idaho, and western Montana (Ketcheson et al. 1991). The zone occurs at elevations ranging from 500 to 1450 m in the northern part of its range, and from 1200 to 1450 m in the southern part. These forests have an interior continental climate, characterized by cool wet winters and warm dry summers. The zone is one of the wettest in the interior of BC (Ketcheson et al. 1991). Morainal soils, with loamy or silty surface textures, occur throughout the ICH. The ICHmw2 is composed of complex (mixed-species, multi-cohort) stands, where western hemlock (Tsuga heterophylla (Raf.) Sarg.) and western redcedar (Thuja plicata Donn) constitute the climax trees species. Other trees species present are given in Table 1 (Ketcheson et al. 1991, Braumandl and Curran 1992). It supports 14 commercial tree species. Along with this complex mixture of tree species, ICHmw2 often includes substantial and diverse shrubs, herbs, mosses and lichens. Table 1. Local and scientific names, and species codes for trees found in ICHmw2. Local Name Scientific Name Code1 black cottonwood Populus trichocarpa Torr. & Gray Act Douglas-fir Pseudotsuga menziesii var. glauca (Beissn.) Franco Fd grand fir Abies grandis (Doug.) Lindl. Bg hybrid spruce Picea engelmannii Parry x glauca (Moench) Voss Sx lodgepole pine Pinus contorta Dougl. Var. latifolia PI paper birch Betula papyrifera Marsh. Ep subalpine fir Abies lasiocarpa (Hook.) Nutt. Bl trembling aspen Populus tremuloides Michx. At water birch Betula occidentalis Ew willow Salix sp. W western hemlock Tsuga heterophylla (Raf.) Sarg. Hw western larch Larix occidentalis Nutt. Lw western redcedar Thuja plicata Donn Cw western white pine Pinus monticola Dougl. Pw western yew Taxus brevifolia Tw Decades-old policies of excluding hardwoods from management plans and considering them as weed species has led to less diverse stands (Oliver and Larson 1996). However 1 Tree species codes follow the British Columbia Ministry of Forests, Inventory Branch Standards. 4 today, hardwood species are considered in the management and modelling of mixed stands. Stand composition is not only important because of its role as seed source, but it also affects the characteristics of seedbeds. In boreal forests, it was demonstrated that hardwood leaf litter restricts regeneration more than conifer needle or mass seedbeds (Kneeshaw and Bergeron 1999). Although some trees reproduce effectively by vegetative propagation, all the commercial tree species of BC reproduce by seed (Lavender et al. 1990). Uneven-aged management has been used interchangeably with all-aged, or all-sized management, where all age or size classes from regeneration to the maximum size of tree are represented. Most mixed-species stands are the result of natural regeneration (Burkhart and Tham 1992), and the ICHmw2 stands are no exception (Lavender et al. 1990). The complex stands resulted from sporadic forest disturbances in the past. Fire, and other natural disturbances such as windthrow, insects, disease, slides, and avalanches constitute the most common natural disturbance agents (Anonymous 1998, Boisvenue 1999). Also, an increase in human-induced disturbance through the use of partial cutting in recent years has made multi-cohort mixed stands more common (Smith et al. 1996), although partial cutting has been used in the East Kootenays for over a century (Przeczek, 2001). The increase in partial cutting in BC was mainly due to the implementation of the Forest Practices Codes of BC Act in 1995, that legislated the management of a range of non-timber values (Sacenieks and Thompson 2000) such as watershed management, biodiversity and habitat management, timber production, and visual quality. Pest outbreaks are increasingly apparent in ICH. The main pests are: laminated root rot (Phellinus weirii), armillaria root rot (Armillaria ostoyae), white pine blister rust (Cronartium ribicola), spruce beetle (Dendroctonus rufipennis), dwarf mistletoe (Aceuthobium americanum), dwarf larch mistletoe (Arceuthobium laricis), spruce leader weevil (Pissodes terminalis), hemlock sawfly (Neodiprion tsugae), and Douglas-fir beetle (Dendroctonuspseudotsugae) (Boisvenue 1999). Multi-cohort stands possess a wide range of structures and histories and their development is not random (Oliver and Larson 1996) and is predictable. They can occur as mosaics of small single-cohort stands, have a variety of diameter distribution patterns, including reverse J shape, and some of their small trees can be older than large trees. Multi-cohort stands formed by mosaics of small single cohorts generally develop after many small disturbances (Oliver and Larson 1996). Most mixed species stands develop vertical stratification by species as a consequence of species competition and developmental pattern (Smith et al. 1996). 2.2 Regeneration Regeneration constitutes the crucial stage of forest stand dynamics. Success is determined by many factors, particularly shade tolerance, regeneration mechanism and requirements, and competitiveness on a particular growing site (McClure and Lee 1993, Oliver and Larson 1996, Miller and Kochenderfer 1998). According to Greene (2000), harvested stands can be regenerated naturally by: (1) advance regeneration that was established before harvesting, (2) asexual basal sprouts or root suckers, and (3) post-5 harvest sexual recruitment. Because regeneration mechanisms and reproductive potential provide different competitive advantages following disturbances, knowledge of species regeneration mechanisms is necessary to efficiently regenerate and manage complex stands (Oliver and Larson 1996). Although all tree species can regenerate sexually from seed, some rely heavily on asexual reproduction for their survival and growth (Smith et al. 1996). Asexual reproduction includes sprouting, layering, and suckering. A pre-established root system and food reserves provide vegetatively reproducing tree species with advantages over species that reproduce from seed; the former species start growing immediately after disturbance, whereas the latter may take many years to establish (Oliver and Larson 1996). Natural regeneration from seed is spatially sensitive and requires proximity to a seed source for its success (Hof and Bevers 2000). Along with seed source, suitable microsites and a minimal competition from other vegetation are the most common limiting factors (Delong et al. 1997, Lavender et al. 1990, Densmore et al. 1999, Shearer and Schmidt 1999, Stewart et al, 2001). In the absence of any restriction, seed production was found to be directly proportional to individual tree basal area and inversely proportional to seed mass (basal area was a good predictor in a sexual recruitment model) (Greene 2000). Generally, disturbances do not occur at random; their types and frequencies shape the structure of forest communities (Oliver and Larson 1996). Disturbances that eliminate individuals or groups of trees create gaps in the forest canopy and trigger changes in stand environmental conditions, such as amount of radiation and soil moisture and nutrients levels (McClure and Lee 1993). The size of artificially created gaps was found to influence species composition and abundance in boreal forests (McClure and Lee 1993). In temperate forests, shade-intolerant species are associated with large gaps, whereas small gaps contained more shade-tolerant species (Oliver and Larson 1996). At a fine-scale, regeneration is more influenced by site factors; particularly the slope, aspect, site series, topographic slope position, and elevation (Ferguson et al. 1986, Ferguson and Carlson 1993, DeLong 1996). Tree regeneration patterns in BC's southern coast old-growth forests are influenced by elevation (Brett 1997), whereas percent slope is a significant factor in seedling establishment in southern Appalachian forests (Clinton et al. 1994). Northern aspects can have an important effect on the regeneration recruitment of subsequent regeneration and on release of advance regeneration in Nelson region (Delong 1996). The mosaic of these microsites shapes the site regeneration pattern (Brett 1997). Not surprisingly, regeneration species composition is influenced by pre harvest stand composition (Przeczek 2001). Regeneration can also be regulated by seedbed. Physical characteristics such as soil type and forest floor, can be modified by various treatments (e.g., mechanical scarification, prescribed burning, brushing). Logging operations were found to have increased mineral soil exposure and enhanced the prevalence of fine wood debris on the ground (Burton et al. 2000). Many studies have shown that regeneration is sensitive to seedbed type and that rotten wood and mineral soils support the highest germination (Burton et al. 2000). Advance regeneration is not tightly regulated by these site treatments, but often they are 6 not protected from their effect. Advance regeneration is subject to harvest injuries resulting in increased mortality (Tesch et al. 1993). McCaughey and Ferguson (1988) demonstrated that advance regeneration was the highest on non-treated plots followed by the mechanically scarified and burned plots. In their study, Sacenieks and Thompson (2000) found more than 85% of the germination occurred on mineral soil. Regeneration of severely disturbed stands (clearcuts) depends on the dormant soil seed bank or on seed coming from adjacent stands. Seed-tree, shelterwood, and coppice methods reflect decreasing disturbance and the regeneration depends mainly on established advance reproduction. Site preparation treatments can reflect the disturbance types and therefore can be crucial in the establishment and the development of the regeneration. Appropriate site preparation that exposes mineral soil is argued to exert a positive effect on natural regeneration abundance, and the site requires less basal area to secure acceptable regeneration (DeLong 1994). However, disturbance of the forest floor usually destroys advance regeneration. Seedbeds on low brush sites can regenerate longer (DeLong 1994). On more brushy sites, advance regeneration can be considered as a means of efficiently occupying the sites. On severe moisture deficit sites, the shelterwood system was reported to be a requirement for successful regeneration (DeLong 1994). Residual shelter can prevent frost from damaging regeneration, particularly on flat sites. Regeneration mechanisms allow different species to survive after different disturbances (Oliver and Larson 1996). Complex stands rarely have a uniform regeneration pattern; the regeneration period may extend through the entire rotation and can take place by various means. Many unmanaged forests in western North America are two- or multi-storied stands with the lower story comprised of advance regeneration (Helms and Standiford 1985). Advance regeneration is related to the shade tolerance of the tree species, and to habitat type (Fergusson and Carlson 1993). Recently, promotion of advance regeneration management is gaining strong support and is being considered as a viable reforestation alternative in sites with a reasonable chance of success (Ferguson and Adams 1980, Korpela and Tesch 1992, Kneeshaw and Bergeron 1996). Such management can effectively reduce silvicultural costs, while ensuring permanent site occupancy (Przeczek 2001). In the ICH zone, advance regeneration was found to have good potential for forest renewal (DeLong 1997, Deverney and DeLong 1999). Management of advance regeneration in the ICHmw2 can allow the development of naturally adapted trees, substantially lower costs by eliminating or reducing site preparation and planting, and reduce from brush colonization (DeLong 1997, Deverney and DeLong 1999). However, advance regeneration can be damaged considerably during harvesting operations (Haveraaen et al. 1997). If advance regeneration is protected, the rotation can be substantially reduced and the costs associated with site preparation and planting are not needed (Ferguson and Adams 1980). The complexity of the ICHmw2 stands arises mainly from differences in silvical characteristics (silvics), germination requirements, and recruitment strategies among tree species. Knowledge of these factors is essential to predicting regeneration establishment. Recruitment strategies are closely associated with the shade tolerance of species. The 7 ICHmw2 presents a full spectrum of species tolerance ranging from very shade intolerant to very highly shade tolerant species. Western redcedar, western hemlock, subalpine fir, and western yew are highly shade tolerant species. With the exception of western cedar that requires disturbed mineral soil for its regeneration, the other species grow and germinate on a variety of seedbeds, provided the moisture is not a limiting factor (Burns and Honkala 1990, Peterson et al. 1998). Western recedar and western hemlock are co-climax in ICHmw2 and, depending on the type of disturbance, both species reproduce sexually and asexually. Although vegetative reproduction is prevalent on undisturbed and partially disturbed areas, they can also regenerate on open forest floor where their seedlings are often subject to brush competition (Peterson et al. 1998). For most of the highly shade tolerant species, large seed crops occur every three to four years (Burns and Honkala 1990, Peterson et al. 1998). Grand fir and spruce are shade tolerant species. Their seeds germinate on all seedbeds and both have good seed crops every two to five years. Douglas-fir and western white pine are intermediate shade tolerant species. They develop on soils that originated from a considerable array of parent materials (Burns and Honkala 1990. White pine requires mineral soil to enhance seed germination and seedling survival. Good seed crops of Douglas-fir occur two to ten years, whereas a prolific seed years for white pine occur every three to seven years. Shade tolerant and semi-tolerant species are commonly found as advance regeneration in complex stands (McCaughey and Ferguson 1988). Lodgepole pine, western larch, paper birch, black cottonwood, western willow, and trembling aspen are highly shade intolerant and all grow on a wide variety of soils. Paper birch, black cottonwood, and trembling aspen can regenerate from sprouts and stumps, or root suckers following logging or fire (Burns and Honkala 1990, DeLong et al. 1997). Good seed crops occur every three to four years for lodgepole pine and aspen, are highly variable over a one to ten year range for western larch, and are usually produced every year for birch, willow and black cottonwood (Burns and Honkala 1990). Regeneration establishment modelling has been based on controlled experiments and case history methods in the past (Ferguson et al. 1986). The modelling followed different approaches: tabular methods (Staebler 1949, Ek et al. 1997), succession models (Botkin et al. 1972, Shugart et al. 1973, Kimmins 1993), and matrix models (Favrichon 1998). The presence of advance regeneration can be a challenge to predicting regeneration by obscuring and confusing the patterns (Smith et al. 1996). Even when disentangling post-disturbance regeneration from advance regeneration was possible, the regeneration model explained only about 50% of the variation in boreal forests (Greene 2000). Advance regeneration development models had low predictive capabilities, and the high variation left unexplained by such models limited their operational use in boreal forests (Kneeshaw and Bergeron 1996). 2.3 Imputation Methods Imputation involves replacing missing (i.e., not sampled) measurements for any unit in the population with measurements from another unit with similar characteristics (Rubin 1987, Ek et al. 1997, Van Deusen 1997). In forestry, imputation techniques have been used for forest inventory (Moeur and Stage 1995), modelling (Rubin 1987), regeneration 8 prediction (Ek et al. 1997), and is being explored for use in growth and yield modelling (Temesgen and LeMay 2000b). Unlike the information provided by classic sampling and estimation techniques, such as stratified sampling or regression, imputation methods: 1) provide a mixture of spatial and temporal information on regeneration attributes considered important in combination. This allows complex relationships to be maintained. Ek et al (1997) attributed this to the similarity between the variance-covariance matrix of the population and the samples. 2) are often not vulnerable to violation of a random sampling assumptions. This advantage is important since it allows the use of any form of data. 3) are flexible and easy updated. As new ground-based inventory data become available, they can be added to the database and used thereafter. Imputation methods include tabular imputation, nearest neighbor, most similar neighbor, k-nearest neighbor, and geo-statistical estimation. 2.3.1 Tabular Imputation A tabular imputation model was developed to estimate post-harvest stand characteristics by Ek et al. (1997). A simple tabular analysis of forest inventory plot data that showed tree and stand attributes by forest cover type was used. The output tables generated were used as input regeneration to growth models and were projected further into the future. This approach was used to relate growth and yield model inputs to aerial attributes by Temesgen and LeMay (2000a). 2.3.2 Nearest Neighbor Method (NN) The coarsest imputation approach (known as random imputation) is where a reference unit is picked randomly from the inventoried units to replace a target unit. Moeur (2000) stated that the use of the auxiliary variables can refine and filter the selection of random imputation. The selection of the reference unit is based on the minimum Euclidean distance, computed on the entire set of chosen auxiliary variables. 2.3.3 Most Similar Neighbor Method (MSN) As well as the auxiliary (independent) variables used in the N N method, M S N takes also into account inventory (dependent) variables and the relationship among them to guide the selection of the appropriate reference stand. The most similar unit is selected based on different distance measures on the auxiliary variables weighted by the importance of the inventory variables (correlation coefficient between the auxiliary and inventory variables). Moeur and Stage (1995) and Moeur (2000) used Euclidean distance. The more accurate imputed estimates obtained by Moeur (2000) resulted from weighting the Euclidean distance using canonical correlation coefficients. Reasonable imputation results were obtained at a 20% threshold of sampled stands under common sampling conditions (Moeur 2000, Temesgen and LeMay 2000b). 9 Moeur and Hershey (1998) compared three MSN techniques that assessed the value of including location information to estimate forest species composition. These techniques were: 1) "spatially naive MSN" developed from the inventory and low resolution data excluding location information; 2) "partially spatially informed MSN", where the geographic coordinates of the sample plot and grid cell locations were added to the variables used in the previous MSN; and 3) "fully spatially informed MSN", where a spatial variogram function was added to the previous MSN. The selection of the most similar neighbour (sample plot) was based upon its satellite signature (Landsat T M spectral bands and band transformations). Differences in the results obtained by the three M S N methods were subtle, but the partially and fully spatially informed MSN produced better estimates of species composition. 2.3.4 K-Nearest Neighbor (K-NN) Unlike MSN, where measured reference stand attributes were used to find a single nearest neighbor, the K-NN method uses the weighted average (or unweighted) of the attributes of a chosen number of reference units to compute target unit estimates (Haara et al. 1997). Thus, post-harvest stand characteristics of a target stand (or plot) can be predicted with a weighted average of the attributes of the K-NN reference stands (or plots). Haara et al. (1997) found that the results and the accuracy obtained by the K-NN method were similar to those obtained by conventional methods (Weibull distribution). According to Maltamo and Kangas (1998), the K-NN method requires three decisions to be made before its application: (1) identify the distance function type to be used to find the most similar reference units; (2) determine the number of nearest neighbors to be used; and (3) specify the weighting function form for the reference units. Maltamo and Kangas (1998) tested the performance of three different methods of K - N N for predicting the diameter distribution of a target stand. The methods studied were: (1) Weibull distributions of k-nearest neighbors, (2) distributions of k-nearest neighbors smoothed with the kernel method, and (3) empirical distributions of the k-nearest neighbors. The latter approach provided the most accurate prediction, but the first two approaches performed quite well also. 2.3.5 Geostatistical Estimation (GS) This approach may be used to estimate the distribution of tree species across the landscape. Estimation is based on the observed spatial distribution of the tree species, without taking into account their relationships with other species or other covariates such as lower tree layers. Thus, predictions developed by GS preserve only the spatial structure inherent in the sample data used. To interpolate species distribution maps from sampled to unsampled stands, Moeur and Hershey (1998) used sequential Gaussian conditional simulation (sgCS), combined 10 separately with indicator Kriging (IK) and sequential indicator conditional simulation (siCS). The process used for each combination had two steps. The first consisted of estimating species occurrence using Boolean or IK techniques, and the second estimated species percent by basal area per acre using sgCS. They assumed that broad-scale species variation could be adequately represented; however, accurate fine-scale species distribution cannot be expected when using only sample plot data. Thus, the accuracy of the data source, reference forest cover maps in this case, limited the reliability of the estimates. 11 3. Methods 3.1 Sampling Procedures Used in 1998 Data were first collected in the summer of 1998 in ICHmw2 stands in the vicinity of Nelson, BC that were partially disturbed in the last 30 years. More details of the sampling design and plot measurement procedures are given in Boisvenue (1999). Boisvenue (1999) attributed the poor performance of the re-calibrated Prognosis regeneration equations, in part, to the sampling design and data collected. According to her, the plot distribution did not present the full range of site series and species mixtures, including under-representation of more open stands. Based on Boisvenue's (1999) recommendations, the sampling procedure used for the summer 2000 field season was modified slightly from that used in 1998. A brief description of the design used follows. 3.2 Sampling Procedures Used in 2000 Sampling covered the entire ICHmw2, irrespective of ownership. Because of budget and time constraints, the polygons chosen were limited to those less than a two-hour drive from the forest district offices. The sampling frame was comprised of polygons that were accessible, were disturbed between five and 25 years ago, and had residual crown closures less than 20 percent (visually estimated). From the total number of polygons identified, priority was given to those presenting different ranges of site preparation, regeneration methods, aspect, slope, elevation and the identified site series taken from the Ministry of Forests' silvicultural (ISIS) database. Polygons were selected and subsequently located using ISIS and the inventory database, along with topographical maps of Arrow and Kootenay Lake Districts. Once sites were selected, plots were established using systematic sampling with a random start. Plots were established at least 50 m from the roads or any other openings to avoid edge effects. The number of plots established on a selected polygon and the distance between plots depended on the size of the polygon and the degree of structure variability present. Sites with a high degree of structure variability were sampled more heavily than more homogenous sites. On most sites, a distance of 100 m was used between plots. At least two plots were established on each polygon. For each plot established, the BEC site series was identified and recorded, along with other site factors. Site information recorded included: elevation, slope (percent), slope position, aspect (degrees), and site preparation whenever it was identifiable. Any other information deemed of importance was also recorded. For the consistency, the same sampling used to collect data for developing the regeneration component of the Northern Idaho variant of the growth and yield model 12 Prognosis (Ferguson and Carlson 1986) was used in this study. Trees on each plot were characterized as regeneration, small trees, or large trees. Established regeneration was defined as being at least 15 and 30 cm tall for shade tolerant and shade intolerant species, respectively, and less than 2.0 cm diameter outside bark at breast height of 1.3 m above ground (dbh) (Ferguson et al. 1986; Ferguson and Carlson 1993). Small trees had a dbh between 2.0 and 7.5 cm, and large trees were greater than 7.5 cm dbh. Concentric plots were used to sample the three tree types (Figure 1). Large trees were sampled with a 11.28 m radius (0.04 ha) plot. These trees were tallied to identify overstory species composition, to estimate retention level and residual basal area, and consequently to study the resultant impact of residual cover on regeneration establishment and growth. Dbh and species were recorded for all tallied trees. If numbers of trees allowed, two trees were chosen randomly for each species present and their heights measured. Other relevant information, such as presence of scars, diseases, fire signs and any other physical deformation, was also recorded. Small trees were sampled using a 3.99 m radius (0.005 ha) plot. For all small trees tallied, dbhs and heights were measured. Small trees were sub-sampled for total height and five-year height growth. Two trees of each determinant species, when more than two were present, were selected randomly and felled for measurement when whorls could not be confidently counted. For non-determinant species, all trees were felled, sectioned and checked until the 5-year height increment was found. The previous 5-years height growth was measured as of the end of the previous growing season to ensure that all trees sampled reflected the same growing period. Regeneration was sampled using a 2.07 m radius (0.00135 ha) plot. All established and viable natural regeneration was counted and tallied into height classes. Height classes used were: (1) 15 - 49.9 cm; (2) 50 - 99.9 cm; (3) 100 - 129.9 cm; and (4) >130 cm. Trees greater than 2 cm dbh, tallied also as small trees, were noted to avoid double counting on plot summaries. Regeneration was sub-sampled for height and total age for some of the "best trees" on each plot. Following Ferguson and Carlson (1993), the criteria for "best trees" were: (1) the two tallest trees, regardless of species, (2) the one tallest tree of each additional species present, and (3) the tallest of the remaining trees until at least four were sampled. If only one species was present on the plot, height and total age measurements were taken on the four tallest trees. According to Wellner (1940), often more trees occupy a stocking plot than will survive to rotation and best trees are more likely to survive than others. Non-determinant species were destructively sub-sampled for total age and height; for determinant species, these measurements were made on standing trees whenever possible. Tree condition, such as any evidence of damage, disease, or insects, was noted as well. When the regeneration center plot was not stocked, one of the four regeneration satellite plots was selected randomly and used for "best tree" sampling. To provide information about stocking probability, four regeneration satellite plots were established at 11.28 m from the central plot, along cardinal directions (Figure 1). Within each satellite regeneration plot, regeneration was tallied by species and height class. 13 Also, whether regeneration was advance (age >3 years) or subsequent (age <3 years) to the most recent disturbance was estimated (Ferguson and Carlson 1986). Regeneration plot (radius = 2.07m) Large tree plot (radius= 11.28m) Small tree plot (radius = 3.99m) Satellite plot (radius = 2.07 Figure 1. Plot layout for sampling regeneration, small and large trees. 3.3 Analyses Procedures 3.3.1 Data Preparation and Summary The data collected during the two field seasons were entered into Excel spreadsheets, separated into plot information, large tree, small tree, and regeneration components. The files were manipulated to provide various data summary tables. For further summaries and analyses, the data were transferred to S AS files (Statistical Analysis Systems Institute (SAS) 1991). For the imputation analysis, most of the 1998 data collected by Boisvenue (1999) were combined with the 2000 data. The plots retained were those that were disturbed (clear-cut or partially cut) and harvested between 5 and 25 years ago. A preliminary analysis to determine correlation between the amount of regeneration and the variables considered in this study was accomplished using the generalized linear model (GENMOD) with the SAS software. Owing to low representation of some categorical variables, certain variables were combined into larger classes. As regeneration is a count variable, the Poisson distribution was selected as the response probability distribution and "log" as the link function. A significance level of 5% was chosen as the acceptable level of significance for testing the parameters included in the model. 14 To prevent the possibility of zero error degrees of freedom, the number of dependent variables in the M S N analysis was limited. The 15 species present in this study were grouped into four ecological guilds (three shade tolerance species groups plus a hardwood group) based on the recommendations by Temesgen and LeMay (2000b) to generate tree lists by species group or species guild rather than individual tree species to obtain possibly better estimates. The hardwood group included cottonwood, trembling aspen, white birch, Douglas maple, willow and yew1; the shade tolerance groups were combined according to the work previously done by Boisvenue (1999). The shade intolerant species group included lodgepole pine and larch, the shade tolerant species group was composed of grand-fir, subalpine-fir, western redcedar, hemlock, and spruce; and the shade semi-tolerant species group included Douglas-fir and white pine. 3.3.2 Tabular Imputation Models Tabular imputation models were developed by obtaining simple averages, based on the theoretical and empirical knowledge that time-since-disturbance, basal area (Kneeshaw and Bergeron 1996, Lieffers et al. 1996, Eastham and Jull 1999, Greene et al. 1999, Greene 2000), and site series are important parameters that would affect regeneration establishment. This was also confirmed by the results of the preliminary GENMOD analysis. These three variables were selected as main factors in this study. Plot and individual tree information were used to create tables that displayed average stems per hectare by species groups by site class at some time following disturbance (harvesting) for different residual basal area categories. Site classes were determined by grouping similar site series. The years since last disturbance were divided into 5-year classes. A basal area per ha level of 5 m2/ha was chosen to divide the residual basal area (BA) into two categories, dividing the data approximately equally. Within each residual basal area category, plot aggregation was based on time-since-disturbance class interval and site class criteria. It was assumed that trees belonging to the same plot, block, and time-since-disturbance class had roughly the same stand history. Initially, tables showing the average regeneration per hectare by site class and time-since-disturbance class for each residual basal area category were created. To examine patterns of species distribution, these tables were disaggregated by shade tolerance groups (and later by species) and into four height classes which are: (1) 15 - 49.9 cm; (2) 50 - 99.9 cm; (3) 100 - 129.9 cm; and (4) >130 cm. For each cell in the regeneration tables, the standard error of the mean was calculated and used to study of the patterns of variability within (tables) and among all models (all tables). Following the protocol used by Ek and others (1997), means, standard deviations and coefficients of variation were used to test whether the initially heterogeneous regeneration became more stable at some time following the disturbance. 1 Although western yew is a coniferous species, it was placed together with the hardwood species because it is rare, not commercial, and because it is coded as mountain hemlock and not preojected in the present BC version of Prognosis . 15 To test the stability of the tabular imputation, the full data set was randomly split into five subsets (20%). Each subset represented target plots and the remaining 80% of the plots were used to construct the tables (labelled as Run 1 to Run 5). Each target plot was assigned to a specific table from which regeneration estimates were imputed even if the table was based on only one plot. Initially, any table based on less than 3 plots was excluded. However, this approach was abandoned because the biases obtained were high and consistently negative, indicating that this approach led to overestimation of the regeneration. For the target plots that mapped onto tables that had no plots, the table with the closest stand conditions (in either direction- drier or wetter) was chosen. The observed and the predicted regeneration of target plots were compared using a combination of the number of matched categories and RMSE. RMSE was calculated as follows: where n is the number of regeneration variables (16), yi is the actual amount of regeneration of each regeneration variable and j?. is the estimated amount of regeneration of each regeneration variable of a particular target plot. A good match was defined as exactly predicting the presence of regeneration in at least 15 out of the 16 regeneration variables of each plot (4 species groups by 4 height classes). A moderate match included all the plots that had between 8 and 14 agreements between the actual and the predicted regeneration cells. Finally, all the plots that showed less than 8 agreements were classified as poor matches. Within each match category, target plots were classified into low (<1000), medium (1000-2000), and high (>2000) RMSE. The same comparison was also performed using the combination of the number of matched categories and the ratio of the RMSE to the actual regeneration of each target plot. Within each match category, target plots were classified into low (<=0.20), medium (0.20-0.40), and high (>0.40) ratios. Where n is the number of regeneration variables (16), yi is the actual amount of regeneration of each regeneration variable and y is the estimated amount of regeneration of each regeneration variable of a particular target plot. Residual plots of the most important independent variables versus the bias were used to identify outlier target plots. The identified outlier plots, along with the plots that were poorly matched and had high RMSE, were further examined to detect possible factors that could have caused highly biased results and poor predictions. First, the characteristics of the imputation tables from which the regeneration was imputed were analyzed using standard deviations, standard errors, and coefficient of variations. Second, the individual auxiliary variables of the outlier plots were compared to the average values of the continuous auxiliary variables and the number by category of the class variables in the reference plots. RMSE = 16 3.3.3 The M S N Method Data identical to that used for the tabular imputation models were summarized, formatted, and analyzed using SAS and MSN software provided by Moeur2. Three MSN analyses were conducted using different levels of categorical dependent variables involving: (1) four height classes (as defined earlier); (2) two height classes (0.15 to 1.30 m and > 1.3 m); and ( 3) no height classes. MSN analysis requires three steps (Moeur 2000): (1) establish canonical correlations between the amount of regeneration by height class (Y set) and the full coverage of plot information level variables (X set) to calculate weights for the neighbor similarity function; (2) select the most similar sampled plot based on the plot level variables, weighted by correlations to the amount of regeneration, and assign its regeneration to the target plot; and (3) test the accuracy by comparing the imputed regeneration (predicted) to their observed values. For each M S N type, five runs were performed to assess the appropriateness and the stability of the approach. As with the tabular approach, the sample was randomly split into five data sets (20%). In each run, one data set represented target plots and the remaining 80% of the plots represented reference plots. Reference plots were those plots assumed to have complete coverage of attributes. These included plot indicator attributes that were provided by Ministry of Forests' silviculture data base (ISIS), maps and stand records from the first-phase sample (history), plot information recorded on the field, and the corresponding ground data obtained during the second-phase sample (data collection). Target plots were excluded from model development and reserved for testing the accuracy of the estimates. Only site and overstory variables were assumed to be available for target plots. The most similar neighbour for each target plot was selected from the reference plots, and the neighbour's regeneration conditions were imputed to the target plot. The dependent variables (Y set) that were used in the MSN analysis were the amount of regeneration per hectare (SPH) by species group and four height classes, two height classes or no height classes. The independent variables (X set) that were used in this analysis were those that are commonly measured to describe the stands. They included: aspect (radians), elevation (m), slope (%), site series, time-since-disturbance, residual basal area per hectare (BA), number of residual trees per hectare (TPH), crown competition factor (CCF), site preparation (class value) and slope position (class value). Site preparation and slope position classes were each represented by five dummy variables. Basal area per ha and number of residual trees per ha were assumed known, since they can be measured for an existing stand or predicted using Prognosis . Ground inventory and plot information attributes retained for these analyses are listed in Table 2. After substituting the values of the reference plot for the target plot, regeneration by species group with and without height classes of the target and the selected reference 2 United States Department of Agriculture, Forest Service, Intermountain Research Station in Moscow, Idaho (1999). 17 (most similar) plots were compared using bias (mean deviation), mean absolute deviation, and the precision (root mean square error- RMSE). Based on the three criteria, the best M S N type was further analyzed. As with the tabular approach, the target and the most similar reference plots were compared using a combination of the number of matched categories and RMSE, and the combination of the number of matched categories and the ratio of the RMSE to the actual regeneration of each target plot. The classification of target plots into match, RMSE, and ratio categories was described in tabular approach. The plots that were deemed to be "good" matches, but had high RMSE were examined to detect specific characteristics responsible for producing high errors. Plots of relevant auxiliary variables versus the bias were used to identify the plots and the factors that could affect the MSN performance and produce highly biased results. All the plots that were outside the band limited by -1000 and +1000 regenerated stems/ha were considered as outliers and were further analyzed, along with the plots classified as "poor match and high RMSE". First, the auxiliary variables of all identified plots and their most similar neighbour were descriptively compared. Next, the average values of the continuous auxiliary variables and the number by category of the class variables of target plots and their most similar neighbour plots were also compared. Table 2. Ground inventory and plot information attributes used in the M S N analyses. Inventory Variables Plot Information Attributes (Regeneration per ha) MSN 1 (by four height classes): Species group and height class (16 variables) MSN 2 by (two height classes): Species group and height class (8 variables) MSN 3 (no height classes): Species group (4 variables) All Three Types of Analyses: Number of years since disturbance Site series Aspect (radians) Elevation (m) Slope (%) Residual trees per ha (TPH) Residual basal area per ha (BA) Crown competition factor (CCF) Slope position: lower, level, middle, plateau, upper, and none Site preparation: none, burning (burn), Brushing (brush), brushing and burning (bbrush), and mechanical (mech) 18 3.3.4 Comparison of the Two Approaches The predictive capability of the tabular imputation and M S N methods were compared. Both methods were tested using the bias, the mean absolute deviation, and the RMSE on the datasets. This comparison also included the combination of criteria already defined: (1) the number of matched categories and RMSE, and (2) the number of matched categories and the ratio of the RMSE to the actual regeneration of each plot. 3.3.5 Sensitivity of Prognosis80 to MSN and Tabular Regeneration Predictions The Prognosis80 model was used to evaluate the sensitivity of yield projections over 50 years to regeneration predictions from the developed M S N and tabular imputation models. Specifically, differences in 50-year volume yield projection for a target plot using its true regeneration and its estimated regeneration were determined. The plots classified as "good match-low RMSE", "moderate match-medium RMSE", and "poor match-high RMSE" represent the best, moderate, and unsatisfactory regeneration predictions, respectively. For each imputation approach, sensitivity analysis was carried out on 16 randomly chosen target plots: four plots from each of the two first classes and eight plots from the third. This analysis used tree lists from the 16 target plots and their selected most similar neighbours, resulting in 32 simulations for each approach. The input data used in the Prognosis80 model simulations included the observed tree list (small and large trees) for the target plots, the observed regeneration, and the plot information, particularly site series, aspect, slope, elevation, and year of disturbance. The runs were repeated using the imputed regeneration together with the other information for the target plots. All the trees that had dbhs between 2.0 and 7.5 cm within the 3.99 m small tree plot were considered as small trees when computing the tree lists. This avoided double counting of regeneration best trees as small trees. Yield differences and standard deviations of these differences were determined by imputation method and regeneration prediction category. 19 4. Results 4.1 Summary of the Combined 1998 and 2000 Data Seventeen plots were discarded from the 1998 sample data since they did not meet the required selection criteria. Two plots were cut more than 25 years ago and 15 plots were not disturbed at all. The remaining data comprised 333 plots sampled from 138 polygons. Table 3 provides ranges of data for eight variables for the combined 1998 and 2000 data. Table 3. Number of plots in the combined 1998 and 2000 data set summarized by variable class. Years Since Last No. Plots Site Preparation No. Plots Residual Basal No. Plots Disturbance Method Area (m2/ha) 2 15 Brushing 22 0 33 3 17 Burning 88 1 -5 134 4 8 Burning and Brushing 16 5 - 10 55 5 16 Mechanical 13 10- 15 32 6 23 None 194 15-20 28 7 22 20-25 9 8 8 25-30 12 9 19 30-35 6 10 36 35-40 7 11 32 >40 17 12 21 Elevation (100 m) 13 14 <800 34 Slope Position 14 8 8-9 24 Crest 7 15 2 9-1 33 Lower 30 16 7 10-11 56 Depression 11 17 13 11-12 52 Middle 220 18 20 12-13 46 Plateau 15 19 11 13-14 58 Toe 6 20 4 14-15 27 Top 4 21 12 15-16 3 Upper 28 23 8 Level 10 24 6 Blank 2 25 11 Aspect Site Series E 57 Slope Percent 02 0 Flat 6 03 114 N 36 0- 10 56 04 88 NE 30 10-20 66 01 54 NW 22 20-30 72 05 54 S 57 30-40 62 06 7 SE 35 40-50 40 07 13 . sw 59 50-60 19 08 3 w 31 >60 18 About half of the plots were disturbed in the last 10 years and nearly 28% between 15 and 25 years ago. About 55% of the plots occurred on southerly (warmer) exposures (S, 20 SE, SW, W), over 43% on northerly (colder) exposures (E, N, NE, and NW), and 2% on flat sites. Nearly 59% were found on low to moderate slopes (less than 30 percent). With the exception of elevations more than 1500 m, the plots covered the full range of elevation classes and most plots (66%) were located on mid-slopes. The range of residual basal areas sampled was wide, ranging from 0 to 92 m2/ha. One hundred sixty-six plots had basal areas less or equal than 5 m2/ha, and 167 plots had basal areas larger than 5 m2/ha. A little more than the half of the plots (59%) had no site preparation; four different site preparation techniques were used on the remaining plots, with burning being the most predominant (over 26%). Fifteen species were found in the overstory. 4.2 Regeneration Composition The regeneration was highly variable, ranging from 0 to 124,081 per ha and averaging 9518 seedlings per ha overall. The average regeneration per hectare were 4643, 2376, 1410, and 1089 for shade tolerant, shade semi-tolerant, hardwood, and shade intolerant species respectively. Thirty-six plots had no regeneration. The species composition of the overstory was led by shade tolerant species, comprising 66% of the large trees, followed by shade semi-tolerant species comprising 16%. Shade intolerant and hardwood species comprised 11 and 6.5% of the overstory, respectively. Figure 2 shows the distribution pattern of the average residual stems/ha of all species combined over all plots. The diameter distribution follows a reverse J-shape form, with the majority of the trees in the smaller diameter classes. 700 600 500 400 in E 2 300 200 100 0 0-5 2.5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 >45 47.5 5-cm diameter classes and midpoint Figure 2. Diameter distribution for all species combined. 21 Mechanically treated (scarified) plots had the most regeneration, followed by non-treated plots (Figure 3). Regeneration on the prescribed burn and brushed sites was significantly less abundant. The regeneration of shade tolerant species was substantially decreased on treated sites (Table 4). Prescribed burning decreased it even further than mechanical treatment. ]Tolerant QSemi-tolerant @Hardwood • Intolerant 1 2 3 4 5 Time-since-disturbance group Figure 3. Average regeneration per ha by: a) site preparation, b) aspect, c) time-since-disturbance classes, and d) time-since-disturbance for species groups. 22 Table 4. Average regeneration per ha by species groups and by site preparation treatments. Site Species group All species preparation Tolerant Semi-tolerant Intolerant Hardwood None 6070 2550 1129 1593 11342 Mechanical 3887 5772 6086 1429 14174 Burn 2491 1942 887 1334 6654 Brush 2601 1329 665 645 5240 Figure 3 shows that aspect is an important variable contributing to regeneration. North, northeast, and east aspects contained significantly more regeneration than south and west aspects, and flat terrain. The highest regeneration was attained between 5 to 10 years after disturbance. Afterwards, there was a constant decrease in regeneration until it reached its lowest density level between 20 and 25 years after harvesting. Although shade tolerant species constantly accounted for the largest component of regeneration abundance, Figure 3d shows that this species group predominated the regeneration between 5 to 10 years after harvesting. Hardwood species, and to a lesser extent shade intolerant species, showed an increase during the first two periods. Shade semi-tolerant species displayed greatest regeneration abundance between 10 and 25 years after harvesting. (A) D e n s e s t a n d s ] Tolerant FU Serri-tolerant n Hardw ood • Intolerant 18000 c o 15000 4 12000 c D) CU 1 2 3 4 5 T i m e - s i n c e - d i s t u r b a n c e g r o u p (B) O p e n s t a n d s 0 Tolerant n Serri-tolerant @ Hardw ood • Intolerant 18000 15000 4 12000 4 - -o '-^ n <D C 0) O) Q) 9000 6000 3000 1 2 3 4 5 T i m e - s i n c e - d i s t u r b a n c e g r o u p Figure 4. Average regeneration per ha by years since disturbance and species groups for dense and open stands (dense stands: BA/ha > 5m2; open stands <=5m2). 23 When the regeneration was stratified by stand type, more regeneration was evident on dense stands (Figure 4). During most of the observation period, shade tolerant species dominated species composition and reached its peak between 5 and 10 years post-harvest. Open stands were first predominately regenerated by hardwood and shade intolerant species, but shade tolerant species become prominent 20 years after disturbance. Regeneration abundance changed considerably with residual basal area, slope, and aspect (Table 5). The highest regeneration occurred on dense stands and on cool sites that had slopes ranging from 20 to 40%, followed by sites that occured on 5 to 20% slopes and greater than 40% slopes. Warm sites and dense stands occupied the second position; their highest regeneration was attained on steep slopes (>40%). These sites may occur in higher elevations. Open stands displayed the same trends as the dense sites with respect to slope and aspect. However, the difference in regeneration between warm and neutral (flat) sites was not significant in open stands. Table 5. Regeneration per ha by basal area, aspect, and slope classes. B A class Aspect class1 Slope class Regeneration Total Dense Neutral 1 15603 2 0 3 0 4 0 15603 Cool 1 6770 2 14462 3 25714 4 12879 59825 Warm 1 16346 2 8389 3 10650 4 9756 45141 Open Neutral 1 16594 2 0 3 0 4 0 Cool 1 1932 2 6103 3 9032 4 6637 Warm 1 372 2 7297 3 4064 4 6643 18376 1 Aspect classes: neutral = flat; cool = north, northeast, northwest, and east; warm = south, southeast, southwest, and west. 2 Slope classes: 1:0- 5%; 2: 5 - 20%; 3: 20 - 40%; and 4: > 40%. 24 4.3 Tabular Imputation 4.3.1 The Tabular Imputation Model The tabular imputation model used a data set made up of 333 plots from 138 blocks. The site series were combined into five site classes: (1) dry: site series 02 and 03; (2) slightly dry: site series 04; (3) mesic: site series 01; (4) slightly wet: site series 05; and (5) wet: site series 06, 07 and 08. The years since last disturbance were classified into five-year time-since-disturbance classes and the residual basal area was stratified into two categories (< 5.0 m 2 representing open stands and > 5.0 m 2 representing dense stands). Tables 6 and 7 show the average regeneration per ha by time-since-disturbance class and site class for each residual basal area category. For both residual basal area categories, data existed for most of the site and time-since-disturbance classes. For the dense category, no plots were sampled on wet sites for time-since-disturbance classes 1 and 3 and regeneration was not found for the wet sites for time-since-disturbance class 2. For the open category, only wet sites for the first time-since-disturbance class lacked sampled plots. Table 6. Average regeneration per ha by time-since-disturbance class interval and site class for basal area class "Dense" (* indicates no plots). Time-since- Site Class disturbance class Dry Slightly dry Mesic Slightly Wet Wet 1(1-5) 13663 9389 5944 10933 * 2(6-10) 4969 16853 32568 6316 0 3 (11-15) 15253 20592 12482 1486 * 4(16-20) 4458 6316 14024 10897 3220 5 (21-25) 5015 6439 7616 13077 6687 Table 7. Average regeneration per ha by time-since-disturbance class interval and site class for basal area class "Open" (* indicates no plots). Time-since- Site Class disturbance class Dry Slightly dry Mesic. Slightly Wet Wet 1 (1 - 5) 7430 9288 11145 1672 * 2(6-10) 4776 12956 5480 5052 2972 3 (11-15) 6538 4334 14365 2724 1486 4(16-20) 6780 9659 2043 4235 2415 5(21-25) 8173 1486 0 3344 2477 Most regeneration was found on mesic sites for both dense and open stands, but at different times after harvesting (Tables 6 and 7). Within each time-since-disturbance class for both types of stands, the amount of regeneration varied with site conditions. For dense stands, the most regeneration was found on dry, mesic, slightly dry, mesic and 25 wet sites for time-since-disturbance classes 1, 2, 3, 4 and 5, respectively. Slightly dry, mesic and slightly wet sites had the highest amount of regeneration over all. Tables 8 to 17 present species composition and their frequencies by time-since-disturbance class for the residual basal area categories and site classes. More than 15 species contributed to the regeneration (nine softwood and six hardwood species). Due to the large number of species, cottonwood, trembling aspen, white birch, Douglas maple, yew and willow were grouped into a hardwood species group. These species, with the exception of yew, are shade intolerant and behave biologically and ecologically similarly. Species composition for the dry sites is given in Tables 8 and 9. Dense stands were dominated by shade semi-tolerant and shade tolerant species during all time-since-disturbance intervals. Shade intolerant species (hardwood, western larch, and lodgepole pine) became prominent five years after harvesting and were present thereafter (Table 8). Shade intolerant species, especially hardwood, dominated the species composition for the first four time-since-disturbance classes in open stands (Table 9). Shade tolerant species, together with Douglas-fir, dominated dry and open stands 20 years after disturbance. Table 8. Average regeneration per ha by species and time-since-disturbance class for basal area category "Dense" and "Dry" sites. Time-since- Species Total disturbance Bg Bl Cw Fd Hw Lw PI Pw Sx Hardwood class 1(1-5) 0 83 2146 3467 2023 206 1073 1321 1651 1692 13663 2(6-10) 0 279 1532 1300 0 0 232 279 93 1254 4969 3 (11-15) 481 0 981 7692 175 1005 2448 787 44 2142 15690 4(16-20) 0 0 0 743 0 0 0 743 0 0 1486 5(21-25) 186 0 0 2415 0 743 186 186 0 1300 5015 Table 9. Average regeneration per ha by species and time-since-disturbance class for basal area category "Open" and "Dry " sites. Time-since- Species Total disturbance Bg Bl Cw Fd Hw Lw PI Pw Sx Hardwood class 1(1-5) 0 1486 637 1592 106 425 743 106 531 1804 7430 2(6-10) 35 35 708 425 142 743 1769 106 0 814 4776 3 (11-15) 111 186 520 929 149 1152 483 223 2118 2043 6501 4(16-20) 0 93 929 2415 0 0 1115 93 93 2043 6780 5 (21-25) 0 0 1486 2972 1486 1486 0 0 743 0 8173 26 In dense and slightly dry stands, western redcedar, western hemlock, and Douglas-fir constituted the bulk of the species for the first three time-since-disturbance intervals (Table 10). Douglas-fir, grand fir and subalpine fir were the major species components during the later two time-since-disturbance intervals. Table 10. Average regeneration per ha by species and time-since-disturbance class for basal area category "Dense" and "Slightly Dry" sites. Time-since- Species Total disturbance Bg Bl Cw Fd Hw Lw PI Pw Sx Hardwood class 1(1-5) 1148 540 2634 1486 2094 338 203 675 0 270 9389 2(6-10) 101 169 2837 3816 7160 0 34 743 0 1993 16853 3 (11-15) 318 1274 5201 3609 1274 2654 0 3078 212 2972 20592 4(16-20) 0 1858 372 3344 0 0 0 0 372 372 6316 5(21-25) 1238 62 867 1672 495 0 0 1548 0 557 6439 In open, slightly dry stands, shade intolerant species (hardwoods, lodgepole pine, and western larch) were the most prevalent for the first 10 years (Table 11). Douglas-fir was consistently present; it dominated species composition in these stands for the last three time-since-disturbance class intervals. Table 11. Average regeneration per ha by species and time-since-disturbance for basal area category "Open" and "Slightly Dry" sites. Time-since-disturbance Species Total class Bg Bl Cw Fd Hw Lw PI Pw Sx Hardwood 1(1-5) 0 0 1238 743 0 619 2601 0 0 4087 9288 2(6-10) 46 232 929 1579 1347 557 3761 46 604 3854 12956 3 (11-15) 0 0 0 2229 124 743 248 124 0 867 4334 4(16-20) 372 0 0 5944 0 372 0 0 0 2972 9659 5(21-25) 0 0 372 743 0 0. 372 0 0 0 1486 The majority of regeneration in dense stands across all time-since-disturbance classes on mesic sites was composed of western redcedar and western hemlock (Table 12). Hardwood species were relatively important in the third time-since-disturbance interval. In this class, Douglas-fir dominated the species composition; it was second behind western hemlock in the fourth time-since-disturbance interval. In open stands on mesic sites, western larch, hardwood and Douglas-fir were the leading species during the first 10 years after harvesting (Table 13). Afterwards, shade tolerant species (especially western redcear and spruce) were dominant. They were accompanied by hardwood, Douglas-fir and lodgepole pine. 27 Table 12. Average regeneration per ha by species and time-since-disturbance class for basal area category "Dense" and "Mesic" site series. Time-since-disturbance Spe cies Total class Bg Bl Cw Fd Hw Lw PI Pw Sx Hardwood 1(1-5) 0 0 2972 372 2229 0 0 372 0 0 5944 2(6-10) 248 248 4334 1300 23838 62 1300 619 0 557 32506 3 (11-15) 0 2526 297 4012 743 149 0 892 892 2972 12482 4 (16-20) 186 557 2879 2972 4830 372 0 650 279 1300 14024 5 (21-25) 0 186 2229 372 2601 0 0 0 743 1486 7616 Table 13. Average regeneration per ha by species and time-since-disturbance class for basal area category "Open" and "Mesic" sites. Time-since-disturbance Species Total class Bg Bl Cw Fd Hw Lw PI Pw Sx Hardwood 1 (1 - 5) 0 0 1486 2229 743 4458 0 743 0 1486 11145 2(6-10) 0 0 93 1393 1115 279 372 0 279 1950 5480 3 (11-15) 83 743 5779 908 578 660 83 165 3385 1321 13705 4(16-20) 0 0 372 0 557 0 186 0 186 743 2043 5(21-25) 0 0 0 0 0 0 0 0 0 0 0 With the exception of time-since-disturbance class 3, where western larch was the sole species present, western hemlock, western redcedar, grand fir, and Douglas-fir dominated slightly wet, dense stands (Table 14). Grand fir was the leading species for time-since-disturbance classes 4 and 5. Like most of the previous open stands, hardwood was the major component of the regeneration immediately after disturbance in the slightly wet and open stands (Table 15). After the second time-since-disturbance class, regeneration of shade tolerant species increased and remained dominant thereafter. Shade semi-tolerant and shade intolerant species were present during the entire time period, but to a lesser extent in the older time-since-disturbance classes. Table 14. Average regeneration per ha by species and time-since-disturbance class for basal area category "Dense" and "Slightly Wet" sites. Time-since-disturbance Species Total class Bg Bl Cw Fd Hw Lw PI Pw Sx Hardwood 1(1-5) 0 212 3927 1274 4883 106 106 0 425 0 10933 2(6-10) 0 0 4830 0 743 743 0 0 0 0 6316 3 (11-15) 0 0 0 0 0 1486 0 0 0 0 1486 4(16-20) 5201 0 1486 0 1981 0 0 743 991 495 10897 5 (21-25) 6687 0 2675 3566 892 0 0 0 446 0 14266 28 Table 15. Average regeneration per ha by species and time-since-disturbance class for basal area category "Open" and "Slightly Wet" sites. Time-since-disturbance Species Total class Bg Bl Cw Fd Hw Lw PI Pw Sx Hardwood 1(1-5) 0 0 0 0 0 0 0 372 0 1300 1672 2(6-10) 0 297 1486 149 297 149 0 149 297 2229 5052 3 (11-15) 83 165 413 660 248 248 0 0 660 248 2724 4 (16-20) 0 297 1858 520 669 74 74 74 223 446 4235 5 (21-25) 0 929 372 464 0 0 0 93 1022 464 3344 As was noted previously, no information was available on the wet sites during the first and third time-since-disturbance classes for dense stands and for the first time-since-disturbance class for open stands (Table 16). Although shade intolerant species were present, shade semi-tolerant species constituted most of the regeneration in open stands for the second time-since-disturbance class (Table 17). For the third time-since-disturbance class, approximately similar regeneration levels of hardwood and western redcedar were found. Western redcedar and hardwood comprised most of the regeneration for dense stands in the older time-since-disturbance classes. Surprisingly, the open stands were dominated by a shade tolerant species (western redcedar), although shade semi-tolerant and shade intolerant species were present as well. Table 16. Average regeneration per ha by species and time-since-disturbance class for basal area class "Dense" and " Wet" sites (* indicates no plots). Time-since-disturbance Species Total class Bg Bl Cw Fd Hw Lw PI Pw Sx Hardwood 1(1-5) * * * * * * * * * * 2(6-10) 0 0 0 0 0 0 0 0 0 0 0 3 (11-15) * * * * * * * * * * * 4(16-20) 0 0 2972 0 0 0 0 0 248 •" . 0 3220 5 (21-25) 0 0 0 0 0 0 0 0 0 6687 6687 Table 17. Average regeneration per ha by species and time-since-•disturbance class for basal area class "Open' 'and "Wet" sites (* indicates no plots). Time-since-disturbance Species Total class Bg Bl Cw Fd Hw Lw PI Pw Sx Hardwood 1(1-5) * * * * * * * * * * * 2(6-10) 0 186 557 1115 186 186 186 0 372 186 2972 3 (11-15) 248 0 495 0 0 0 0 0 0 743 1486 4(16-20) 0 0 1486 372 0 0 0 0 372 186 2415 5 (21-25) 0 124 1610 124 0 0 0 124 124 372 2477 29 Breaking down the species composition tables by height class created tables for 50 regeneration conditions. Tables 18 and 19 are examples of these tables, containing information on the amount of regeneration per ha by shade tolerant group, species, height class on dry sites for dense and open stands that were disturbed during the first time-since-disturbance interval. Tables in Appendix I cover the other combinations of conditions. These tables can be used to provide young stand data for any existing individual-tree or whole stand based growth and yield model. As Prognosis80 grows stands based on the interaction among trees, it can use the data from the developed tables or by randomly selecting a single plot from those having the desired characteristics. For example, using the means, regeneration of 13663 stems per ha would be estimated for dense and dry stands 2.5 years (midpoint of time-since-disturbance class 1) after disturbance (Table 18). For an open stand, 7430 stems per ha would be estimated (Table 19). The information provided for species composition by height class can be used to help differentiate between advance and subsequent regeneration, based on knowledge of average height growth rates. Table 18. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 18 Bg 0 0 0 0 0 Bl 0 41 41 0 83 Cw 991 743 165 248 2146 Hw 1445 165 206 206 2023 Sx 1486 83 41 41 1651 Tolerant 3921 1032 454 495 5903 Fd 2064 660 330 413 3467 Pw 826 289 41 165 1321 Semi-tolerant 2889 949 372 578 4788 Hardwood 454 248 248 743 1692 Lw 165 41 0 0 206 PI 1032 0 41 0 1073 Intolerant 1195 41 41 0 1280 Al l Species 8462 2270 1115 1816 13663 30 Table 19. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 7 Bg 0 0 0 0 0 Bl 1486 0 0 0 1486 Cw 0 425 0 212 637 Hw 0 106 0 0 106 Sx 318 106 0 106 531 Tolerant 1804 637 0 318 2760 Fd 1380 212 0 0 1592 Pw 106 0 0 0 106 Semi-tolerant 1486 212 0 0 1698 Hardwood 0 425 425 955 1804 Lw 425 0 0 0 425 PI 531 106 106 0 743 Intolerant 955 106 106 0 1168 All Species 4246 1380 531 1274 7430 4.3.2 Validation of the Tabular Imputation Model Validation tests showed that cell averages based on less than 10 plots resulted in very high standard errors of the mean (SEM), reaching 500% of the mean in some cases. SEM decreased for those predictions based on between 10 and 20 plots (see examples in Tables 20 and 21. Appendix II covers the remainder of the validation tables). Table 20. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Dry" sites. Site Number of Species Height class Total plots 1 2 3 4 Dry 18 Bg 0 • 0 0 0 0 Bl 0 41 41 0 57 Cw 524 334 128 120 895 Hw 966 128 168 206 1175 Sx 1093 57 41 41 1163 Tolerant 1344 324 200 225 2174 Fd 892 323 161 371 1083 Pw 429 249 41 165 812 Semi-tolerant 883 379 162 396 1265 Hardwood 371 208 104 618 1042 Lw 128 41 0 0 145 PI 738 0 41 0 736 Intolerant 736 41 41 0 880 Total 2902 587 296 774 3253 31 Table 21. Standard error of the mean regeneration per ha by height class, species for time-since-disturbance class 1, basal area class "Open" and "Dry" sites. Site Number of Species Heij *ht class Total plots 1 2 3 4 Dry 7 Bg 0 0 0 0 0 Bl 903 0 0 0 903 Cw 0 425 0 - 212 637 Hw 0 106 0 0 106 Sx 221 106 0 106 420 Tolerant 840 411 0 221 1324 Fd 548 212 0 0 677 Pw 106 0 0 0 106 Semi-tolerant 513 212 0 0 682 Hardwood 0 274 221 531 1571 Lw 221 0 0 0 221 PI 212 106 106 0 324 Intolerant 137 106 106 0 454 Total 1510 937 352 1035 2507 The question of whether regeneration becomes more stable with increasing time-since-disturbance in these complex stands, as is the case for even-aged stands, was addressed using the means, standard deviations, and coefficients of variation. Average regeneration per hectare for various conditions, with their respective standard deviations and coefficients of variation, are given in Tables 22 and 23 for dense and open stands, respectively. For dense stands, coefficients of variation were high in the early time-since-disturbance classes and decreased with increasing time-since-disturbance class in dry conditions. Decreases in variability were more or less constant. For the rest of the conditions examined, coefficients of variation fluctuated with time-since-disturbance and no clear trends were evident. The lack of trend may indicate that regeneration is constantly occurring in complex stands and the mortality might take part at this stage. Also, it is likely that the regeneration present after disturbance is dominated by advance regeneration. 32 Table 22. Regeneration per ha (SPH) with corresponding standard deviations (STD) and coefficients of variations (CV) for dense stands (* indicates no plots). Site Series Years Since Disturbance SPH STD CV Dry 1-5 13663 13802 1.01 6-10 4969 4618 0.93 11-15 15690 13275 0.84 16-20 1486 1051 0.71 21-25 5015 2134 0.43 Slightly dry 1-5 9389 8460 0.90 6-10 16853 21625 1.28 11-15 20592 11659 0.57 16-20 6316 1576 0.25 21-25 6439 6457 1.00 Mesic 1-5 5944 8460 1.41 6-10 32506 38698 1.19 11-15 12482 11236 0.90 16-20 14024 15688 1.12 21-25 7616 7919 1.04 Slightly wet 1-5 10933 15092 1.38 6-10 6316 6830 1.08 11-15 1486 0 0 16-20 10897 15179 1.39 21-25 14266 20998 1.47 Wet 1-5 * * * 6-10 0 0 0 11-15 * * * 16-20 3220 4947 1.54 21-25 6689 0 0 The performance of the tabular model was also evaluated by using combinations of: (1) the number of match categories and the RMSE and (2) the number of matched categories and the ratio of the RMSE to the observed regeneration of target plots for the five sets tested (Tables 24 and 25). On average, only 2.4% of the plots (1.6 out of 66.6) were classified as a good match and there were as many moderate as poor matched categories (49%). The combination "moderate match-low RMSE" had the highest percentage of 37% followed by "moderate match-high RMSE" with 27%. The percentage in "poor match-low RMSE" and "poor match-high RMSE" were 21 and 16%, respectively. The 22% of the plots that had high RMSE were shared almost equally between the moderate and poor match categories. 33 Table 23. Regeneration per ha (SPH) with corresponding standard deviations (STD) and coefficients of variations (CV) for open stands (* indicates no plots). Site Series Years Since Disturbance SPH STD CV Dry 1-5 7430 6632 0.89 6-10 4776 6342 1.33 11-15 6501 5800 0.89 16-20 6780 6686 0.99 21-25 8173 0 0 Slightly dry 1-5 9288 2648 0.29 6-10 12956 11804 0.91 11-15 4334 2634 . 0.61 16-20 9659 2644 0.27 21-25 1486 1051 0.71 Mesic 1-5 11145 0 0 6-10 5480 6009 1.10 11-15 13704 18452 1.35 16-20 2043 2670 1.31 21-25 0 0 0 Slightly wet 1-5 1672 2455 1.47 6-10 5052 2800 0.55 11-15 2724 3174 1.17 16-20 4235 8267 1.95 21-25 3344 3051 0.91 Wet 1-5 * * * 6-10 2972 2350 0.79 11-15 1486 1966 1.32 16-20 2415 3344 1.38 21-25 2477 1975 0.80 Using the ratio of RMSE to the observed regeneration per ha for target plots (Table 25), the results were: 1) the percentage of the plots that had low and high ratios were equal to those that had low and high RMSE; 2) the percentage of the plots classified as having medium ratios was smaller than the percentage of the plots classified by the first comparison as medium RMSE; 3) For plots with zero regeneration (11%), the ratio was undefined; and 4) the percentage of plots that belong to the "good match-undefined ratio" combination was classified by the first comparison as "good match-low RMSE". Unlike using RMSE, the combination "moderate match-low ratio" had the highest percentage of about 29% followed by "poor match-low ratio" with 19%. 34 Table 24. Results of the comparison between true and tabular imputed regeneration per ha for the target plots using a combination of RMSE and match category for each of the five runs separately, and averaged over the five runs. R M S E No. Target Match Category Total Plots for Each Good Moderate Poor Run 68 2 22 12 36 65 1 15 16 32 Low 65 0 18 14 32 64 0 21 12 33 71 52 10 16 28 Average 66.6 1.0 17.2 14.0 32.3 68 0 7 12 19 65 2 6 13 21 Medium 65 0 10 8 18 64 0 12 7 19 71 1 7 13 21 Average 66.6 0.6 8.4 10.6 19.6 68 0 6 7 13 65 0 2 10 12 High 65 0 8 7 15 64 0 6 6 12 71 0 12 10 22 Average 66.6 0 6.8 8.0 14.8 68 2 35 31 68 65 3 23 39 65 Total 65 0 36 29 65 64 0 39 25 64 71 3 29 39 71 Average 66.6 1.6 32.4 32.6 66.6 4.3.3 Causes of Poor Regeneration Predictions for the Tabular Procedure Residuals for the tabular procedure were plotted over important variables. Figure 5 shows the scatter plot of bias versus four independent variables for Run 1 (20% of data reserved for testing). Similar results were obtained for the other four runs and their figures are given in Appendix VI. On average, about 8% of target plots had residuals of more than 1000 stems/ha (outliers). The outlier plots tended to have very large or very small stand density variable values (TPH, BA, and CCF),.compared to the average values given in the appropriate table, resulting in a poorer match. Tables that served as the imputation pool for these plots had very high coefficients of variation. The CV's ranged from 90 to 400%. 35 Table 25. Results of the comparison between true and tabular imputed regeneration per ha for the target plots using a combination of the ratio of RMSE to the actual regeneration and plot match category. Ratio No. Target Match Category Total Plots for Each Good Moderate Poor Run 68 0 19 14 33 65 2 15 19 36 Low 65 0 15 9 24 64 0 25 9 34 71 0 22 12 34 Average 66.6 0.4 19.2 12.6 32.2 68 1 4 11 16 65 1 3 6 10 Medium 65 0 11 8 19 64 0 7 5 12 71 1 1 8 10 Average 66.6 0.6 5.2 7.6 13.4 68 0 7 2 9 65 0 4 10 14 High 65 0 6 7 13 64 0 5 9 14 71 0 3 15 19 Average 66.6 0.2 5.0 8.6 13.8 68 1 5 4 10 65 0 1 4 5 Undefined 65 0 4 5 9 (regeneration=0) 64 0 2 2 4 71 1 3 4 8 Average 66.6 0.4 3.0 3.8 7.2 68 2 35 31 68 65 3 23 39 65 Total 65 0 36 29 65 64 0 39 25 64 71 3 29 39 71 Average 66.6 1.6 32.4 32.6 66.6 36 TPH versus Bias 3000 2000 1000 0 -1000 -2000 SI - i -. • • v. 2000 4000 6000 TPH Aspect versus Bias 3000 2000 <g 1000 ffl 0 -1000 -2000 20 40 60 Aspect 80 Figure 5. Scatter plot of the regeneration bias versus residual basal area of large trees, residual number of trees (TPH), crown competition factor (CCF), and aspect for 68 target plots in Run 1 of the Tabular model. Bias is observed minus predicted regeneration averaged over all plots. 4.4 The MSN Models For M S N 1 (4 height classes), 16 regeneration variables and eight continuous and two class plot information variables were used for each plot. Along with eight continuous and two class plot information variables, MSN 2 (two height class) and M S N 3 (no height classes) made use of eight and four regeneration variables, respectively. Table 26 shows simple cross-correlations between ground (Y) and continuous variables for MSN 1, Run 1. Similar results were obtained for the other four runs (Appendix III). 37 Table 26. Simple correlations between the auxiliary and ground variables used in M S N analysis of Run 1 (n = 265). SPH1 Time- since-disturbance Site series Aspect Elevation Slope TPH 2 BA 3 CCF 4 Toll -0.083 -0.126 -0.117 -0.256 -0.020 0.080 0.240 0.261 Tol2 -0.090 -0.130 -0.048 -0.049 -0.005 0.124 • 0.138 0.142 Tol3 -0.091 0.033 -0.001 -0.050 -0.062 0.134 0.193 0.204 Tol4 0.098 -0.012 -0.028 -0.021 -0.017 0.320 0.115 0.143 Semil -0.084 -0.090 -0.000 -0.145 -0.009 -0.085 0.131 0.139 Semi2 -0.007 -0.077 -0.040 -0.073 0.003 -0.086 -0.043 -0.046 Semi3 -0.014 -0.052 -0.030 -0.058 0.131 0.109 0.012 0.006 Semi4 -0.150 -0.050 0.020 -0.058 0.005 0.111 -0.037 -0.038 Intoll -0.114 -0.097 -0.004 0.078 -0.082 -0.019 -0.105 -0.118 Intol2 -0.046 -0.088 0.001 0.073 -0.077 0.110 -0.104 -0.111 Intol3 -0.020 -0.055 0.094 0.036 -0.060 0.097 -0.083 -0.091 Intol4 -0.018 0.001 0.040 0.023 -0.104 0.157 -0.090 -0.089 Hardl -0.090 -0.028 -0.028 -0.111 0.032 -0.029 -0.022 -0.014 Hard2 0.011 -0.039 -0.094 -0.145 0.046 0.006 -0.064 -0.063 Hard3 -0.110 -0.001 -0.025 -0.077 0.022 -0.065 -0.081 -0.085 Hard4 0.004 -0.092 0.046 -0.019 0.127 0.007 -0.098 -0.103 ^ o l refers to shade tolerant species, semi to shade semi-tolerant species, intol to shade intolerant species, and hard to hardwood species; the numbers refer to height classes 1 to 4. 2 TPH refers to the number of residual trees per hectare. 3 BA refers to the residual basal area per hectare. 4 CCF refers to the crown competition factor Correlations between the regeneration and the auxiliary variables were low. The highest correlation coefficient for Run 1 was obtained between elevation and shade tolerant species height class 1 and was -0.26. Basal area and crown competition factor were moderately correlated in most cases with shade tolerant species height classes 1 and 2, with coefficients ranging from 0.20 to 0.30. Trees per ha had a correlation coefficient of 0.32 with shade tolerant species height class 4. In general, all measures of density, namely BA, TPH, and CCF were moderately well correlated with most of the regeneration variables. The strength of the relationship between ground and plot information variables drove the selection of the most similar reference plot. Tables of the canonical correlation reports from the five runs showed that eight canonical vectors explained 90% of the variance (Table 27). Basal area, crown competition factor, and trees per ha had the largest canonical coefficients in the most canonical variates. Basal area, crown competition factor, and trees per ha consistently had the highest coefficients and, therefore, carried high weights for obtaining the most similar neighbours for all five runs (Appendix IV). 4.4.1 Comparison of M S N Models A summary of the three criteria used to compare among the three M S N types are presented in Table 28. The bias, mean absolute deviation, and RMSE were calculated over all of the regeneration variables and over all target plots combined. 38 Table 27. Canonical coefficients weighted by canonical correlation for the 18 auxiliary variables for Run 1. (Bold numbers indicates relatively high coefficients). Variable Variatel Variate2 Variate3 Variate4 VariateS Variate6 Variate7 Variate8 Time-since -0.11220 -0.05404 0.19786 -0.14400 0.08884 -0.01527 -0.01028 -0.03792 Site series -0.03518 -0.07140 0.00514 0.01129 0.09569 -0.11389 -0.10985 -0.08610 Aspect -0.17061 -0.08270 -0.6064 -0.17876 0.04868 -0.00401 -0.03182 0.04779 Elevation -0.19927 0.02084 -0.23967 0.05452 0.06969 -0.06801 -0.03396 -0.01922 Slope -0.01506 -0.08299 -0.01975 -0.18998 0.00415 -0.02188 0.06398 -0.06561 TPH -0.27466 -0.33113 0.02123 0.21458 -0.00391 0.02021 0.03531 -0.01574 BA -1.62710 0.24643 0.10652 0.08284 -0.82738 -0.23636 -0.08002 -0.19089 CCF 1.93698 -0.34058 -0.17218 -0.20087 0.89688 0.26591 -0.00354 0.07759 Unexpectedly, the MSN Type 3, with less information, was less biased than M S N Type 2 (55 versus 42) (Table 28). However, MSN Type 2 was considerably more precise than MSN Type 3. MSN Type 1 was superior to the two other M S N types, with the lowest criteria values. Hence, the MSN Type 1 model was further analyzed. Table 28. Bias, mean absolute deviation (MAD), and RMSE values for the three types of MSN for each of five runs and averaged over the five runs. No. M S N Type 1 M S N Type 2 M S N Type 3 Run Target (Four height classes) (Two height classes) (No height class) Plots for Each Bias MAD RMSE Bias MAD RMSE Bias MAD RMSE Run 1 68 36 638 1,432 111 813 1,492 43 2,250 3,193 2 65 -35 666 1,547 61 800 1,601 -3 2,073 3,200 3 65 154 576 1,214 120 718 1,234 1 2,192 3,103 4 64 -143 792 1,802 -111 880 1,661 230 1,981 2,879 5 71 58 594 1,323 93 791 1,405 -59 2,166 3,099 Mean 66.7 14 653 1,463 55 801 1,479 42 2,133 3,095 4.4.2 M S N Type 1 Model 4.4.2.1 Variable Validation To check whether the reference plots constituted a reasonable pool for estimating the target plots, the M S N report provides a test of validity for the selected variables. For each reference plot, its second most similar neighbour was assigned (the most similar being the plot itself) and paired t-tests were used to compare the observed and predicted values (test for average difference is equal to zero). Table 29 shows the results of 16 regeneration variables and six selected overstory variables using reference observations for Run 1. Similar results were obtained for the other four runs and their tables are given in Appendix V. In two out of the five MSN runs, only two significant differences (a=0.05) existed between the observed and predicted values for number of residual trees per ha (shade intolerant species in Run 1). These results confirmed that the reference plots represented the target plots well and that estimates were reasonably accurate. 39 Table 29. Average observed versus average predicted regeneration per ha for the 265 reference plots of Run 1. SPECIES' OBSERVED PREDICTED STD DIFF 4 RESID 2 MEAN RMSE 5 R-SQ 6 PROB >T MEAN STD.DEV 3 MEAN STD.DEV MEAN STD.DEV Toll 1790.472 5846.993 1184.385 2319.511 0.025 0.227 606.087 5587.686 0.1032 0.099 Tol2 487.404 913.566 427.117 840.496 0.016 0.339 60.287 1259.449 0.0007 0.332 Tol3 205.615 470.781 187.857 469.840 0.008 0.278 17.758 619.932 0.0174 0.569 Tol4 309.117 777.651 218.694 670.576 0.020 0.238 90.423 1063.683 0.0044 0.070 Semil 1242.102 3058.170 1401.921 3743.925 0.009 0.274 -159.81 4685.457 0.0040 0.406 Semi2 490.672 1326.874 556.562 1639.911 0.013 0.390 -65.891 2029.786 0.0059 0.457 Semi3 128.974 409.047 154.208 469.881 0.011 0.276 -25.234 615.214 0.0007 0.568 Semi4 183.649 560.178 217.294 595.506 0.011 0.262 -33.645 779.412 0.0087 0.363 Intoll 375.713 1 163.393 281.792 809.875 0.013 0.202 93.921 1425.527 0.0001 0.203 lnto!2 259.351 931.520 144.396 560.511 0.019 0.181 114.955 1081.654 0.0006 0.048* Intol3 98.132 471.641 67.291 408.564 0.021 0.409 30.842 608.378 0.0027 0.293 Intol4 246.736 1441.196 220.106 1261.485 0.003 0.169 26.630 1507.493 0.1475 0.766 Hardl 186.453 919.773 173.834 949.892 0.002 0.257 12.619 1338.878 0.0006 0.826 Hard2 194.864 915.742 193.460 966.846 0.000 0.445 1.404 1323.957 0.0001 0.981 Hard3 175.238 760.402 227.106 831.003 0.014 0.307 -51.868 1140.696 0.0006 0.288 Hard4 601.411 1603.193 772.909 1974.383 0.023 0.327 -171.49 2432.384 0.0084 0.118 Site series 3.487 1.503 3.570 1.301 0.012 0.163 -0.083 1.145 0.4584 0.388 TPH 996.887 1031.581 889.906 870.217 0.021 0.100 106.981 531.347 0.7459 0.192 BA 9.871 12.954 8.586 12.173 0.021 0.151 1.284 9.210 0.5449 0.108 Elevation 1117.491 228.854 1118.011 225.627 0.001 0.153 -0.521 132.690 0.6883 0.980 Time-since-disturbance 11.340 6.156 11.189 5.956 0.007 0.182 0.151 4.199 0.5783 0.707 CCF 47.145 58.652 40.983 54.866 0.024 0.144 6.162 37.283 0.6275 0.095 Tol refers to shade tolerant species, semi to shade semi-tolerant species, intol to shade intolerant species, and hard to hardwood species. The numbers refer to height classes 1 to 4. 2RESID refers to Observed-Predicted. 3STD refers to standard deviation. 4STD DIFF refers to standardized difference values. 5RMSE: root mean square error. 6R-SQ: coefficient of determination. * indicates a significant difference from a mean of zero (a = 0.05). 4.4.2.2 Frequency Selection of Target Plots Another useful diagnostic tool for measuring the quality of the sampling and the prediction is the number of times each reference plot was selected as a second-MSN for both reference and target plots, and the normalized distance associated with them. For the reference plots, on average about 15 plots were selected three times as most similar neighbours, three plots were selected four times, and one plot was selected five times. However, only about two reference plots were selected three times as most similar neighbours for target plots. The MSN distance distributional statistics for target plots 40 provided in the M S N report showed that over than 70% of the distances between the target plots and their most similar neighbour reference plots had values within the first three distance distributional classes (out of 10). These results indicate the closeness of the prediction. Poor fits between target plots and their selected MSN, indicated by extreme distance values were negligible. As the MSN runs used different data and variable sets, comparisons of distances among runs was impossible. 4.4.2.3 Performance of the MSN Type 1 Model The comparison between the target plots and their selected most similar neighbour was conducted in two different ways, each using a combination of two different criteria. First, the number of match categories and the RMSE resulted in classifying the plots into nine different plot categories (Table 30). About 82% of the plots were classified as "moderate match" and nearly 48% of the plots had low RMSE. The combination "moderate match-low RMSE" was highest at 37 % followed by "moderate match-medium RMSE" and "moderate match-high RMSE". "Good match-low RMSE" and "poor match-high RMSE" combinations represent the best and the worst predictions and represent about 11% and 2.5% of the matches respectively. Table 30. Results of a comparison between true and most similar neighbour data for the target plots using a combination of RMSE and match category. R M S E Sample Size Match Category Total Good Moderate Poor 68 12 19 0 31 65 6 28 0 34 Low 65 5 31 0 36 64 8 17 0 25 71 5 27 0 32 Average 66.6 7.2 24.4 0.0 31.6 68 2 18 0 20 65 3 16 1 20 Medium 65 1 17 0 18 64 1 20 1 22 71 2 20 2 24 Average 66.6 1.8 18.2 0.8 20.8 68 2 13 2 17 65 1 10 0 11 High 65 1 7 3 11 64 0 14 3 17 71 2 13 0 15 Average 66.6 1.2 11.4 1.6 14.2 68 16 50 2 68 65 10 54 1 65 Total 65 7 55 3 65 64 9 51 4 64 71 9 60 2 71 Average 66.6 10.2 54.0 2.4 66.6 41 Three of the nine combinations were chosen to illustrate graphically the comparison between the target and the predicted regeneration (Figure 6). For the "good match-high RMSE", all the plots had at least 13 cells with no regeneration (zeros), the regeneration differences between the filled-in cells were very high, and the regeneration type (advance and subsequent) was mismatched between some of the target and their neighbour plots. Table 31. Classification results of the comparison between true and most similar neighbour data for the target plots using the combination of ratio of RMSE to the actual regeneration and plot match category. Ratio Sample Size Match Category Total Good Moderate Poor 68 7 24 1 32 65 4 25 1 30 Low 65 2 27 2 31 64 4 23 3 30 71 4 26 1 31 Average 66.6 4.2 25.0 1.6 30.8 68 3 13 0 16 65 2 14 0 16 Medium 65 3 12 1 16 64 1 12 1 14 71 1 17 1 19 Average 66.6 2.0 13.6 0.6 16.2 68 0 9 1 10 65 2 12 0 14 High 65 1 8 0 9 64 3 13 0 16 71 0 13 0 13 Average 66.6 1.2 11.0 0.2 12.4 68 6 4 0 10 65 2 3 0 5 Undefined 65 1 8 0 9 (regeneration^)) 64 1 3 0 4 71 4 4 0 8 Average 66.6 2.8 4.4 0.0 7.2 68 16 50 2 68 65 10 54 1 65 Total 65 7 55 3 65 64 9 51 4 64 71 9 60 2 71 Average 66.6 10.2 54.0 2.4 66.6 42 Poor Match - High RMSE 12000 -10000-TO £ 8000-O rat 6000 o c a> O) 4000-0) a. 2000-0-|P70-1 r_P61-1 . • • _ n ,n n II n I . I Tl T2 T3 T4 SI S2 S3 S4 ll 12 13 14 HI H2 H3 H4 Species group Moderate Match - Moderate RMSE re 4000 3500 3000 Q 2500 S 2000 0) c 0) 1500 O) _; 1000 500 0 IF51-2 DPI4-1 I tl Tl T2 T3 T4 SI S2 S3 S4 ll 12 13 14 HI H2 H3 H4 Species group Good Match - Low RMSE IP12-1 DF12-2 800-r 7CO- • re 600 • o 5 C 0 -re k_ 4 0 > -V c 3 0 0 -Re 2 0 0 -100 • 0 -T l T2 T3 T4 SI S2 S S) 11 12 13 14 HI H2 H3 H4 Species group Figure 6. Observed and estimated regeneration of three plots illustrating three different criteria combinations. The black bar is the true regeneration of the target plot, and the white bar is the regeneration of the selected reference plot by MSN as the most similar neighbour (T: shade tolerant species, S: shade semi-tolerant species, I: shade intolerant species, and H: hardwood species. Numbers 1 to 4 refers to height classes). A comparison using a combination of the number of matched categories and the ratio of the RMSE to the observed regeneration of target plots provided 12 plot combination categories (Table 31). The notable differences from the first comparison are that: (1) the 43 "poor match-high ratio" plots combination, considered as representing the unsatisfactory predictions, decreased from 2.4 to 0.3%; (2) the undefined plot category represented about the 11%; an undefined ratio is defined as a plot that had no regeneration (zero) but its RMSE was greater than zero (this fact resulted from an over-estimation); and (3) 4% of the combination "good match-undefined ratio" was classified by the first comparison as "good match-low RMSE" combination. Like the first comparison, the combination "moderate match-low ratio" had the highest percentage of about 38% followed by "moderate match-medium ratio" and "moderate match-high ratio" classes with 20 and 17%, respectively. Two of the 11% of the plots classified as "good match-undefined ratio" represented perfect matches. These plots were classified as "good match-low RMSE" by the first comparison. The remaining plots were previously classified as having moderate to high RMSE. 4.4.2.4 Causes of Extreme Regeneration Predictions The plot of the bias versus the most important independent variables, particularly basal area of large trees, trees per ha, crown competition factor, and aspect displayed the same distribution form and revealed no pattern in any of the five data sets. However, about 9% of the plots were outside the band bounded by ± 1000 stems per ha. Figure 7 shows the distribution for Run 1. Graphs for other runs are given in Appendix VI. Close examination of these outlier plots showed disparities between the trees per ha, basal area, and crown competition factor for the observed plot relative to the paired reference plots (Table 32 for Run 1; tables for the other runs are given in Appendix VII). Table 32. Comparison between the auxiliary variables of the outlier target plots and most similar neighbour plots for Run 1. Plot Yrsince Siteprep Site Aspect Elevation Slope Slpos. TPH BA C C F Adv. series Regen 72-1 21 none 05 164 1090 50 Middle 825 33.57 150.59 No r _ _ ~ 23 - none ' 04". ' . 22S .'Middle; H f 5 2 5 - •'28.0.4- 125.27 • Y e s ! 62-2 9 none 03 202 1190 16 Middle 1600 0.85 6.26 No [j-,(i-2 10 none .:, 04 1140 8 ' Middle 111125 4.23", 20.40 • N o J i 124-2 8 none 01 66 640 34 Middle 825 44.67 205.93 No : 124-4 none 01 n i l 25' Middle ~ 1450 29.23 147.85" " No Yrsince: time-since-disturbance, Siteprep: site preparation, Slpos: slope position, TPH: number of residual trees per ha, BA: residual basal area per ha, CCF: crown competition factor. * shaded rows represents selected most similar neighbour plots. Comparing the average values of the continuous auxiliary variables and the number by category of the class variables of outlier target plots with those of their paired reference plots for the plots that were poorly predicted (poor match-high RMSE), confirmed the disagreement between the target plots' stand density indicators (BA, TPH, and CCF) and those of their paired reference (Tables 33 and 34). Difference in regeneration composition (advance and subsequent) appears to be another factor that could influence the predictions. Three of the five runs experienced this difference. Tables covering other runs are given in Appendix VIII. 44 TPH v e r s u s Bias w re 5 3000 2000 1000 -I 0 -1000 -2000 i % 2000 4000 6000 T P H CCF v e r s u s Bias re m 3000 2000 1000 I • 0 -1000 -f -2000 - t 0 200 400 CCF 600 A s p e c t v e r s u s Bias 3000 2000 -I w 1000 re CO 0 -1000 -j -2000 0 20 40 60 80 A s p e c t Figure 7. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 68 target plots in Run 1 of the MSN model. Bias is observed minus predicted regeneration. 45 Table 33. Average values of the auxiliary variables of the reference and target (outliers) plots of Run 1. Plot Type Yrsince Siteprep #. SS # Aspect # Elevation Slope Slposit # T P H B A C C F 997 10 47 Reference 11 Bbrush 11 01 44 Flat 4 1117 27 Level 11 (265 Brush 16 03 91 N 30 Lower 35 plots) Burn 70 04 72 NE 24 Middle 178 Mecha. 11 05 43 E 45 Plateau 11 None 157 06 04 SE 28 Upper 30 07 08 S 43 08 03 SW 46 W 25 NW 20 Target 13 Bbrush 0 01 1 Flat 0 973 33 Level 0 (3 plots) Brush 0 03 1 N 0 Lower 0 Burn 0 04 0 NE 1 Middle 3 Mecha. 0 05 1 E 0 Plateau 0 None 3 06 0 SE 0 Upper 0 07 0 S 2 08 0 SW 0 W 0 NW 0 1083 26 121 Yrsince: time-since-disturbance, Siteprep: site preparation, SS: site series, Slposit: slope position, TPH: number of residual trees per ha, BA: residual basal area per ha, CCF: crown competition factor. Table 34. Comparison between auxiliary variables values of the plots that had "poor match and high RMSE" with those of their selected most similar neighbour plots (shaded rows represent the selected most similar neighbour plots). Plot Yrsince Siteprep Site Aspect Elevation Slope SI T P H B A C C F Adv. series position Regen Run 1 70-1 10 None 04 SW 1190 52 Middle 1400 0.7 6 No t 61-1 _ None 04 " : r - :i22*6 % 35 Middle "'r160CT 1.7 11 '•' 106-6 7 None 04 SE 955 33 Middle 0 0 0 No .66-2 . , . .H - None 04 E 990 .• 2S ""~M"idJlc 250 " "6- • .4 - " N<LJ Run 3 43-1 10 None f)l E 1380 25 Middle 850 34 142 Yes OO-I 10 Vine 01 ISllP 1145 24 Middle 525 19 " 74 j N o J 104-3 12 Mech 03 E 780 8 Middle 425 12 66 No H4-2 12 Mixh 03 "SE 785 IS Middle ^J25 ' .5.2" 3 24 -""'"' " N o ~l 136-1 10 None 04 S 815 32 Middle 625 3.8 21 No f-81-2 . " 9 " None " ^ 0 4 ^ • SVJT" • ' -90W 32 TMiddfc * 110.6 PSow) Run 4 19-1 13 None 03 s 1230 28 Middle 2625 2.6 18 No 61-1 None -. ' 04 s '""1220 35 Middle 1600" 1 7 " Yes ] 66-2 i i None 04 E 990 28 Middle 250 6 24 No 100-6 llll^i None 04 Sb 95^  ...33 Middle llHiil 9.:' •• i l l i l " > l d _ J 96-6 6 None 04 SW 1018 12 Middle 3050 12.6 67 Yes • 85-1 """""l 1 - Burn • •' 03 N -2ii tMiddle : 3250 • 9 . - 45- NoTTl Yrsince: time-since-disturbance, Siteprep: site preparation, Slpos: slope position, TPH: number of residual trees per ha, BA: residual basal area per ha, CCF: crown competition factor, adv. Regen.: advance regeneration . * shaded rows represents selected most similar neighbour plots. 46 4.5 Comparison of Approaches Like MSN, the tabular model with four height classes (Type 1) produced the lowest values for the three criteria compared to using two or no height classes (Types 2 and 3) (Tables 35 to 37). Table 35 shows that the bias produced by the M S N model was low compared to the tabular method. Although M A D did not differ substantially between the methods and both had almost the same RMSE levels, M S N produced slightly lower values. The ranges of the three criteria values were wider for the M S N approach. Table 35. Bias, mean absolute deviation (MAD), and RMSE values of Type 1 M S N and the corresponding tabular approach for each run and averaged over the five runs. Run Number of target plots Four Height Classes M S N Tabular Bias M A D R M S E Bias M A D R M S E 1 68 36 638 1,432 -110 698 1,472 2 65 -35 666 1,547 -188 705 1,407 3 65 154 576 1,214 -144 773 1,578 4 64 -143 792 1,802 -99 660 1,298 5 71 58 594 1,323 -200 813 1,701 Mean 66.6 14 653 1,463 -148 730 1,491 Unlike the MSN approach, where biases alternated between negative and positive values, the tabular approach produced consistently negative biases (Table 35). This was due to the rule set for assigning imputation tables to target plots that did not possess corresponding tables. This situation occurred when, for example, a given table was based on only two plots and both plots were in target data set. All the candidate plots that experienced this problem and belonged to either dry and wet sites were assigned regeneration from tables for mesic and slightly dry stands that had more abundant regeneration. Table 36. Bias, mean absolute deviation (MAD), and RMSE values for Type 2 M S N and the corresponding tabular approach for each run and averaged over the five runs. Run Number of target plots Two Height Classes M S N Tabular Bias M A D R M S E Bias M A D R M S E 1 68 111 813 1,492 -557 1,203 2,098 2 65 61 800 1,601 -612 1,185 1,989 3 65 120 718 1,234 -626 1,231 2,104 4 64 -111 880 1,661 -518 1,077 1,860 5 71 93 791 1,405 -655 1,404 2,287 Mean 66.6 55 801 1,479 -594 1,220 2,068 47 Table 37. Bias, mean absolute deviation (MAD), and RMSE values of Type 3 M S N and the corresponding tabular approach for each run and averaged over the five runs. Run Number of target plots No Height Classes M S N Tabular Bias M A D R M S E Bias M A D R M S E 1 68 43 2,250 3,193 -788 2,504 3,568 2 65 -3 2,073 3,200 -939 2,281 3,121 3 65 1 2,192 3,103 -903 2,470 3,460 4 64 230 1,981 2,879 -608 2,250 3,026 5 71 -59 2,166 3,099 -911 2,742 3,852 Mean 66.6 42 2,133 3,095 -830 2,449 3,406 The approaches were also compared using the combination of the criteria previously used for assessing the MSN Type 1 model. The results of the combination of number of matched categories with RMSE, and number of matched categories with the ratio of RMSE to the actual plot regeneration for tabular and MSN models are shown in Tables 24 and 25, and 30 and 31, respectively. The results achieved with the M S N model were quite different from those produced by the tabular model. When the "match category-RMSE" combination was used (Tables 24 and 30), on average, both approaches yielded almost the same percentage of RMSE categories (low, medium, and high RMSE). However, 86% of the plots classified by the MSN approach were comprised of plots that were good and moderate matches; only 51% were produced by tabular approach. The tabular approach produced as many moderate as poor matched categories (Table 24). MSN showed a clear superiority over the tabular approach by classifying 10% more of the plots as "good match-low RMSE", and 10% plots less in "poor match-high RMSE" combinations (Tables 24 and 30). Similarly, using the number of matched categories with the ratio of RMSE to the actual regeneration combination, the MSN approach consistently produced higher percentages of plots that fell in the "good match with low ratio" combination. For four runs out of five, no plot was classified in the unsatisfactory performance category represented by the combination "poor match-high ratio" combination (Tables 25 and 31). The tabular approach resulted in classifying 13% of the plots in the "poor match-high ratio" combination. 4.5 Sensitivity of Prognosis 8 0 to M S N and Tabular Regeneration Predictions Testing the sensitivity of Prognosis30 to M S N regeneration predictions revealed that small volume differences existed between the observed and predicted regeneration for the three fit categories (Table 38). Ranges of differences were observed within each of the three fit categories. As expected, the highest differences were observed in the "poor match-high RMSE" plot category and the standard deviations of volume differences were smaller for the "good match-low RMSE" plot category. Plots 2 (106-6) and 4 (104-3) of the "poor match-high RMSE" plot category are examples of Prognosis80 apparent sensitivity and insensitivity to MSN regeneration predictions, respectively. Examining 48 the characteristics of these plots showed that Plot 4 and its most similar neighbour had the same site series and aspect, were highly stocked, and both had regeneration in height classes 3 and 4, considered as having a high probability of survival. Plot 2 differed with its selected most similar neighbour plot in aspect, slope, stand density measures, residual trees composition, and had a disproportionate amount of regeneration in height classes 3 and 4. Examining the remaining plots did not show any pattern that enabled identification of sensitive variables. Table 38. Summary of sensitivity analysis for the MSN Model Category Plot Plot Plot type Regeneration TPH 1 Merchantable Difference STD 2 Average number id volume difference Good 1 57-2 Observed 0 900 308.6 50.1 -9.7 Match 58-2 Predicted 0 308.6 & 2 114-2 Observed 743 825 265.7 " " 32.8 Low 114-4 Predicted.: 0 232.9 RMSE "12-2 Observed 743 275 240.4 -81.9 12-1 Predicted 743" "322.3 4 12-1 Observed 743 . 275 58.8' 104 12-2 Predicted 743 48.4 Moderate 1 93-1 Observed 10402 1400 437.4 -51.5 74.8 7.5 Match 29-2 Predicted 11888: & 2 29-3 Observed 7430 475 306.1 -29 Medium Tl#2; Predicted ~ ~ ~ 17089" • IJPIX RMSE _ 125-1 Observed 6687 0 111.7 I" 111.7" 86-1 Predicted 0 0 4 116-1 Observed 8916 375 308.7 "99-4 Predicted I486 '310" Poor 1 70-1 Observed 26748 J400-. 113.6 :132.6_ 91.6 21.5 Match "61-1 Predicted 89l6 " 246.2 & 2~~Z 106-6 Observed 4458 M2 2 170.6 High 66-2 Predicted 22290 "171.6" RMSE 43-1 Observed 19318 33 f -39.8 60-1 Predicted, 178321 370.8 104-3 Observed 33435 425 273.5 Z...J 0.5" 104-2 Predicted 14117' 273 5 136-1 Observed 17089 625 312.5 65.9 81-2 Predicted '""' 14860 246.6 6 19-1 Observed 8173 2625 258 22.1 61-1 Predicted 89161 235.9" ~_T7 66-2 Observed 22290 425_ 603.9 96 106-0 _Predicted 4458 507.9" 8 96-6 Observed 15603 3075" 258.8 -10.9 85-1 Predicted 8961 269.7' . A TPH: number of residual trees per ha; STD: standard deviation of the difference Table 39 shows the results of the sensitivity analysis of Prognosis'^ for the tabular regeneration predictions. On average, the differences of the projected merchantable volumes of the three plot categories were small. Nevertheless, the standard deviation of the "poor match-high RMSE" plot category was more than three times higher than the two other plot categories. The variability of the volume differences for the two other categories was almost equal and their standard deviations were higher than their 49 respective average differences in volume. Individually, some of the plots classified as "poor match-high RMSE" yielded small differences in their projected volumes and were comparable to the plots in the two other fit categories. Unexpectedly, and unlike MSN, those plots classified as "moderate match-medium RMSE" had slightly smaller average differences and standard deviations than the plots classified as "good match-low RMSE". Table 39. Summary of sensitivity analysis for the Tabular Model Category Plot Plot_id Plot type Regeneration TPH 1 Merchantable Difference STD 2 Average # volume diff. Good 1 65-2 Observed 743 400 _ 328.4 95.4 46.5 25.8 Match " " 45' Predicted 0 233.o" & 2 135-2 Observed 0 1485" 444.3 ~0 Low 23 Predicted 0 ----- ,444.3" RMSE 37-2 Observed "" 743 240.1 7.9 "61 Predicted 0 " 232.2" "A " 140-6 Observed 0 4"5 1ft (> 0 34 Predicted 0 16.6 Moderate 1 51-2 Observed 6687 825 212.3 -85.1 44.36 -19.3 Match 40 Predicted 13005" 297.4" & .J?. 122-1 Observed 2972 l"650" 634.4" J)J Medium ""40" Predicted 13005 635.1 RMSE 3 122-2 Observed 2229 1275 601.3 I. „ -3-5 _ 40 Predicted 12136 604.S ~~4 132-3 Observed 14860 1150 232~.8~ 5S Predicted -• 5674 220^ 8 Poor 1 49-1 Observed 5201 3275 294.2 1J.5 142.87 -39.4 Match 50 Predicted 15285 ..' 282.7"" & 2 70-1 Observed 26748 1400 113.6 . . . . High "29 Picdklcd 12402 315.1 RMSE " 3~ 14-1 Observed 2972 0 332.2 135.4 " 41' " •Predicted 16346 196.8" 4 89-2 Observed 11145 300 327.1 J7~.9 16 PrahUfl 17157 . 309.2 _J? 106-4 Observed "2972 325 273.2 15.4 2S Predicted "18327 257.8 ft 36-1 Observed 34178 1400 2<)ft4 -295.5 " 29 Predicted 11395 501,9 ~T..~ 7-1 Observed 50524 _400" 277.2 "-"641 16" Predicted 10.ST 341.3 Observed 2927 ' 50 362.4 61.4 Predicted ft, •r • • \ TPH: number of residual trees per ha; STD: standard deviation of the difference Plots 1 (49-1) and 6 (36-1) are examples of cases that generated contrasting results (small and big differences) for the "poor match-high RMSE" plot category. Examining the plots' characteristics revealed clear differences in species composition and type of regeneration between the target plots and those of the tables from where the estimates were imputed. For plot 1 with a small volume difference, the observed regeneration in height classes 3 and 4 were closely predicted by tabulation, especially in two of the species groups. Target plot 6, which yielded the biggest merchantable volume difference, 50 had more shade tolerant and semi-tolerant species, whereas its corresponding table contained only serai shade intolerant species. There was no single variable that was apparent in the sensitivity analysis that provided a pattern to the results. The results showed that poor regeneration prediction did not necessarily impact on the merchantable volume yield projected over 50 years, but that there was a higher probability of getting very close agreements in the "good match-low RMSE" plot category. 51 5. Discussion Results of this study provided information about regeneration and the performance of imputation techniques in predicting the establishment of regeneration in complex stands in the ICHmw2 variant in the vicinity of Nelson. Regeneration is an important component of stand dynamics and today's decisions on its establishment will affect the development of these stands for many decades. The natural regeneration present was highly variable and the average regeneration per hectare found was consistent with another study carried out on partially cut stands of the same variant (Delong and Butt 1994). However, the sampling design did not allow determination of the regeneration status (advance and subsequent). In this study, advance regeneration became apparent only when a seedling was chosen as a "best tree" and destructively sampled for age. However, the best trees were not randomly selected and any attempt to predict the age of the non-sampled seedlings would be biased. Similar studies in the ICH zone have shown that advance regeneration made up 10 to 13% of the regeneration (Delong and Butt 1994, Delong 1994, Peterson et al, 1998). In contrast, Sacenieks and Thompson (2000) found advance regeneration was the largest component of the natural regeneration in the Interior Douglas-Fir Dry Mild biogeoclimatic subzone (IDFdm2) 10 years after harvesting. Due to reliance on the artificial regeneration, particularly plantating, advance regeneration is often overlooked and not protected during harvesting. As a consequence, it suffers considerable damage that can cause sudden or slow death (Tesch et al. 1993, Delong and Butt 1994). Pothier (1996) found that mechanical harvesting destroyed up to 60% of advance regeneration in boreal forests. It is probable that the proportion of advance regeneration in ICHmw2 is higher than 13% and that studies conducted on similar sites under-estimated it by not accounting for damage caused by harvesting and site preparation. The species composition of the natural regeneration reflected the species composition of the residual overstory. On average (by plot and per hectare), the shade tolerant and shade semi-tolerant species predominated. The hardwood species had slightly larger numbers of residual trees than shade intolerant species, but showed lower regeneration. About 11% of the sampled plots had no regeneration and field observations showed high invasion by ground vegetation. However, the current conditions of the sites that were disturbed many years ago do not represent the same conditions that existed immediately following the disturbance. High brush levels may have partially or totally inhibited the regeneration establishment on those sites. According to Seidel (1979), seedbeds on sites with low brush potential stay receptive much longer. Scarified sites were well stocked followed closely by non-treated sites. This is in accordance with Delong's (1994) results. Regeneration on intact sites (no site preparation) was dominated by shade tolerant species, whereas shade intolerant species were prominent on scarified sites. There seemed to be a direct relationship between the 52 species composition and the site preparation treatment. Probably scarification exposed mineral soil and destroyed partially or entirely advanced regeneration. Ferguson and Carlson (1993) reported mechanical or prescribed burning treatments generally increase the abundance of subsequent regeneration but decrease advance regeneration. According to Peterson et al. (1998) and Delong (1996), advance regeneration was abundant in ICHmw2 and advance regeneration of western redcedar was high, providing a good potential for release. Ferguson et al. (1986) also noted that western redcedar often occurs as advance regeneration when found in the understory. As McClure and Lee (1993) found in their study, probably most shade tolerant species in ICHmw2 occur as advance regeneration and only the knowledge of pre-harvest stand conditions may help determining the abundance of advance regeneration and the damage that it may have suffered during the harvesting and site preparation phases. Aspect was an important factor that contributed to the regeneration abundance. This supports the findings of other researchers (Ferguson et al, 1986, Butt and Bancroft 1990, Delong 1994, Przeczek 2001). Sites conditions of cool aspects (light, substrate, soil moisture and nutrients) may favour seed germination, germinant survival, and growth of seedlings. According to Delong (1996), sites in the ICHmw2 may have enough moisture available and competition for light may be the more significant limiting factor. In contrast to Williamson's (1973) study, where regeneration density of Douglas-fir in the Western Oregon cascades increased with the time-since-disturbance, this study showed that the regeneration was variable. The highest regeneration level was reached five to ten years after disturbance, followed by a slight decrease to its initial level five years later (15 years after disturbance). Figure 3d (page 22) showed dominance of shade tolerant species five to 10 years after disturbance. This period may correspond to a delay of one to five years prior to the release of post-harvest advance regeneration. Braumandl and Curran (1992) and Helms and Standiford (1985) reported the same period of response of advance regeneration to disturbance in ICHmw2 and in California respectively. Shade intolerant and hardwood species were favoured in the short term. Establishment of young seedlings of shade intolerant and hardwood species 25 years after disturbance indicates a long-term receptiveness of the sites to natural regeneration. The mixed species composition of the stands was evident. Fifteen species were tallied in the overstory. Even though plots were selected from a range of regeneration methods taken from the ISIS database (e.g., clearcut, seedtree, shelterwood, and tree selection), many stands did not fit the defined methods and considerable variation existed within stands. Consequently, residual basal area was substituted for the regeneration method for characterizing the stands. Sampling was concentrated in partially disturbed and open stands; more than 85% of plots had basal areas less than 20 m 2. As the plots were harvested within the last 25 years, variations in basal area within and between the stands resulted mostly from forest canopy manipulations. The regeneration composition of dense and open stands agreed with the theory of natural succession. In open stands, where light availability was not limiting, pioneer species increased in proportion at the expense of climax species. Shade tolerant species 53 increased their abundance after 10 years; probably the response of advance regeneration to release was triggered after the level of resources (light and nutrients) on the sites decreased to the point that the fast-growing species were not competitive anymore (Puettman et al. 1996). The success of the tabular and MSN imputation approaches depends largely on the data used for analysis. The mixed species composition of the stands was apparent from the tables. Developed tables 18 and 19 (pages 30 and 31) illustrate the tabular approach and show the variation in the regeneration per ha by shade tolerance group by height class on dry sites for dense and open stands during the first 5-year period after disturbance. About 15 species were present in both tables and all these species contributed to the basal area of the residual trees used to classify the stands. Dense stands tend to have more regeneration than open stands. Shade tolerant and shade semi-tolerant species dominated the regeneration of dense stands. These results are consistent with the literature. High standard errors of the mean for the developed tables and the lack of an apparent regeneration trend lead to the question of whether the stratification of chosen variables for imputation was valid. Stratification by site series, basal area, and time-since-disturbance are supported by the significance of these variables in predicting the regeneration regression model and by theory. The time-since-disturbance is important to the succession of species, to the delay in response to release of advance regeneration, and to the development of invading shrubby competitors. However, perhaps the 5-year classes are not needed and only two 10-year classes would be sufficient for such a short period of study. The B E C system combines climatic, vegetation and site information (Braumandl and Curran 1992). Site series is used as surrogate for climate, moisture and nutrient regimes, and effect of competition from ground vegetation. As the number of wet sites was small, probably the stratification of the site series into three or less classes (dry, mesic, and wet) would improve the predictions. The effect of basal area seems to be mainly through seed supply. A cutoff of 5-m2 basal area was arbitrarily used to classify the number of plots into open and dense stands. This cutoff might seem low; however, selection of a higher level would result in creating tables with small sample sizes. Nyland (1997) considered a basal area of 15 m 2 per ha as low in uneven-aged northern hardwood stands, whereas a basal area greater than 40 m 2 was considered too high to enable natural regeneration in ICH zone (Delong 1994). It is also probable that the basal area is not contributing very much to the regeneration establishment and, consequently, is not needed. Several studies have found poor or no correlation between the basal area per ha and regeneration (Delong 1994, Kneeshaw and Bergeron 1996, Lundqvist and Fridman 1996, Sacenieks and Thompson 2000); regeneration was more affected by factors such as site conditions and competition from ground vegetation. Analyses aimed at determining useful values at which the chosen variables should be stratified were not conducted in this work. The choice and the number of variables were constrained by the available data used for the imputation. Adequate choice of variables and good stratification would necessarily uncover the variation translated to the model from the inherent diversity in the data itself. This feature will ensure realistic predictions 54 and measurement of the variation of the models that would not be obtained by using conventional methods. Unlike the regeneration imputation models of Ek et al. (1997), where coefficients of variation associated with the regeneration were stable at a given time after disturbance, continuing fluctuations of the coefficients of variation in this study suggest that the regeneration in these complex stands is very dynamic and variable. Probably other factors such as mortality and shift of a part of regeneration to the small tree strata are major components of the dynamic process. As more data become available, these models are easily updated or tailored to specific sites, treatments, and to a particular management plans or predictive models. Correlations between the regeneration and most of the independent variables were low. These might indicate that the independent variables are not useful predictors or the regeneration is highly variable. Although GENMOD analysis showed that basal area per ha, time-since-disturbance, and site series were important variables to predict the regeneration, descriptive analyses and the results of imputation approaches provided substantial evidence for the second alternative. Delong and Butt's (1994) findings were also consistent with these results. Trees per ha, basal area per ha, and crown competition factor were the highest correlated variables with the regeneration and they carried high weights in the selection of most similar neighbour plot. Little differences existed among the MSN runs and the procedure appears to be robust. According to the criteria used in the comparison, the three types of M S N had very low biases but the precision of MSN Types 1 and 2 were better and almost identical. As was expected, M S N Type 1, using four height classes, was the most accurate and was further analyzed. The reference plots estimates of the MSN Type 1 constituted a reasonable pool for target plots, indicating that field sampling covered the existing range of conditions. This was also supported by the small number of times each reference plot was chosen as the most similar neighbour for target plots Unlike tabular imputation, MSN modelling was done plot by plot. Stands of ICHmw2 are heterogeneous and microsite variation among plots within a stand affects regeneration success. The tabular approach predicts the regeneration by averaging the regeneration of the plots that have the same stand characteristics used in the tabulation process. The MSN regeneration predictions may have retained the variation inherent in the data, while some variation might be slightly reduced by the averaging effect of the tabular approach. Like predictions from the MSN Type 1 model, predictions using the tabular model with four height classes were more accurate than those using two or no height classes. This was an expected result; as more variables are included in the model, the accuracy of the predictions increase. The MSN model is able to make use of all available variables (continuous, categorical, or interval) and any kind of data (remote sensed and spatial data). However, the tabular approach is restricted to a few very important variables. 55 Although both approaches resulted in good predictions, M S N was more accurate. This was an expected result, because the MSN predictions are selected from the actual sample plots. Tabular imputation results may have been affected by averaging the regeneration of different plots within the group, by imputing the regeneration to the target plots from less reliable tables, or by using poorly stratified variables. Also, the wider range of bias, M A D , and RMSE obtained by M S N may indicate how it preserved the range of regeneration estimates inherent in the data itself. This is very useful for some purposes, where it may be more important to estimate extreme values than the means. When the combination of number of matched categories with RMSE and with the ratio of RMSE to the actual regeneration were compared, predictions of the M S N were also superior. The MSN results were closer to the actual distribution of regeneration categories (species group by height class) than those of the tabular approach. Also, the alternation between negative and positive biases for the MSN approach may be a good indication of reasonable predictions. Those provided by the tabular approach were constantly negative. The ability of MSN to use transformed attributes such as canopy structure information for wildfire or wildlife, enhances its flexibility and capacity to provide detailed information for different models, ranging from individual-tree or stand models to process-based models. Unsatisfactory predictions of the MSN were few and corresponded to those target plots that displayed mismatches of trees per ha, basal area per ha, and crown competion factor with their most similar neighbour. These variables drove the selection of the most similar neighbour plot, and the selected reference plots may be the closest that are available in the pool of the reference dataset. However, most of these target plots had larger basal areas per ha and smaller trees per ha than their selected neighbours. These results point to the usefulness of separating the basal area per ha and trees per ha into basal area per ha and trees per ha of small and large trees. Dense plots that contain a higher number of large trees may be undersampled. Moeur and Stage (1995) reported that poor MSN performance has been noted mainly for under-representation of particular conditions. This information is valuable since it gives indication of what conditions should be targeted for additional sampling to improve the predictions. The matching process also accounted for correlations between regeneration and the independent variables through canonical correlations. The presence of advance regeneration might have been another factor that increased prediction biases. Besides the causes cited for MSN, the tabular approach also is affected by the reliability of the tables used for imputation. Increasing the sample size of tables that were based on a small number of plots will definitely increase the precision of the predictions and the confidence of users. Other variables, such as seed crops, weather, bud and seed banks, diseases, insects, and competition from ground vegetation were cited in the literature as affecting regeneration establishment patterns. According to Fergusson et al. (1986), these variables can be represented without bias through random selection of sample plots, and sampling across a wide range of dates can average out their effects. Effects of these variables were indirectly accounted for in predicting the regeneration in this study through the use of 56 surrogate variables that can improve the predictions and substantially reduce the cost associated with field sampling. The good performances of both MSN and tabular approaches in predicting the • RP regeneration m ICHmw2 were corroborated by the insensitivity of Prognosis to using either observed or predicted values for the first 50 years of the projection. However, longer periods of simulation might reveal poorer results, particularly using the tabular predictions. The results of the sensitivity analysis should be interpreted cautiously and considered approximate rather than exact. Currently Prognosis does not include hardwood species component explicitly; rather they are treated as mountain hemlock1 (Hm) and modelled using the Northern Idaho equation. Hardwood species are an important part of ICHmw2 stand composition; therefore the projection of treelists containing hardwood species as inputs to Prognosis80 may yield unreliable volumes. Several target plots with large MSN distances had smaller prediction errors (measured by bias and root mean square error) than other target plots with smaller distances. This is not in agreement with Moeur and other's argument (1995) that unsampled plots without reasonable MSN candidates will have relatively greater MSN distances than unsampled plots with very similar neighbours. This is true only when regeneration is highly correlated with the independent variables. The M S N approach to predicting regeneration in complex stands was not only successful in this application, but improvements are possible. Such improvements can result from including spatial and geographic data that can easily be obtained from different sources (maps, aerial photos, satellite imagery). For example, regeneration may be predicted across different biogeoclimatic zones, planning units such as watersheds, or/and forest districts. Inclusion of geographic coordinates will refine the search of the most similar neighbour plot within a reasonable vicinity of the area to be analyzed. Even though the M S N Type 1 model (with more variables) was the best predictive model, M S N Type 2 (with two variables) performed almost equally well and calls into question whether four height classes are needed. As the Prognosis projects the regeneration based on the actual height and not on height class category, classifying the regeneration into two height classes will reduce the number of variables and facilitate the prediction of advance and subsequent regeneration. 1 The current version (2) of Prognosis3 0 recognizes only Pw, Lw, Fd, Bg, Hw, Cw, PI, Se, Bl, Py as leading species and treats the rest of species as being mountain hemlock (Hm). 57 6. Conclusions Shortage of data combined with lack of balanced data across the conditions present were cited as the main factors that precluded successful regeneration predictions in a previous study in the ICHmw2 (Boisvenue 1999). The main objectives of this study were to explore the applicability of using MSN and tabular imputation approaches to predict regeneration in these complex stands. It is clear that the performances of the imputation techniques depend implicitly on the data used in the analysis. As was hypothesized, both approaches were successful in predicting regeneration by making use of available data and avoiding distributional assumptions. Projections of volume by Prognosis80 for a 50-year period were not sensitive to differences in regeneration predictions from either imputation approach. The tabular approach had a simple structure and provided realistic and detailed postharvest regeneration by species group and height class for specified conditions. Modelled conditions were: two residual density classes, five time-since-disturbance classes, and five site groups. Lack of obvious trends in the tabulated regeneration may be due to the dominance of advance regeneration present in the study area. This hypothesis reflects limitations imposed by the sampling design. Separating advance and subsequent regeneration would likely make tabular predictions even more successful. The MSN procedure appears to be robust. Its strengths were the flexibility to make use of a large number of variables of different types and the ability to predict regeneration on plot by plot basis. The M S N approach was a better predictor of regeneration than the tabular approach. Including location information should enhance the quality of the predictions. The results confirmed that imputation techniques were successful in predicting regeneration establishment in the complex stands of ICHmw2. Numbers of unsatisfactory predictions using either approach were small and corresponded to target plots that had different density indicator variables than their predicted plots. The use of tables with low reliability as an imputation pool for target plots in the tabular approach, along with possible presence of advance regeneration in both approaches may have affected the predictions. An increase in the number of neighbours might improve the accuracy of estimates. K-nearest neighbour (K-NN) or k most similar neighbour (KMSN) could be explored to predict regeneration in complex stands of ICHmw2. 58 Literature Cited Anonymous. 1998. The state of Canada's forests- Highlights. For. Chron. 74:22. Barg, A.K. , and R. L. Edmonds. 1999. Influence of partial cutting on site microclimate, soil nitrogen dynamics, and microbial biomass in Douglas-fir stands in western Washington. Can. J. For. Res. 29: 705-713. Boisvenue, C. 1999. 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Oregon. 13 pp. 63 Appendix I - Tabular Imputation Models1 Table 1.1. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Slightly Dry" sites. Site Number Species Heij ;ht class All of plots 1 2 3 4 Heights Slightly 11 Bg 1013 135 0 0 1148 Dry Bl 405 68 68 0 540 Cw 1418 946 203 68 2634 Hw 540 338 675 540 2094 Sx 0 0 0 0 0 Tolerant 3377 1486 946 608 6417 Fd 946 135 338 68 1486 Pw 540 135 0 0 675 Semi-tolerant 1486 270 338 68 2161 Hardwood 270 0 0 0 270 Lw 203 135 0 0 338 PI 135 68 0 0 203 Intolerant 338 203 0 0 541 All Species 5471 1959 1283 675 9389 Table 1.2. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and "Slightly Dry" sites. Site Number of Species Height class All plots 1 2 3 4 Heights Slightly 6 Bg 0 0 0 0 0 Dry Bl 0 0 0 0 0 Cw 867 372 0 0 1238 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 867 372 0 0 1238 Fd 743 0 0 0 743 Pw 0 0 0 0 0 Semi-tolerant 743 0 0 0 743 Hardwood 495 619 1981 991 4087 Lw 619 0 0 0 619 PI 2229 372 0 0 2601 Intolerant 2848 619 1981 991 3220 All Species 4953 1362 1981 991 9288 e 1.3. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area c ass "Dense" and "Mesic" sites. Site Number of Species Height class All plots 1 2 3 4 Heights Mesic 2 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 372 2229 372 0 2972 Hw 1858 372 0 0 2229 Sx 0 0 0 0 0 Tolerant 2229 2601 372 0 5201 Fd 0 372 0 0 372 Pw 0 372 0 0 372 Semi-tolerant 0 743 0 0 743 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 2229 3344 372 0 5944 1 Tables showing the conditions that were not represented in this study (three conditions that had the number of plots equal to zero) are not included in this Appendix. 64 Table 1.4. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and "Mesic" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 1 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 743 743 0 0 1486 Hw 743 0 0 0 743 Sx 0 0 0 0 0 Tolerant 1486 743 0 0 2229 Fd 743 1486 0 0 2229 Pw 743 0 0 0 743 Semi-tolerant 1486 1486 0 0 2972 Hardwood 0 1486 0 0 1486 Lw 3715 743 0 0 4458 PI 0 0 0 0 0 Intolerant 3715 743 0 0 4458 All Species 6687 4458 0 0 11145 Table 1.5. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 7 Bg 0 0 0 0 0 Wet Bl 0 106 0 106 212 Cw 2123 955 531 318 3927 Hw 4776 0 0 106 4883 Sx 425 0 0 0 425 Tolerant 7324 1061 531 531 9447 Fd 1274 0 0 0 1274 Pw 0 0 0 0 0 Semi-tolerant 1274 0 0 0 1274 Hardwood 0 0 0 0 0 Lw 106 0 0 0 106 PI 106 0 0 0 106 Intolerant 212 0 0 0 212 All Species 8810 1061 531 531 10933 Table 1.6. Average regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 4 Bg 0 0 0 0 0 Wet Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 0 0 0 0 0 Pw 372 0 0 0 372 Semi-tolerant 372 0 0 0 372 Hardwood 0 0 557 743 1300 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 372 0 557 743 1672 65 Table 1.7. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 16 Bg 0 0 0 0 0 Bl 186 93 0 0 279 Cw 836 418 0 279 1532 Hw 0 0 0 0 0 Sx 93 0 0 0 93 Tolerant 1115 511 0 279 1904 Fd 1207 46 46 0 1300 Pw 139 139 0 0 279 Semi-tolerant 1347 186 46 0 1579 Hardwood 418 46 511 279 1254 Lw 0 0 0 0 0 PI 46 186 0 0 232 Intolerant 46 186 0 0 232 AH Species 2926 929 557 557 4969 Table 1.8. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 21 Bg 35 0 0 0 35 Bl 0 0 35 0 35 Cw 601 35 35 35 708 Hw 106 35 0 0 142 Sx 0 0 0 0 0 Tolerant 743 71 71 35 920 Fd 318 106 0 0 425 Pw 106 0 0 0 106 Semi-tolerant 425 106 0 0 531 Hardwood 0 142 71 601 814 Lw 389 283 71 0 743 PI 566 495 35 672 1769 Intolerant 955 778 106 672 2512 All Species 2123 1097 248 1309 4776 Table 1.9. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Slightly Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 22 Bg 68 34 0 0 101 Dry Bl 101 34 34 0 169 Cw 1756 608 270 169 2837 Hw 7059 101 34 0 7160 Sx 0 0 0 0 0 Tolerant 8984 777 338 169 10267 Fd 3344 304 68 101 3816 Pw 642 68 0 34 743 Semi-tolerant 3985 372 68 135 4559 Hardwood 1317 270 203 203 1993 Lw 0 0 0 0 0 PI 34 0 0 0 34 Intolerant 34 0 0 0 34 All Species 14320 1418 608 507 16853 66 Table 1.10. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Slightly Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 16 Bg 46 0 0 0 46 Dry Bl 93 93 0 46 232 Cw 557 93 232 46 929 Hw 372 418 139 418 1347 Sx 511 0 93 0 604 Tolerant 1579 604 464 511 3158 Fd 604 511 93 372 1579 Pw 0 0 46 0 46 Semi-tolerant 604 511 139 372 1625 Hardwood 464 557 743 2090 3854 Lw 0 510 46 0 557 PI 232 1115 511 1904 3761 Intolerant 232 1625 557 1904 4318 All Species 2879 3297 1904 4876 12956 Table 1.11. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Mesic" sites. Site Number of plots Species Heij ;ht class All Heights 1 2 3 4 Mesic 12 Bg 0 186 62 0 248 Bl 62 0 62 124 248 Cw 3467 557 186 124 4334 Hw 21795 1734 124 186 23838 Sx 0 0 0 0 0 Tolerant 25324 2477 433 433 28667 Fd 1238 62 0 0 1300 Pw 433 186 0 0 619 Semi-tolerant 1672 248 0 0 1919 Hardwood 0 248 124 186 557 Lw 62 0 0 0 62 PI 495 557 186 62 1300 Intolerant 557 557 186 62 1919 All Species 27553 3529 743 681 32506 Table 1.12. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Mesic" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 8 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 93 0 0 0 93 Hw 743 186 0 186 1115 Sx 93 186 0 0 279 Tolerant 929 372 0 186 1486 Fd 372 743 186 93 1393 Pw 0 0 0 0 0 Semi-tolerant 372 734 186 93 1393 Hardwood 929 0 93 929 1950 Lw 186 0 93 0 279 PI 0 279 93 0 372 Intolerant 186 279 186 0 650 All Species 2415 1393 464 1207 5480 67 Table 1.13. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 2 Bg 0 0 0 0 0 Wet Bl 0 0 0 0 0 Cw 4458 372 0 0 4830 Hw 743 0 0 0 743 Sx 0 0 0 0 0 Tolerant 5201 372 0 0 5573 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 372 372 0 0 743 PI 0 0 0 0 0 Intolerant 372 372 0 0 743 All Species 5573 743 0 0 6316 Table 1.14. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 5 Bg 0 0 0 0 0 Wet Bl 0 297 0 0 297 Cw 743 446 149 149 1486 Hw 297 0 0 0 297 Sx 0 0 0 297 297 Tolerant 1040 743 149 446 2378 Fd 0 0 149 0 149 Pw 149 0 0 0 149 Semi-tolerant 149 0 149 0 297 Hardwood 149 0 0 2080 2229 Lw 149 0 0 0 149 PI 0 0 0 0 0 Intolerant 149 0 0 0 149 All Species 1486 743 297 2526 5052 Table 1.15. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Wet 2 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 0 0 0 0 0 68 Table 1.16. Average regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Wet 4 Bg 0 0 0 0 0 Bl 0 0 0 186 186 Cw 372 186 0 0 557 Hw 0 0 186 0 186 Sx 0 186 0 186 372 Tolerant 372 372 186 372 1300 Fd 743 372 0 0 1115 Pw 0 0 0 0 0 Semi-tolerant 743 372 0 0 1115 Hardwood 0 0 0 186 186 Lw 0 186 0 0 186 PI 186 0 0 0 186 Intolerant 186 186 0 0 372 All Species 1300 929 186 557 2972 Table 1.17. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 17 Bg 393 44 0 44 481 Bl 0 0 0 0 0 Cw 219 350 262 87 918 Hw 131 44 0 0 175 Sx 44 0 0 0 44 Tolerant 787 437 262 131 1617 Fd 4982 2142 306 262 7692 Pw 393 262 44 87 787 Semi-tolerant 5376 2404 350 350 8479 Hardwood 44 262 175 1661 2142 Lw 437 437 44 87 1005 PI 1267 612 219 350 2448 Intolerant 1705 1049 262 437 3453 All Species 7911 4152 1049 2579 15690 Table 1.18. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 20 Bg 111 0 0 0 111 Bl 74 111 0 0 186 Cw 74 74 223 149 520 Hw 0 74 37 37 149 Sx 223 0 0 0 223 Tolerant 483 260 260 186 1189 Fd 372 297 37 223 929 Pw 186 334 37 74 631 Semi-tolerant 557 632 74 297 1560 Hardwood 223 372 111 1412 2118 Lw 0 297 297 557 1152 PI 223 0 0 260 483 Intolerant 223 297 297 817 1635 All Species 1486 1560 743 2712 6501 69 Table 1.19. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Slightly Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 7 Bg 212 106 0 0 318 Dry Bl 318 849 106 0 1274 Cw 3397 1380 106 318 5201 Hw 212 743 106 212 1273 Sx 212 0 0 0 212 Tolerant 4352 3078 318 531 8279 Fd 2654 637 212 106 3609 Pw 1380 1698 0 0 3078 Semi-tolerant 4033 2335 212 106 6687 Hardwood 106 212 212 2441 2972 Lw 1486 849 212 106 2654 PI 0 0 0 0 .0 Intolerant 1486 849 212 106 2654 All Species 9977 6475 955 3184 20592 Table 1.20. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Slightly Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 6 Bg 0 0 0 0 0 Dry Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 124 0 0 0 124 Sx 0 0 0 0 0 Tolerant 124 0 0 0 124 Fd 991 991 124 124 2229 Pw 124 0 0 0 124 Semi-tolerant 1115 991 124 124 2353 Hardwood 0 124 372 372 867 Lw 619 124 0 0 743 PI 0 0 124 124 248 Intolerant 619 124 124 124 991 All Species 1858 1238 619 619 4334 Table 1.21. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Mesic" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 5 Bg 0 0 0 0 0 Bl 1189 297 297 743 2526 Cw 149 0 0 149 297 Hw 446 149 0 149 743 Sx 0 149 297 446 892 Tolerant 1783 594 594 1486 4458 Fd 2378 892 0 743 4012 Pw 594 0 297 0 892 Semi-tolerant 2972 892 297 743 4904 Hardwood 0 149 446 2378 2972 Lw 149 0 0 0 149 PI 0 0 0 0 0 Intolerant 149 0 0 0 149 All Species 4904 1635 1337 4607 12482 70 Table 1.22. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Mesic" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 9 Bg 83 0 0 0 83 Bl 743 0 0 0 743 Cw 4458 1321 0 0 5779 Hw 413 83 83 0 578 Sx 3220 165 0 0 3385 Tolerant 8916 1569 83 0 10567 Fd 495 165 83 165 908 Pw 165 0 0 0 165 Semi-tolerant 660 165 83 165 1073 Hardwood 0 248 0 1073 1321 Lw 330 330 0 0 660 PI 0 0 0 83 83 Intolerant 330 330 0 83 743 All Species 9907 2312 165 1321 13705 Table 1.23. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 1 Bg 0 0 0 0 0 Wet Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 0 743 0 743 1486 PI 0 0 0 0 0 Intolerant 0 743 0 743 1486 All Species 0 743 0 743 1486 Table 1.24. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 9 Bg 83 0 0 0 83 Wet Bl 165 0 0 0 165 Cw 83 248 0 83 413 Hw 165 83 0 0 248 Sx 413 248 0 0 660 Tolerant 908 578 0 83 1569 Fd 495 165 0 0 660 Pw 0 0 0 0 0 Semi-tolerant 495 165 0 0 660 Hardwood 0 83 0 165 248 Lw 248 0 0 0 248 PI 0 0 0 0 0 Intolerant 248 0 0 0 248 All Species 1651 826 0 248 2724 71 Table 1.25. Average regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 et 3 Bg 248 0 0 0 248 Bl 0 0 0 0 0 Cw 0 495 0 0 495 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 248 495 0 0 743 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 743 743 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 248 495 0 743 1486 Table 1.26. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 2 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 372 372 0 0 743 Pw 743 0 0 0 743 Semi-tolerant 1115 372 0 0 1486 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 1115 372 0 0 1486 Table 1.27. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 8 Bg 0 0 0 0 0 Bl 0 0 93 0 93 Cw 93 279 186 372 929 Hw 0 0 0 0 0 Sx 0 0 93 0 93 Tolerant 93 279 372 372 1115 Fd 836 929 279 372 2415 Pw 93 0 0 0 93 Semi-tolerant 929 929 279 372 2508 Hardwood 372 1579 93 0 2043 Lw 0 0 0 0 0 PI 743 . 279. 93 0 1115 Intolerant ' 743 279 93 0 1115 All Species 2136 3065 836 743 6780 72 Table 1.28. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Slightly Dry" sites. Site Number of Species Height class All plots 1 2 3 4 Heights Slightly 2 Bg 0 0 0 0 0 Dry Bl 1486 372 0 0 1858 Cw 0 0 0 372 372 Hw 0 0 0 0 0 Sx 372 0 0 0 372 Tolerant 1858 372 0 372 2602 Fd 372 743 372 1858 3344 Pw 0 0 0 0 0 Semi-tolerant 372 743 372 1858 3344 Hardwood 0 0 0 372 372 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 Al l Species 2229 ,1115 372 2601 6316 Table 1.29. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Slightly Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 4 Bg 372 0 0 0 372 Dry Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 372 0 0 0 372 Fd 1486 2415 557 1486 5944 Pw 0 0 0 0 0 Semi-tolerant 1486 2415 557 1486 5944 Hardwood 0 186 0 2786 2972 Lw 186 186 0 0 372 PI 0 0 0 0 0 Intolerant 186 186 0 0 372 All Species 2043 2786 557 4272 9659 Table 1.30. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Mesic" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 8 Bg 186 0 0 0 186 Bl 279 93 93 93 557 Cw 1393 929 93 464 2879 Hw 3715 650 186 279 4830 Sx 186 93 0 0 279 Tolerant 5758 1765 372 836 8730 Fd 2693 93 93 93 2972 Pw 650 0 0 0 650 Semi-tolerant 3344 93 93 93 3622 Hardwood 186 0 0 1115 1300 Lw 93 93 93 93 372 PI 0 0 0 0 0 Intolerant 93 93 93 93 372 All Species 9380 1950 557 2136 14024 73 Table 1.31. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Mesic" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 4 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 372 0 0 372 Hw 186 186 0 186 557 Sx 0 186 0 0 186 Tolerant 186 743 0 186 1115 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 743 743 Lw 0 0 0 0 0 PI 0 186 0 0 186 Intolerant 0 186 0 0 186 All Species 186 929 0 929 2043 Table 1.32. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 3 Bg 2229 1238 495 1238 5201 Wet Bl 0 0 0 0 0 Cw 1486 0 0 0 1486 Hw 991 495 248 248 1981 Sx 743 248 0 0 991 Tolerant 5449 1981 743 1486 9659 Fd 0 0 0 0 0 Pw 248 495 0 0 743 Semi-tolerant 248 495 0 0 743 Hardwood 0 0 248 248 495 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 5696 2477 991 1734 10897 Table 1.33. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 10 Bg 0 0 0 0 0 Wet Bl 74 74 74 74 297 Cw 1486 74 0 297 1858 Hw 520 74 0 74 669 Sx 223 0 0 0 223 Tolerant 2303 223 74 446 3046 Fd 223 149 74 74 520 Pw 0 0 74 0 74 Semi-tolerant 223 149 148 74 594 Hardwood 0 0 223 223 446 Lw 0 0 0 74 74 PI 0 0 74 0 74 Intolerant 0 0 74 74 148 All Species 2526 372 520 817 4235 74 Table 1.34. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Wet 3 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 743 743 495 991 2972 Hw 0 0 0 0 0 Sx 248 0 0 0 248 Tolerant 991 743 495 991 3220 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 991 743 495 991 3220 Table 1.35. Average regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Wet 4 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 372 557 372 186 1486 Hw 0 0 0 0 0 Sx 186 0 0 186 372 Tolerant 557 557 372 372 1858 Fd 186 0 0 186 372 Pw 0 0 0 0 0 Semi-tolerant 186 0 0 186 372 Hardwood 0 0 0 186 186 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 743 557 372 743 2415 Table 1.36. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 4 Bg 0 0 186 0 186 Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 186 0 186 Fd 2043 186 186 0 2415 Pw 186 0 0 0 186 Semi-tolerant 2229 186 186 0 2601 Hardwood 0 0 557 743 1300 Lw 186 186 0 372 743 PI 0 0 0 186 186 Intolerant 186 186 0 558 929 All Species 2415 372 929 1300 5015 75 Table 1.37. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 1 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 0 743 743 1486 Hw 0 743 0 743 1486 Sx 743 0 0 0 743 Tolerant 743 743 743 1486 3715 Fd 1486 743 0 743 2972 Pw 0 0 0 0 0 Semi-tolerant 1486 743 0 743 2972 Hardwood 0 0 0 0 0 Lw 743 0 0 743 1486 PI 0 0 0 0 0 Intolerant 743 0 0 743 1486 All Species 2972 1486 743 2972 8173 Table 1.38. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Slightly Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 12 Bg 929 124 0 186 1238 Dry Bl 62 0 0 0 62 Cw 681 0 62 124 867 Hw 372 62 62 0 495 Sx 0 0 0 0 0 Tolerant 2043 186 124 310 2662 Fd 991 186 62 433 1672 Pw 310 495 186 557 1548 Semi-tolerant 1300 681 248 991 3220 Hardwood 0 0 0 557 557 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 3344 867 372 1858 6439 Table 1.39. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Slightly Dry" sites. Site Number of Species Height class All plots 1 2 3 4 Heights Slightly 2 Bg 0 0 0 0 0 Dry Bl 0 0 0 0 0 Cw 372 0 0 0 372 Hw 0 0 0 0 0 Sx 0 0 ' 0 0 0 Tolerant 372 0 0 0 372 Fd 0 0 0 743 743 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 743 743 Hardwood 0 . 0 b 0 0 Lw 0' 0 0 0 0 PI 0 0 0 372 372 Intolerant 0 0 0 372 372 All Species 372 0 0 1115 1486 76 Table 1.40. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Mesic" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 4 Bg 0 0 0 0 0 Bl 0 0 0 186 186 Cw 0 372 0 1858 2229 Hw 0 0 0 2601 2601 Sx 0 0 0 743 743 Tolerant 0 372 0 5387 5758 Fd 0 0 0 372 372 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 372 372 Hardwood 0 0 0 1486 1486 Lw 0 o •• • 0 0 0 PI 0 . 0 0. 0 0 Intolerant 0 0 0 0 0 All Species 0 372 0 7244 7616 Table 1.41. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Mesic" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 1 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 0 0 0 0 0 Table 1.42. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 5 Bg 5944 743 0 0 6687 Wet Bl 0 0 0 0 0 Cw 1040 1337 149 149 2675 Hw 297 149 297 149 892 Sx 0 149 0 297 446 Tolerant 7281 2378 446 594 10699 Fd 3269 297 0 0 3566 Pw 0 0 0 0 0 Semi-tolerant 3269 297 0 0 3566 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 10550 2675 446 594 14265 77 Table 1.43. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 8 Bg 0 0 0 0 0 Wet Bl 929 0 0 0 929 Cw 0 0 0 372 372 Hw 0 0 0 0 0 Sx 650 93 0 297 1022 Tolerant 1579 93 0 650 2322 Fd 279 93 0 93 464 Pw 0 93 0 0 93 Semi-tolerant 279 186 0 93 557 Hardwood 0 0 0 464 464 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 1858 279 0 1207 3344 Table 1.44. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Wet" sites. Site Number of Species Height class All plots 1 2 3 4 Heights Wet 1 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 6687 6687 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 0 0 0 6687 6687 Table 1.45. Average regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Wet 6 Bg 0 0 0 0 0 Bl 124 0 0 0 124 Cw 991 124 0 495 1610 Hw 0 0 0 0 0 Sx 124 0 0 0 124 Tolerant 1238 124 0 495 1858 Fd 124 0 0 0 124 Pw 124 0 0 0 124 Semi-tolerant 248 0 0 0 248 Hardwood 0 248 0 124 372 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 1486 372 0 619 2477 78 Appendix II- Validation Tables1 Table II. 1. Standard error of the mean regeneration per ha by height class and species for Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 11 Bg 875 135 0 0 1009 Dry Bl 117 68 68 0 376 Cw 999 348 104 68 1148 Hw 334 209 406 414 944 Sx 0 0 0 0 0 Tolerant 1048 265 376 411 1713 Fd 680 91 338 68 729 Pw 414 135 0 0 544 Semi-tolerant 729 151 338 68 1196 Hardwood 151 0 0 0 151 Lw 145 91 0 0 232 PI 91 68 0 0 145 Intolerant 154 105 0 0 348 All Species 2093. 523 540 406 2551 Table II.2. Standard error of the mean regeneration per ha by height class and species for Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 6 Bg 0 0 0 0 0 Dry Bl 0 0 0 0 0 Cw 589 254 0 0 829 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 589 254 0 0 829 Fd 470 0 0 0 470 Pw 0 0 0 0 0 Semi-tolerant 470 0 0 0 470 Hardwood 367 355 1405 313 1702 Lw 298 0 0 0 298 PI 1383 372 0 0 1544 Intolerant 1204 372 0 0 1352 All Species 1113 403 1418 367 1081 Table II.3. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Mesic" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 2 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 372 2229 372 0 2972 Hw 1858 372 0 0 2229 Sx 0 0 0 0 0 Tolerant 1486 1858 372 0 5201 Fd 0 372 0 0 372 Pw 0 372 0 0 372 Semi-tolerant 0 0 0 0 743 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 2229 3344 372 0 5944 1 Tables showing the conditions that were not represented in this study (three conditions that had the number of plots equal to zero) are not included in this Appendix 79 Table II.4. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and " M e s i c " sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 1 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 Al l Species 0 0 0 0 0 Table II.5. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Dense" and "Slightly Wet" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Slightly 7 Bg 0 0 0 0 0 Wet Bl 0 106 0 106 212 Cw 833 505 212 221 1635 Hw 4776 0 0 106 4760 Sx 425 0 0 0 425 Tolerant 4397 483 212 212 5338 Fd 927 0 0 0 927 Pw 0 0 0 0 0 Semi-tolerant 927 0 0 0 927 Hardwood 0 0 0 0 0 Lw 106 0 0 0 106 PI 106 0 0 0 106 Intolerant 137 0 0 0 212 Al l Species 4061 483 212 212 5704 Table II.6. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 1, basal area class "Open" and "Slightly Wet" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Slightly 4 Bg 0 0 0 0 0 Wet Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 0 0 0 0 0 Pw 372 0 0 0 372 Semi-tolerant 372 0 0 0 372 Hardwood 0 0 557 743 1300 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 Al l Species 372 0 557 743 1227 80 Table II.7. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Dry" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Dry 16 Bg 0 0 0 0 0 Bl 127 93 0 0 202 Cw 395 214 0 134 680 Hw 0 0 0 0 0 Sx 93 0 0 0 93 Tolerant 384 222 0 134 658 Fd 964 46 46 0 1007 Pw 75 101 0 0 150 Semi-tolerant 955 107 46 0 1053 Hardwood 418 46 417 279 646 Lw 0 0 0 0 0 PI 46 186 0 0 188 Intolerant 46 186 0 0 188 Al l Species 1060 267 415 292 1154 Table II. 8. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 21 Bg 35 0 0 0 35 Bl 0 0 35 0 35 Cw 601 35 35 35 635 Hw ' 106 35 0 0 110 Sx 0 0 0 0 0 Tolerant 605 49 49 35 739 Fd 131 58 0 0 141 Pw 58 0 0 0 58 Semi-tolerant 131 58 0 0 163 Hardwood 0 110 71 372 515 Lw 167 130 71 0 285 PI 177 322 35 497 895 Intolerant 193 326 78 497 908 Al l Species 891 372 107 598 1384 Table II.9. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Slightly Dry" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Slightly 22 Bg 47 34 0 0 56 Dry Bl 101 34 34 0 138 Cw 664 275 126 68 914 Hw 4335 56 0 0 4378 Sx 0 0 0 0 0 Tolerant 4233 265 127 68 4372 Fd 1762 126 47 74 1817 Pw 241 47 0 34 249 Semi-tolerant 1720 127 47 79 1906 Hardwood 693 270 171 140 1342 Lw 0 0 0 0 0 PI 34 0 0 0 34 Intolerant 34 0 0 0 34 Al l Species 4581 362 205 179 4610 81 Table 11.10. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Slightly Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 16 Bg 46 0 0 0 46 Dry Bl 93 93 0 46 232 Cw 349 63 188 46 421 Hw 325 225 101 418 1020 Sx 232 0 93 0 237 Tolerant 417 227 213 417 1316 Fd 237 211 63 136 484 Pw 0 0 46 0 46 Semi-tolerant 237 211 75 136 485 Hardwood 345 186 395 918 1715 Lw 0 370 46 0 415 PI 112 708 376 1139 2158 Intolerant 112 750 375 1139 2205 Al l Species 1008 915 825 1820 2951 Table II. 11. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Mesic" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 12 Bg 0 186 62 0 248 Bl 62 0 62 124 248 Cw 1800 276 133 83 1963 Hw 9253 1537 83 186 10098 Sx 0 0 0 0 0 Tolerant 8651 1490 143 214 11464 Fd 504 62 0 0 534 Pw 143 186 0 0 301 Semi-tolerant 420 190 0 0 723 Hardwood 0 248 83 133 344 Lw 62 0 0 0 62 PI 495 557 133 62 1172 Intolerant 494 557 133 62 1167 Al l Species 10677 1628 330 266 11171 Table 11.12. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Mesic" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Mesic 8 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 93 0 0 0 93 Hw 466 186 0 186 659 Sx 93 " 122 0 0 195 Tolerant 438 199 0 186 756 Fd 281 643 186 93 1083 Pw 0 0 0 0 0 Semi-tolerant 281 643 186 93 1083 Hardwood 929 0 93 624 1199 Lw 186 0 93 0 195 PI 0 195 93 0 281 Intolerant 186 195 122 0 296 Al l Species 1139 800 279 909 2115 82 Table 11.13. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Slightly Wet" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Slightly 2 Bg 0 0 0 0 0 Wet Bl 0 0 0 0 0 Cw 3715 372 0 0 4087 Hw 743 0 0 0 743 Sx 0 0 0 0 0 Tolerant 2780 372 0 0 4830 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 372 372 0 0 0 PI . 0 0 0 0 0 Intolerant 372 372 0 0 0 Al l Species 4830 0 0 0 4830 Table 11.14. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Slightly Wet" sites. Site Number of plots Species Heig ht class Al l Heights 1 2 3 4 Slightly 5 Bg 0 0 0 0 0 Wet Bl 0 182 0 0 182 Cw 743 446 149 149 779 Hw 297 0 0 0 297 Sx 0 0 0 297 297 Tolerant 728 407 149 297 952 Fd 0 0 149 0 149 Pw 149 0 0 0 149 Semi-tolerant 149 0 149 0 182 Hardwood 149 0 0 1398 1370 Lw 149 0 0 0 149 PI 0 0 0 0 0 Intolerant 149 0 0 0 149 Al l Species 1308 576 297 1460 1252 Table 11.15. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Dense" and "Wet" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Wet 2 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 Al l Species 0 0 0 0 0 83 Table 11.16. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 2, basal area class "Open" and "Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Wet 4 Bg 0 0 0 0 0 Bl 0 0 0 186 186 Cw 372 186 0 0 557 Hw 0 0 186 0 186 Sx 0 186 0 186 372 Tolerant 372 215 186 215 766 Fd 743 372 0 0 1115 Pw 0 0 0 0 0 Semi-tolerant 743 372 0 0 1115 Hardwood 0 0 0 186 186 Lw 0 186 0 0 186 PI 186 0 0 0 186 Intolerant 186 186 0 0 372 All Species 766 356 186 356 1175 Table 11.17. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 17 Bg 271 44 0 44 270 Bl 0 0 0 0 0 Cw 106 182 155 87 363 Hw 71 44 0 0 101 Sx 44 0 0 0 44 Tolerant 259 181 155 95 567 Fd 2007 945 111 126 2971 Pw 248 142 44 60 363 Semi-tolerant 1961 918 113 129 2940 Hardwood 44 155 79 817 873 Lw 143 181 44 60 262 PI 1013 404 106 212 1668 Intolerant 985 403 109 212 1739 All Species 2154 1045 255 954 3220 Table 11.18. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 20 Bg 61 0 0 0 61 Bl 51 81 0 0 119 Cw 74 51 153 87 281 Hw 0 51 37 37 116 Sx 122 0 0 0 122 Tolerant 135 98 155 91 390 Fd 212 136 37 109 384 Pw 74 114 37 51 189 Semi-tolerant 208 145 51 113 365 Hardwood 163 232 111 454 747 Lw 0 136 156 444 634 PI 188 74 0 164 266 Intolerant 188 136 156 457 692 All Species 332 361 280 720 1297 84 Table 11.19. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Slightly Dry" sites. Site Number of plots Species Height class AH Heights 1 2 3 4 Slightly 7 Bg 137 106 0 0 221 Dry Bl 221 849 106 0 1155 Cw 2469 909 106 221 3409 Hw 212 538 106 212 838 Sx 137 0 0 0 137 Tolerant 2243 894 150 267 3879 Fd 957 341 137 106 937 Pw 411 420 0 0 1018 Semi-tolerant 0 0 137 106 931 Hardwood 106 137 137 1392 1842 Lw 873 548 212 106 1620 PI 0 0 0 ' 0 0 Intolerant 849 548 212 106 1620 All Species 3683 2112 267 1401 4407 Table 11.20. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Slightly Dry" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Slightly 6 Bg 0 0 0 0 0 Dry Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 124 0 0 0 124 Sx 0 0 0 0 728 Tolerant 124 0 0 0 124 Fd 457 367 124 124 508 Pw 124 0 0 0 124 Semi-tolerant 418 367 124 124 522 Hardwood 0 124 372 254 728 Lw 355 124 0 0 470 PI 0 0 124 124 248 Intolerant 335 124 124 124 531 Al l Species 534 414 486 228 1075 Table 11.21. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Mesic" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Mesic 5 Bg 0 0 0 0 0 Bl 1189 297 297 743 2526 Cw 149 0 0 149 182 Hw 297 149 0 149 470 Sx 0 149 297 446 720 Tolerant 1066 278 364 665 3170 Fd 1378 720 0 743 1655 Pw 278 0 297 0 278 Semi-tolerant 1127 720 297 743 1736 Hardwood 0 149 446 2378 2972 Lw 149 0 0 0 149 PI 0 0 0 0 0 Intolerant 149 0 0 0 149 Al l Species 1655 922 892 2171 5025 8 5 Table 11.22. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Mesic" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Mesic 9 Bg 83 0 0 0 83 Bl 446 0 0 0 446 Cw 2733 810 0 0 3506 Hw 251 83 83 0 322 Sx 2152 165 0 0 2135 Tolerant 2511 778 83 0 5303 Fd 328 165 83 165 730 Pw 109 0 0 0 109 Semi-tolerant 314 165 83 165 743 Hardwood 0 175 0 582 917 Lw 330 251 0 0 573 PI 0 0 0 83 83 Intolerant 330 251 0 83 567 Al l Species 5133 1158 109 720 6151 Table 11.23. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Dense" and "Slightly Wet" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Slightly 1 Bg 0 0 0 0 0 Wet Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 Al l Species 0 0 0 0 0 Table 11.24. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 9 Bg 83 0 0 0 83 Wet Bl 165 0 0 0 165 Cw 83 248 0 83 330 Hw 165 83 0 0 175 Sx 218 248 0 0 289 Tolerant 206 322 0 83 587 Fd 328 165 0 0 487 Pw 0 0 0 0 0 Semi-tolerant 328 165 0 0 487 Hardwood 0 83 0 109 175 Lw 248 0 0 0 248 PI 0 0 0 0 0 Intolerant 248 0 0 0 248 Al l Species 664 487 0 124 1058 86 Table 11.25. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 3, basal area class "Open" and "Wet" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Wet 3 Bg 248 0 0 0 248 Bl 0 0 0 0 0 Cw 0 495 0 0 495 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 248 495 0 0 743 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 429 429 Lw 0 0- 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 Al l Species 248 495 0 429 1135 Table 11.26. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Dry" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Dry 2 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 372 372 0 0 0 Pw 743 0 0 0 743 Semi-tolerant 372 372 0 0 743 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 Al l Species 1115 372 0 0 743 Table 11.27. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Dry" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Dry 8 Bg 0 0 0 0 0 Bl 0 0 93 0 93 Cw 93 195 186 281 640 Hw 0 0 0 0 0 Sx 0 0 93 0 93 Tolerant 93 195 199 281 819 Fd 260 415 195 281 874 Pw 93 0 0 0 93 Semi-tolerant 233 415 195 281 920 Hardwood 281 1476 93 0 1747 Lw 0 0 0 0 0 PI 506 279 93 0 743 Intolerant 506 297 93 0 743 Al l Species 650 1822 454 421 2364 87 Table 11.28. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Slightly Dry" sites. Site Number of plots Species Height el ass Al l Heights 1 2 3 4 Slightly 2 Bg 0 0 0 0 0 Dry Bl 1486 372 0 0 1858 Cw 0 0 0 372 372 Hw 0 0 0 0 0 Sx 372 0 0 0 372 Tolerant 1115 372 0 372 2601 Fd 372 743 372 1858 3344 Pw 0 0 0 0 0 Semi-tolerant 372 743 372 1858 3344 Hardwood 0 0 0 372 372 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 Al l Species 1486 372 372 1858 1115 Table 11.29. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Slightly Dry" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Slightly 4 Bg 372 0 0 0 372 Dry Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 372 0 0 0 372 Fd 1051 824 356 525 2208 Pw 0 0 0 0 0 Semi-tolerant 1051 824 356 525 2208 Hardwood 0 186 0 467 1455 Lw 186 186 0 0 372 PI 0 0 0 0 0 Intolerant 186 186 0 0 372 Al l Species 824 977 356 1335 1322 Table 11.30. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Mesic" sites. Site Number of plots Species Height class Al l Heights 1 2 3 4 Mesic 8 Bg 122 0 0 0 122 Bl 195 93 93 93 233 Cw 904 557 93 279 1145 Hw 2198 431 122 195 2328 Sx 186 93 0 0 195 Tolerant 1808 505 140 260 3235 Fd 2078 93 93 93 2049 Pw 552 0 0 0 552 Semi-tolerant 2030 93 93 93 2583 Hardwood % 122 0 0 281 521 Lw 93 93 93 93 199 PI 0 0 0 0 0 Intolerant 93 93 93 93 199 Al l Species 5431 1031 272 800 5547 88 Table 11.31. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Mesic" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 4 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 372 0 0 372 Hw 186 186 0 186 557 Sx 0 186 0 0 186 Intolerant 186 303 0 186 711 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 525 743 Lw 0 0 0 0 0 PI 0 186 0 0 186 Intolerant 0 186 0 0 186 Al l Species 186 356 0 929 1335 Table 11.32. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Slightly Wet" sites. Site Number of Species Height class All plots 1 2 3 4 Heights Slightly 3 Bg 2229 893 495 1238 4834 Wet Bl 0 0 0 0 0 Cw 1486 0 0 0 1486 Hw 991 248 248 248 1311 Sx 429 248 0 0 655 Tolerant 0 0 429 1135 8218 Fd 0 0 0 0 0 Pw 248 495 0 0 743 Semi-tolerant 248 495 0 0 743 Hardwood 0 0 248 248 495 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 Al l Species 5329 1786 495 1379 8763 Table 11.33. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 10 Bg 0 0 0 0 0 Wet Bl 74 74 74 74 297 Cw 1405 74 0 164 1376 Hw 520 74 0 74 525 Sx 114 0 0 0 114 Tolerant 1399 114 74 164 2249 Fd 159 99 74 74 351 Pw 0 0 74 0 74 Semi-tolerant 159 99 99 74 411 Hardwood 0 0 223 159 371 Lw 0 0 0 74 74 PI 0 0 74 0 74 Intolerant 0 0 74 74 99 Al l Species 2134 254 314 259 2614 89 Table 11.34. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Dense" and "Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Wet 3 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 743 743 495 991 2972 Hw 0 0 0 0 0 Sx 248 0 0 0 248 Tolerant 655 743 495 991 2856 Fd 0 0 0 . 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 655 743 495 991 2856 Table 11.35. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 4, basal area class "Open" and "Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Wet 4 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 372 557 372 186 1251 Hw 0 0 0 0 0 Sx 186 0 0 186 214 Tolerant 356 557 372 215 1373 Fd 186 0 0 186 215 Pw 0 0 0 0 0 Semi-tolerant 186 0 0 186 215 Hardwood 0 0 0 186 186 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 743 557 372 0 1672 Table 11.36. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 4 Bg 0 0 186 0 186 Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 186 0 186 Fd 929 186 186 0 766 Pw 186 0 0 0 186 Semi-tolerant 803 186 186 0 934 Hardwood 0 0 557 525 1067 Lw 186 186 0 372 743 PI 0 0 0 186 186 Intolerant 186 186 0 356 929 All Species 977 214 703 766 1067 9 0 Table 11.37. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Dry 1 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 0 0 0 0 0 Pw o- o ' • 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 0 0 0 0 0 Table 11.38. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Slightly Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 12 Bg 803 124 0 133 912 Dry Bl 62 0 0 0 62 Cw 560 0 62 124 555 Hw 372 62 62 0 381 Sx 0 0 0 0 0 Tolerant 924 133 84 170 987 Fd 551 97 62 266 654 Pw 214 495 186 378 1173 Semi-tolerant 542 488 190 412 1456 Hardwood 0 0 0 318 318 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 1486 612 250 537 1864 Table 11.39. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Slightly Dry" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 2 Bg 0 0 0 0 0 Dry Bl 0 0 0 0 0 Cw 372 0 0 0 372 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 372 0 0 0 372 Fd 0 0 0 743 743 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 743 743 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 372 372 Intolerant 0 0 0 372 372 All Species 372 0 0 1115 743 91 Table 11.40. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Mesic" sites. Site Number of Species Height class All plots 1 2 3 4 Heights Mesic 4 Bg 0 0 0 0 0 Bl 0 0 0 186 186 Cw 0 372 0 1406 1287 Hw 0 0 0 2134 2134 Sx 0 0 0 743 743 Tolerant 0 372 0 1023 4315 Fd 0 0 0 372 372 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 372 372 Hardwood 0 0 0 803 1051 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 0 372 0 3982 3959 Table 11.41. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Mesic" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Mesic 1 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 0 0 0 0 0 Table 11.42. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Slightly Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Slightly 5 Bg 5944 743 0 0- 6687 Wet Bl 0 0 0 0 0 Cw 728 1337 149 149 2321 Hw • 182 149 182 149 594 Sx 0 149 0 297 297 Tolerant 5636 1252 182 278 6325 Fd 3269 297 0 0 3208 Pw 0 0 0 0 0 Semi-tolerant 3269 297 0 0 3208 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 8911 1888 297 364 9391 92 Table 11.43. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Slightly Wet" sites. Site Number of • plots Species Height class All Heights 1 . 2 3 4 Slightly 8 Bg o- 0 0 0 0 Wet Bl 828 0 0 0 828 Cw 0 0 0 372 372 Hw 0 0 0 0 0 Sx 431 93 0 297 443 Tolerant 836 93 0 431 1064 Fd 195 93 0 93 241 Pw 0 93 0 0 93 Semi-tolerant 195 122 0 93 233 Hardwood 0 0 0 464 464 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 1240 195 0 543 1079 Table 11.44. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Dense" and "Wet" sites. Site Number of Species Height class All plots 1 2 3 4 Heights Wet 1 Bg 0 0 0 0 0 Bl 0 0 0 0 0 Cw 0 0 0 0 0 Hw 0 0 0 0 0 Sx 0 0 0 0 0 Tolerant 0 0 0 0 0 Fd 0 0 0 0 0 Pw 0 0 0 0 0 Semi-tolerant 0 0 0 0 0 Hardwood 0 0 0 0 0 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 0 0 0 0 0 Table 11.45. Standard error of the mean regeneration per ha by height class and species for time-since-disturbance class 5, basal area class "Open" and "Wet" sites. Site Number of plots Species Height class All Heights 1 2 3 4 Wet 6 Bg 0 0 0 0 0 Bl 124 0 0 0 124 Cw 627 124 0 495 728 Hw 0 0 0 0 0 Sx 124 0 0 0 124 Tolerant 565 124 0 495 761 Fd 124 0 0 0 124 Pw 124 0 0 0 124 Semi-tolerant 157 0 0 0 248 Hardwood 0 157 0 124 254 Lw 0 0 0 0 0 PI 0 0 0 0 0 Intolerant 0 0 0 0 0 All Species 879 166 0 486 806 93 Appendix III- Simple Correlations Between Auxiliary and Ground Variables for Runs 2 to 5 of MSN Type 1 Table III. 1. Simple correlations between the auxiliary and ground variables used in MSN analysis of Run 2 (n = 268). Time-since-SPH disturbance Site series Aspect Elevation Slope TPH BA CCF Toll -0.08590 -0.06339 -0.11186 -0.27640 0.04099 0.03390 0.30161 0.31638 Tol2 -0.14678 -0.14465 -0.06811 -0.14826 0.03369 0.09627 0.19604 0.20052 Tol3 -0.15111 -0.01874 -0.05160 -0.07882 -0.00454 0.16091 0.08791 0.10163 Tol4 0.10528 -0.04663 0.02142 -0.03134 -0.07084 0.26170 0.06943 0.09440 Semil -0.06818 -0.04884 -0.00011 -0.12574 -0.00989 -0.05958 0.11963 0.11762 Semi2 0.00178 -0.07338 -0.02196 -0.05105 0.00389 -0.08018 -0.06613 -0.07263 Semi3 -0.02845 -0.06946 -0.02005 -0.04622 0.09961 0.12016 -0.00641 -0.00698 Semi4 0.07782 -0.05542 -0.01234 -0.07905 0.10886 0.21161 -0.00647 0.01917 Intoll -0.16116 -0.08874 0.05621 0.07866 -0.10318 -0.03232 -0.11243 -0.12612 Intol2 -0.08731 -0.10375 -0.00334 0.08796 -0.06967 0.08177 -0.11551 -0.12120 Intol3 -0.02894 -0.05640 0.05144 0.06911 -0.07133 0.04846 -0.08382 -0.09148 Intol4 -0.02011 -0.03694 0.05212 0.02465 -0.11287 0.16737 -0.09258 -0.08985 Hardl -0.11119 -0.03821 0.00074 -0.10582 0.08041 -0.02861 -0.01937 -0.01061 Hard2 -0.02320 -0.05468 -0.03211 -0.15060 0.07850 -0.00764 -0.07455 -0.07314 Hard3 -0.11568 -0.00644 0.01656 -0.09726 0.08591 -0.07047 -0.05447 -0.06278 Hard4 0.05975 -0.07642 0.05921 0.01233 0.10045 0.07783 -0.10613 -0.10234 Tol refers to shade tolerant species, semi to shade semi-tolerant species, intol to shade intolerant species, and hard to hardwood species; the numbers refer to height classes 1 to 4. 2 TPH refers to the number of residual trees per hectare. 3 Ba refers to the residual basal area per hectare. 4 CCF refers to the crown competition factor 94 Table III.2. Simple correlations between the auxiliary and ground variables used in MSN analysis of the Run 3 (n = 268). Time-since-SPH1 disturbance Site series Aspect Elevation Slope TPH BA CCF Toll -0.07643 -0.10572 -0.11947 -0.33768 0.00903 0.03003 0.3059 0.31761 Tol2 -0.13258 -0.10397 -0.06955 -0.16018 0.00891 0.1176 0.22395 0.22973 Tol3 -0.14217 0.02776 0.00913 -0.08339 -0.04381 0.17531 0.13339 0.15476 Tol4 0.04229 0.0416 0.0031 -0.05531 -0.02142 0.16334 0.10062 0.11443 Semil -0.06307 -0.02459 0.00105 -0.13945 -0.00155 -0.03843 0.1668 0.17024 Semi2 0.0504 -0.03601 0.00679 -0.0316 0.07122 -0.07306 -0.10457 -0.11131 Semi3 -0.03107 -0.00868 -0.02679 -0.05272 0.21471 0.13945 -0.00971 -0.00839 Semi4 0.09387 -0.0005 -0.05303 -0.06599 0.13589 0.24973 0.01128 0.0316 Intoll -0.12401 -0.05915 0.05171 0.0907 -0.10407 -0.03191 -0.12032 -0.13465 Intol2 -0.05205 -0.10012 -0.03662 0.05075 -0.09725 0.14504 -0.10194 -0.10787 Intol3 -0.00159 -0.09934 -0.00823 0.0587 -0.03075 0.05674 -0.09637 -0.10554 Intol4 -0.01673 -0.00667 -0.01354 0.03603 -0.08177 0.14215 -0.07865 -0.07654 Hardl -0.08303 -0.04613 0.00168 -0.08632 0.06135 -0.00442 -0.01401 -0.00627 Hard2 0.01529 -0.05246 -0.02124 -0.12372 0.06423 0.02217 -0.06923 -0.06833 Hard3 -0.12612 0.00907 0.01119 -0.13175 0.08567 -0.09934 -0.05907 -0.07008 Hard4 0.00835 -0.05047 0.05954 0.00425 0.09931 0.04983 -0.10993 -0.10994 Tol refers to shade tolerant species, semi to shade semi-tolerant species, intol to shade intolerant species, and hard to hardwood species; the numbers refer to height classes 1 to 4. 2 TPH refers to the number of residual trees per hectare. 3 Ba refers to the residual basal area per hectare. 4 CCF refers to the crown competition factor 95 Table 111.3. Simple correlations between the auxiliary and ground variables used in MSN analysis of Run 4 (n = 269). Time-since-SPH disturbance Site series Aspect Elevation Slope TPH BA CCF Toll -0.07663 -0.11468 -0.12016 -0.31322 -0.00638 0.04055 0.29987 0.31784 Tol2 -0.08333 -0.11237 -0.08057 -0.10933 0.02228 0.07964 0.22088 0.22446 Tol3 -0.11181 0.00143 -0.01005 -0.06836 0.00197 0.16453 0.13634 0.15341 Tol4 0.09519 -0.00927 -0.03672 0.00534 0.00677 0.27803 0.0872 0.1099 Semil -0.07599 -0.09633 -0.02676 -0.10438 -0.00528 -0.04437 0.11906 0.11811 Semi2 -0.02048 -0.08279 -0.02069 -0.06466 0.0198 -0.0816 -0.06562 -0.07151 Semi3 -0.04496 -0.08289 -0.03721 -0.04226 0.16682 0.15987 -0.0316 -0.01926 Semi4 0.03237 -0.07407 -0.03447 -0.09642 0.09524 0.24093 -0.03097 0.00552 Intoll -0.12789 -0.08439 0.08094 0.09047 -0.10444 -0.01499 -0.12345 -0.13201 Intol2 -0.06451 -0.05611 0.01704 0.07087 -0.09925 0.14625 -0.14042 -0.14065 Intol3 -0.02888 -0.03556 0.0362 0.0675 -0.06503 0.07862 -0.09532 -0.10031 Intol4 -0.02471 -0.02074 0.03339 0.02497 -0.11598 0.1582 -0.09114 -0.08896 Hardl -0.05805 -0.00837 -0.02828 -0.12635 0.13456 -0.02174 -0.03627 -0.02936 Hard2 0.04277 -0.0201 -0.01035 -0.14062 0.04735 0.00273 -0.09218 -0.09145 Hard3 -0.10217 0.00275 0.02947 -0.09134 0.06444 -0.07152 -0.06605 -0.07753 Hard4 0.01908 -0.00234 0.0452 -0.01208 0.12033 0.04116 -0.10188 -0.10291 Tol refers to shade tolerant species, semi to shade semi-tolerant species, intol to shade intolerant species, and hard to hardwood species; the numbers refer to height classes 1 to 4. 2 TPH refers to the number of residual trees per hectare. 3 Ba refers to the residual basal area per hectare. 4 CCF refers to the crown competition factor 96 Table III.4. Simple correlations between the auxiliary and ground variables used in MSN analysis of Run 5 (n = 262). SPH1 Time-since-disturbance Site series Aspect Elevation Slope TPH BA CCF Toll -0.08233 -0.14109 -0.09933 -0.29003 0.03801 0.05154 0.22663 0.24108 Tol2 -0.13039 -0.14956 -0.04664 -0.16213 0.02007 0.11167 0.18579 0.19398 Tol3 -0.10442 0.01082 -0.05389 -0.06443 0.00117 0.1343 0.13247 0.14831 Tol4 0.13097 0.00258 0.07421 0.08548 -0.0339 0.25691 0.08642 0.10681 Semil -0.0534 -0.06666 -0.02215 -0.12306 -0.00836 -0.04664 0.13596 0.14 Semi2 -0.02285 -0.08506 -0.01662 -0.06313 0.02226 -0.06449 -0.06191 -0.06611 Semi3 -0.03462 -0.0576 -0.01799 -0.04877 0.15825 0.13648 0.00207 0.00693 Semi4 0.04896 -0.04848 -0.00015 -0.08384 0.09766 0.23229 0.00511 0.029 Intoll -0.10855 -0.08824 0.11024 0.1042 -0.01744 -0.04757 -0.11844 -0.13307 Intol2 -0.08184 -0.09253 0.01837 0.08321 -0.04557 -0.00384 -0.11721 -0.1257 IntoB -0.03637 -0.05959 0.08421 0.0926 -0.06996 0.04511 -0.09708 -0.10479 Intol4 -0.02567 -0.00167 0.04624 0.03237 -0.09728 0.12047 -0.08379 -0.08472 Hardl -0.10077 -0.04757 0.00196 -0.12111 0.0415 -0.00718 -0.02382 -0.01507 Hard2 -0.0921 -0.0422 0.04569 -0.09842 -0.03249 -0.01739 -0.08095 -0.08325 Hard3 -0.06881 -0.01726 0.09695 -0.00748 0.05896 -0.05104 -0.04482 -0.05508 Hard4 0.0355 -0.02163 0.09269 0.0105 0.08357 0.06046 -0.11753 -0.1185 Tol refers to shade tolerant species, semi to shade semi-tolerant species, intol to shade intolerant species, and hard to hardwood species; the numbers refer to height classes 1 to 4. 2 TPH refers to the number of residual trees per hectare. 3 Ba refers to the residual basal area per hectare. 4 CCF refers to the crown competition factor 97 Appendix IV- Canonical Coefficients for Runs 2 to 5 of MSN Type 1 Model Table IV. 1. Canonical coefficients weighted by canonical correlation for the 18 auxiliary variables for Run 2. (Bold numbers indicates relatively high coefficients). Auxialiary Variable Variate 1 Variate 2 Variate 3 Variate 4 Variate 5 Variate 6 Variate 7 Variate 8 Time-since 0.04783 0.19501 0.18914 0.14615 0.10344 0.04513 0.02424 -0.00328 Site series 0.05932 0.01189 0.05239 0.00956 -0.00916 0.0313 0.05654 -0.01847 Aspect -0.11488 0.02538 0.00474 0.0804 0.05044 -0.00077 -0.03309 0.04791 Elevation -0.29468 0.06175 -0.03633 0.05419 -0.01957 0.14286 0.1399 -0.00642 Slope 0.04933 -0.12533 0.04743 -0.01555 0.14248 0.02257 -0.01826 0.12636 TPH -0.30799 -0.12651 0.32221 -0.10511 -0.03717 -0.05665 -0.03299 -0.06312 BA -1.03847 0.30402 -0.6773 -0.15494 0.16075 -0.09446 -0.50131 -0.09141 CCF 1.33564 -0.38482 0.6024 0.38949 -0.22923 0.20771 0.51073 -0.00826 TPH: number of residual trees per ha; BA: basal area per ha; CCF: crown competition factor. Table IV.2. Canonical coefficients weighted by canonical correlation for the 18 auxiliary variables for Run 3. (Bold numbers indicates relatively high coefficients). Auxialiary Variable Variate 1 Variate 2 Variate 3 Variate 4 Variate 5 Variate 6 Variate 7 Variate 8 Time-since -0.02022 0.10821 -0.1529 0.22477 -0.02114 0.1146 -0.01872 -0.02606 Site series 0.06944 -0.04622 0.00583 0.08078 -0.05553 -0.0462 -0.10068 0.13291 Aspect 0.10702 0.08802 -0.07961 -0.05157 -0.06882 -0.04167 -0.07416 0.05466 Elevation 0.26589 0.20112 0.14796 -0.04913 -0.14688 0.13426 -0.02541 -0.02259 Slope 0.07872 -0.05726 -0.22194 0.04253 -0.03533 -0.02319 -0.11841 -0.0945 TPH 0.35978 -0.08371 0.10788 0.17493 0.0506 -0.05092 0.05967 -0.01044 BA 0.71236 0.95032 -0.28834 -0.11516 1.10201 -0.24524 0.07991 -0.69831 CCF -0.93942 -1.16706 0.20863 0.0314 -1.19515 0.44551 -0.06276 0.73609 TPH: number of residual trees per ha; BA: basal area per ha; CCF: crown competition factor. 98 Table IV.3. Canonical coefficients weighted by canonical correlation for the 18 auxiliary variables for Run 4. (Bold numbers indicates relatively high coefficients). Auxialiary Variable Variate 1 Variate 2 Variate 3 Variate 4 Variate 5 Variate 6 Variate 7 Variate 8 Time-since -0.03461 -0.09199 -0.20794 -0.05477 0.12938 0.03082 -0.00848 0.044 Site series 0.02665 0.05219 -0.03 -0.0888 -0.04034 -0.08164 -0.08173 -0.00497 Aspect -0.10564 0.0394 0.03457 -0.01932 0.03992 -0.05132 -0.03078 -0.01727 Elevation -0.28827 0.13716 -0.13546 0.16955 -0.06108 -0.14637 -0.00968 0.08189 Slope 0.12302 0.05994 -0.00484 -0.03339 0.23284 -0.14952 -0.03667 -0.07643 TPH -0.10834 0.39109 -0.04702 -0.13617 -0.11727 0.02973 0.06261 -0.16501 BA -1.9968 -1.0983 0.62459 -0.39333 -0.07852 -0.30932 0.44547 -1.36377 CCF 2.28853 0.94195 -0.7838 0.62421 0.11451 0.2447 -0.43641 1.37614 TPH: number of residual trees per ha; BA: basal area per ha; CCF: crown competition factor. Table IV.4. Canonical coefficients weighted by canonical correlation for the 18 auxiliary variables for Run 5. (Bold numbers indicates relatively high coefficients). Auxialiary Variable Variate 1 Variate 2 Variate 3 Variate 4 Variate 5 Variate 6 Variate 7 Variate 8 Time-since 0.07909 -0.01752 0.12997 0.13147 -0.01473 -0.11472 -0.05332 0.07201 Site series 0.06608 -0.06579 0.04933 0.04171 -0.0759 0.0076 0.03633 -0.05022 Aspect 0.2148 -0.04451 0.01063 -0.04824 0.07025 0.01685 -0.08985 -0.03805 Elevation 0.31233 0.0007 -0.09333 0.09771 -0.07583 0.10595 0.06436 0.00195 Slope -0.05167 -0.07262 -0.07624 0.04615 0.03958 -0.17702 -0.11004 -0.19781 TPH 0.26465 -0.18951 0.12235 -0.15986 0.04727 0.01384 0.10261 -0.11918 BA 0.92795 0.73806 -0.43152 -0.24004 0.02231 0.11748 -0.24702 -0.27251 CCF -1.15527 -0.88166 0.4331 0.50944 -0.01192 -0.11061 0.29787 0.29388 TPH: number of residual trees per ha; BA: basal area per ha; CCF: crown competition factor. 99 Appendix V- Tables of Validation Results For Runs 2 to 5 of MSN Type 1 Table V . l . Results of MSN validation of 16 ground and three selected auxiliary variables using reference observations (268 plots) of Run 2. RESID= Observed-Predicted. OBSERVED PREDICTED STD DIFF 4 n p c i n 2 SPECIES 1 M E A N STD.DEV 3 M E A N STD.DEV M E A N STD.DEV M E A N R M S E5 R-SQ 6 PROB > T Toll 1957.563 5806.653 2150.004 7050.519 0.005 0.149 -192.44 5274.438 0.4618 0.611 Tol2 588.683 1480.194 516.134 928.774 0.014 0.322 72.549 1675.605 0.0083 0.449 Tol3 188.53 460.934 221.806 485.801 '0.015 0.283 -33.276 631.759 0.0127 0.288 Tol4 301.5 739.078 268.929 672.75 0.011 0.319 32.571 947.636 0.0105 0.498 Semil 1158.884 3068.717 1208.787 3309.458 0.003 0.262 -49.903 4470.4 0.0004 0.818 Semi2 499.041 1330.067 499.045 1299.802 0.000 0.335 -0.004 1744.876 0.0143 1.000 Semi3 116.44 389.614 102.578 416.479 0.009 0.376 13.862 558.755 0.0017 0.574 Semi4 225.951 721.068 184.366 576.519 0.011 0.225 41.586 835.351 0.0353 0.361 In toll 403.392 1182.486 451.91 1375.745 0.007 0.249 -48.519 1758.621 0.0038 0.515 Intol2 270.31 910.304 267.537 967.263 0.000 0.219 2.772 1303.281 0.0014 0.965 IntoB 94.261 467.459 74.854 422.365 0.013 0.427 19.407 634.966 0.0002 0.697 Intol4 176.049 1014.935 171.892 908.465 0.001 0.155 4.157 1264.022 0.0195 0.947 Hardl 202.384 991.135 180.205 993.343 0.003 0.204 22.179 1362.609 0.0033 0.719 Hard2 195.455 927.101 246.746 1027.832 0.014 0.364 -51.291 1352.525 0.0022 0.382 Hard3 192.683 872.553 261.993 973.044 0.013 0.256 -69.31 1331.529 0.0012 0.256 Hard4 587.75 1729.879 600.228 1623.234 0.001 0.21 -12.478 2342.509 0.0006 0.906 Site series 3.549 1.546 3.601 1.438 0.007 0.236 -0.052 1.654 0.1509 0.607 TPH 1078.078 1160.336 936.754 949.646 0.025 0.105 141.325 600.988 0.7488 0.104 BA 10.337 13.839 8.474 11.864 0.031 0.115 1.863 7.232 0.7451 0.033* Tol refers to tolerant species, semi to semi-tolerant species, intol to intolerant species, and hard to hardwood species. The numbers refer to height classes 1 to 4. 2RESID= Observed-Predicted. 3STD: standard deviation. 4STD DIFF: standardized difference values. 5RMSE: root mean square error. 6R-SQ: root squared. * indicates a significant difference from a mean of zero (a = 0.05). 100 Table V.2. Results of MSN validation of 16 ground and three selected auxiliary variables using reference observations (268 plots) of Run 3. RESID= Observed. OBSERVED PREDICTED STD DIFF4 RESID2 MEAN SPECIES1 M E A N STD.DEV5 M E A N S T D . D E V M E A N S T D . D E V RMSE5 R-SQ6 PROB > T Toll 2143.776 6781.328 1860.989 6377.404 0.007 0.15 282.787 5874.428 0.3646 0.511 Tol2 553.567 1429.769 531.384 1409.51 0.005 0.448 22.183 1999.036 0.0001 0.812 Tol3 178.362 461.124 207.937 499.876 0.013 0.291 -29.575 649.66 0.008 0.34 Tol4 278.627 718.33 285.556 778.886 0.002 0.355 -6.929 1054.936 0.0001 0.883 Semil 1054.918 2287.179 1009.172 2454.448 0.003 0.211 45.746 2985.289 0.0436 0.804 Semi2 371.511 760.215 367.362 677.914 0.001 0.293 4.149 979.779 0.0057 0.96 Semi3 116.44 400.087 124.757 448.86 0.004 0.274 -8.317 611.748 0.0012 0.746 Semi4 167.731 619.467 134.466 454.678 0.011 0.232 33.265 689.612 0.0424 0.391 Intoll 403.396 1186.418 457.463 1230.185 0.008 0.238 -54.067 1683.841 0.0009 0.469 Intol2 242.586 810.458 163.575 540.921 0.021 0.247 79.011 919.317 0.0159 0.196 Intol3 72.082 263.094 52.675 230.304 0.013 0.239 19.407 355.139 0.0008 0.668 Intol4 196.843 1270.498 180.209 1187.251 0.003 0.229 16.634 1360.337 0.1513 0.832 Hardl 195.455 945.866 263.381 1061.36 0.01 0.208 -67.925 1395.412 0.0015 0.258 Hard2 191.295 928.803 219.019 995.918 0.007 0.372 -27.724 1380.698 0.0008 0.635 Hard3 203.772 838.557 253.675 915.097 0.013 0.342 -49.903 1271.967 0.0024 0.401 Hard4 652.44 1856.86 671.388 2013.03 0.002 0.242 -18.948 2700.187 0.0008 0.868 Site series 3.474 1.525 3.515 1.413 0.007 0.241 -0.041 1.444 0.2695 0.677 TPH 1025.653 1054.752 860.168 890.922 0.031 0.118 165.485 643.176 0.6542 0.036 B A 10.439 13.886 9.122 11.724 0.021 0.142 1.317 9.042 0.5907 0.138 'Tol refers to tolerant species, semi to semi-tolerant species, intol to intolerant species, and hard to hardwood species. The numbers refer to height classes 1 to 4. 2RESID= Observed-Predicted. 3STD: standard deviation. 4STD DIFF: standardized difference values. 5RMSE: root mean square error. 6R-SQ: root squared. 101 Table V.3. Results of MSN validation of 16 ground and three selected auxiliary variables using reference observations (269 plots) of Run 4. RESID= Observed-Predicted SPECIES1 OBSERVED PREDICTED STD DIFF4 RESID2 MEAN RMSE 5 R-SQ6 PROB > T MEAN STD.DEV3 MEAN STD.DEV MEAN STD.DEV Toll 2008.297 6727.361 1909.539 7032.065 0.003 0.181 98.758 7046.665 0.2268 0.817 Tol2 530.788 1423.284 418.004 796.856 0.025 0.366 112.784 1633.324 0 0.214 Tol3 188.751 461.58 166.197 406.871 0.01 0.269 22.554 599.736 0.0027 0.452 Tol4 303.141 781.562 246.52 717.554 0.013 0.232 56.621 1035.844 0.0025 0.258 Semil 1233.294 3001.372 994.364 1904.2 0.015 0.192 238.929 3155.014 0.0574 0.277 Semi2 461.275 1292.769 418.468 785.381 0.01 0.315 42.807 1403.858 0.0247 0.676 Semi3 99.435 311.753 52.48 255.366 0.032 0.255 46.955 382.429 0.0133 0.016* Semi4 207.156 667.172 168.487 442.757 0.013 0.257 38.669 764.858 0.0095 0.358 Intoll 382.561 1144.111 348.045 1009.795 0.005 0.203 34.517 1433.668 0.0141 0.64 Intol2 263.781 849.514 278.974 849.798 0.003 0.222 -15.193 1152.442 0.0064 0.797 Intol3 99.435 469.875 102.197 444.483 0.002 0.444 -2.762 659.269 0.0015 0.955 Intol4 270.688 1458.579 353.558 1707.022 0.009 0.221 -82.87 1969.99 0.055 0.366 Hardl 133.963 652.213 118.77 544.87 0.005 0.287 15.193 854.229 0.0001 0.707 Hard2 158.822 842.96 125.677 508.56 0.011 0.328 33.145 976.069 0.0004 0.524 Hard3 196.108 861.449 201.632 800.634 0.001 0.227 -5.524 1181.779 0.0001 0.929 Hard4 602.138 1722.486 685.922 1820.532 0.008 0.233 -83.784 2512.789 0 0.426 Site series 3.587 1.518 3.558 1.35 0.005 0.234 0.03 1.404 0.2769 0.763 TPH 1032.714 1106.805 903.439 979.336 0.023 0.11 129.275 624.307 0.698 0.119 BA 10.096 14.121 8.404 11.88 0.027 0.113 1.692 7.325 0.7458 0.057 'Tol refers to tolerant species, semi to semi-tolerant species, intol to intolerant species, and hard to hardwood species. The numbers refer to height classes 1 to 4. 2RESID= Observed-Predicted. 3STD: standard deviation. 4STD DIFF: standardized difference values. 5RMSE: root mean square error. 6R-SQ: root squared. * indicates a significant difference from a mean of zero (a = 0.05). 102 Table V.4. Results of M S N validation of 16 ground and three selected auxiliary variables using reference observations (262 plots) of Run 5. RESID= Observed-Predicted. OBSERVED PREDICTED StD DIFF 4 SPECIES' MEAN STD.DEV 3 MEAN STD.DEV MEAN STD.DEV MEAN RMSE R-SQ PROB > T Toll 1811.214 5661.507 1608.683 4831.467 0.006 0.134 202.531 4745.902 0.362 0.563 Tol2 570.966 1453.391 576.634 1486.064 0.001 0.386 -5.668 2007.472 0.0045 0.95 Tol3 190.958 470.106 206.557 477.498 0.007 0.29 -15.599 646.873 0.0047 0.623 Tol4 288.553 691.087 214.111 578.997 0.025 0.286 74.443 852.465 0.0131 0.097 Semil 1270.504 3139.509 1247.821 3017.431 0.001 0.244 22.683 4176.938 0.0064 0.914 Semi2 521.805 1337.119 587.031 1361.165 0.013 0.366 -65.225 1902.929 0 0.47 Semi3 130.45 421.319 141.794 470.045 0.005 0.281 -11.344 627.227 0.0002 0.68 Semi4 225.454 721.526 267.992 768.427 0.011 0.269 -42.538 998.64 0.0109 0.372 Intoll 233.969 682.592 289.275 837.1 18 0.015 0.288 -55.305 1069.987 0.0005 0.228 Intol2 218.363 780.987 249.557 899.398 0.006 0.223 -31.195 1158.925 0.003 0.539 Intol3 93.584 466.398 65.225 238.889 0.019 0.338 28.359 503.801 0.0094 0.331 Intol4 214.111 1342.81 201.347 1235.563 0.002 0.176 12.763 1442.119 0.142 0.879 Hardl 202.767 993.587 144.63 757.201 0.009 0.189 58.137 1267.248 0.0008 0.35 Hard2 168.737 613.143 150.305 523.939 0.006 0.26 18.431 771.984 0.0073 0.637 Hard3 185.752 724.08 204.183 804.787 0.005 0.296 -18.431 1101.136 0.0012 0.692 Hard4 698.107 1814.597 656.038 1732.646 0.004 0.229 42.069 2464.527 0.0013 0.725 Sit series 3.546 1.537 3.683 1.471 0.023 0.258 -0.137 1.556 0.2207 0.473 TPH 975.668 1022.01 847.615 908.76 0.024 0.105 128.053 567.731 0.7094 0.063 BA 10.346 13.705 9.256 12.77 0.018 0.144 1.09 8.798 0.6159 0.616 'Tol refers to tolerant species, semi to semi-tolerant species, intol to intolerant species, and hard to hardwood species. The numbers refer to height classes 1 to 4. 2RESID= Observed-Predicted. 3STD: standard deviation. 4STD DIFF: standardized difference values. 5RMSE: root mean square error. 6R-SQ: root squared. 103 Appendix VI- Scatter Plots of Regeneration Bias Versus Four Auxiliary Variables for MSN Type 1 and its Corresponding Tabular Imputation for Runs 2 to 5 ID TO m TPH versus Bias 3000 2000 -1000 -0 -1000 -2000 0 2000 4000 TPH 6000 CCF vers us Bias 3000 2000 1000 -1000 -2000 .!i 1 • • •• 200 400 CCF 600 Aspect versus Bias 3000 2000 <S 1000 m -1000 -2000 0 f.-' :—• 20 40 60 Aspect 80 Figure VI. 1. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 65 target plots in Run 2 of the M S N model. Bias is observed minus predicted regeneration. 104 A s p e c t v e r s u s Bias 3000 2000 «g 1000 CO 0 -1000 -2000 20 40 60 A s p e c t 80 Figure VI.2. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 65 target plots in Run 3 of the M S N model. Bias is observed minus predicted regeneration. 105 Aspect versus Bias 3000 -I 2000 <g 1000 0 -1000 -l -2000 20 40 Aspect 60 80 Figure VI.3. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 64 target plots in Run 4 of the MSN model. Bias is observed minus predicted regeneration. 106 BA of large trees (BALT) versus bias 3000 2000 1000 -1000 -2000 r -OQ • • • • • 20 40 BALT 60 in ra m TPH vers us Bias 3000 2000 1000 0 -iooo H -2000 1000 2000 3000 4000 TPH Aspect versus Bias 3000 -I 2000 <g 1000 CO. 0 -1000 -2000 20 40 Aspect 60 80 Figure VI.4. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 71 target plots in Run 5 of the M S N model. Bias is observed minus predicted regeneration. 107 V) IS m BA of large (BALT) trees versus bias 3000 2000 1000 0 -1000 -I -2000 0 20 40 60 80 100 BALT Aspect versus Bias 3000 2000 <§ 1000 H 0 -1000 -2000 Or. ^ - > _ ; _ v . 20 40 60 80 Aspect Figure VI.5. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 65 target plots in Run 2 of the tabular imputation model. Bias is observed minus predicted regeneration. 108 BA of large trees (BALT) versus bias 3000 DQ 2000 -I 1000 0 -1000 -2000 20 40 BALT 60 80 TPH versus Bias in ra m 3000 2000 1000 0 -1000 4 -2000 0 5000 TPH 10000 Aspect versus Bias 3000 2000 H <» 1000 0 -1000 -2000 1 .• -20 40 60 Aspect 80 Figure VI.6. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 65 target plots in Run 3 of the tabular imputation model. Bias is observed minus predicted regeneration. 109 TPH versus Bias in ra m 3000 2000 1000 0 -1000 -2000 1000 2000 3000 4000 TPH in CO m CCF vers us Bias 3000 2000 1000 0 -f -1000 --2000 0 100 200 CCF 300 Aspect versus Bias 3000 -2000 -«g 1000 o-r. -1000 -2000 0 20 40 Aspect 60 80 Figure VI.7. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 64 target plots in Run 4 of the tabular imputation model. Bias is observed minus predicted regeneration. 110 BA of large trees (BALT) versus bias 3000 2000 in m 1000 + -2000 0 i * • -1000 20 40 BALT 60 TPH versus Bias m ra m 3000 2000 1000 -I -2000 -1000 - • " " 2000 4000 TPH 6000 Aspect versus Bias 3000 -I 2000 <g 1000 m 0 --1000 • -2000 20 40 Aspect 60 80 Figure VI.8. Scatter plot of the regeneration bias versus residual basal area of large trees (BALT), residual number of trees (TPH), crown competition factor (CCF), and aspect for 64 target plots in Run 5 of the tabular imputation model. Bias is observed minus predicted regeneration. i l l Appendix VII- Comparison Between Auxiliary Variables of Outlier Target Plots and Their Most Similar Neighbour for Runs 2 to 5 Table VII. 1. Comparison between the auxiliary variables for the target plot outliers and most similar neighbour plots for M S N Run 2 (shaded rows represent the M S N plots). Plot Yrs Siteprep Site Aspect Elevation Slope SI TPH BA CCF Adv. series position Regen 126-1 8 None 01 75 575 23 Lower 1250 21.11 106.59 Yes 130-2 2 1 None 03 100 " „ 8 g p l l l _Mkldlc . J 2 7 5 _ 16.901. 83.15" Yes . 60-2 10 None 04 180 ll-4-i 8* Middle 1625 4.29 20.39 No 162-2 :„ 9 " None T 03 , .. ' 202 ll1'!) • 16 Middle - 1600 U.S5 • ' .6.-26 No 1; 1 129-1 3 None 03 172 10 ;" 50 Middle 0 0 0 No 107-1 4~ None 03 80 ' li)15 38 Middle " 250. 5.99. ' 24.46 . No J 131-1 4 ~ None 03 1*94 1020 50 Middle o""" 0 0 " No f 407-1": 4 '...None 03 " 80 - 1( 38 •Middle --;250'- 5,99 24:46 101-1 19 None 01 337 1245 25 Middle 1125 38.21 191.15 No 72-1 ' "21 None 05-' ; 164 " """1090 50 Middle,, "" 33 58 150.58 _ j N o 1 110-1 18 None 01 30 1( 41 Middle 1000 37.98 169.41 No 72-1"" 21 - None 05 " .. * 109i) 50 Middle VI5 33 58 15"0"5iT . No "1 Yrsince: time-since-disturbance, Siteprep: site preparation, Slpos: slope position, TPH: number of residual trees per ha, BA: residual basal area per ha, CCF: crown competition factor. * shaded rows represents selected most similar neighbour plots. Table VII.2. Comparison between the auxiliary variables of the target plot outliers and most similar neighbour plots for M S N Run 3 (shaded rows represent the M S N plots). Plot Yrs Siteprep Site Aspect Elevation Slope SI TPH BA CCF Adv. series position Regen 38-1 11 None 03 170 1140 29 Middle 75 9.78 39.60 No 82-2 "To""" None 01 _ 302 |U(i2 m H i i i Middle 00 0.91 5 33 ' No J 36-1 10 None 04 280 1475 18 Upper 1400 0.78 5.49 No i "36^ *2 10 None ' 04 " " 110 ~7v-" '1445 ': ;io. •. Upp_er_ 1200 - .38*"" 9.54' "Yes""1 21-2 13 Brush 01 14 1445 45 Middle 1450 5.70 29.28 No 27-2 • I P S Brush i)3 ~ : s« 1380 37 Middle-" 1000 "6753 "4.21 130-2 "" 2 None 03 100 320 16 Middle 1275 16 90 83.15 No 115-2 2.7. None 03 • ~ 7 6 l • E F ' f c o 5 Middle 1525 14.38 75.06 No ' -1 Yrs: time-since-disturbance, Siteprep: site preparation, Slpos: slope position, TPH: number of residual trees per ha, BA: residual basal area per ha, CCF: crown competition factor. * shaded rows represents selected most similar neighbour plots. 112 Table VII.3. Comparison between the auxiliary variables of the target plot outliers and most similar neighbour plots for MSN Run 4 (shaded rows represent the M S N plots). Plot Yrs Sitepre Site Aspect Elevation Slope SI. TPH BA CCF Adv. P series position Regen 108-1 11 Burn 01 18 1055 28 Middle 1675 2.75 16.89 No "40-1 ~ 1-1 " None 01 206 1025"' 26 Mid 1200 1.76 . 14.19 Ye.-. 119-4 9 None 01 228 10" 8 Level "250 " 1.22 8.70 " Us 138-2 lT" Burn 04 " 660 0 Level 1200 1.04 "'8.21 • No !• 2 None 04 48 920 25 Mid 1300 6.00 30.58 *~Yes 1 1 5 - : „ 2 03 276 <20. , ' , 5 Middle """ " '1525 14.39 75.06 Us ' 109-3 19 Brush 03 30 5 60 Middle 1425 1.62 13.63 No j> 109-2 19 Brush 03 • 43 . 805 53 - Middle\„ .1075. ;.13.58 ' 115-1 2 None 01 156 815 21 Depression 2525 20.15 102.88 Yes t -130-2" , 2 • • None 03 100 • o "16 • Middle ,' • • 1275 "',16.90 :83.15 . • 113-2 6 None 04 188 0 25 Middle 850 12.13 63.48 Yes 130-2„ , lllfiiSIBi 03' 100""" 0' 16 Mid. ' 1275 ™" 16.90 s- 1- Yes 60-1 10 None 01 94 15 24 Mid 525 18.97 73 60 No l l l l l i i f " Nunc 03 170 1 14.i '""29" Mid 75 9.28 39.60 " N o 134-2 10 None 04 *"'"235 0 22 Middle 850 35.89 170.73 No - 140-5" 10 Nunc 04 . 12 ~f~~ 14™ Middle 1175 •-36.91 177.61 No 122-2 11 None 01 352 615 45 Middle 1275 41.59 185.90 Yes I 124-2-. 8 None 01 66-. ,640 34 . .- Middle , , 825; ,f44.67 ; "•-'--205.93 Yes -Yrs: time-since-disturbance, Siteprep: site preparation, Slpos: slope position, TPH: number of residual trees per ha, BA: residual basal area per ha, CCF: crown competition factor. * shaded rows represents selected most similar neighbour plots. Table VII.4. Comparison between the auxiliary variables of the target plot outliers and most similar neighbour plots for MSN Run 5 (shaded rows represent the MSN plots). Plot Yrs Siteprep Site series Aspect Elevation Slope Si position TPH BA CCF Adv. Regen 7-1 5 None 03 358 1295 19 Lower 400 7.13 31.57 Yes 126-1" None •05 ~ 270 1355 """ 25 1 ouer 600 " 11.2.) 2.26 Yes 109-2 ' 19 Brush 03 43 805""" " Middle" 1075 1.91 13.58 " No" " • 109-3 !• " 1'9 _^jBrush 03 .' 30 825 ~wz Middle; .1425 : 1.62 13.64 .. Nol -| 140-5 10 None 04 12 5 14 Middle 1175 36.91 177.61 No llllpi 8 - l ' - None _ 04 , 6 2 0 ' ' . . . Middle* 850 "T28.29 141.66 Yes • 126-2 8 None 01 69 0 20 Middle 30 47.39 240.20 Yes 124-4 No; 1- 01 i?1511ii (OO- , 25 Middle- 1450 l')22 147.85 No 115-2 None 03 276 - 0 Middle' 25 ' 14.38 ~75 06 * Yes 87-1 IllllSi1 Nunc 04 " llIBIil V20 Middle 50. ""- 6.00" 30.58 Ye"s, 106-1 7 None 04 132 )5 35 Middle •50 22.26 116.77 Yes 106-5 1,, None "04 . • - .124 15 37 "* Middle SW .•'15.79 82 12 J 'No " 2-1 16 None 04 72 1030 42 Middle 1425 1.74 14.51 No ; 108-1 11 Burn - 0 1 . •>:-.,'1055 28 . Middle •'• 1675, - 2.45 16.89 No : Yrs: time-since-disturbance, Siteprep: site preparation, Slpos: slope position, TPH: number of residual trees per ha, BA: residual basal area per ha, CCF: crown competition factor. * shaded rows represents selected most similar neighbour plots. 113 Appendix VIII- Average Values of the Auxiliary Variables of Reference and Target Plot Outliers for Runs 2 to 5 Table VILLI. Average values of the auxiliary variables of the reference and outlier target plots for M S N Run 2. Plot Type Yrsince Siteprep #. SS # Aspect # Elevation Slope Slposit # TPH BA CCF Reference 12 Bbrush 13 01 44 Flat 5 1114 26 Level 10 1078 10.34 49.57 (268 Brush 19 03 87 N 32 Lower 35 plots) Burn 69 04 75 NE 23 Middle 183 Mecha. 8 05 43 E 46 Plateau 10 None 159 06 5 SE 26 Upper 30 07 11 S 45 08 3 SW 49 W 26 NW 16 Target 10 Bbrush 0 01 3 Flat 0 1005 33 Level 0 833 17 122 (6 plots) Brush 0 03 3 N 0 Lower 1 Burn 0 04 1 NE 1 Middle 5 Mecha. 0 05 0 E 1 Plateau 0 None 6 06 0 SE 0 Upper 0 07 0 S 3 08 0 SW 0 w 0 NW 1 Yrsince: time-since-disturbance, Siteprep: site preparation, SS: site series, Slposit: slope position, TPH: number of residual trees per ha, BA: residual basal area per ha, CCF: crown competition factor. Table VIII.2. Average values of the auxiliary variables of the reference and outlier target plots for M S N Run 3. Plot Type Yrsince Siteprep #. SS # Aspect # Elevation Slope Slposit # TPH BA CCF Reference 11 Bbrush 12 01 46 Flat 6 1106 27 Level 10 1026 10 50 (268 Brush 18 03 93 N 27 Lower 40 plots) Burn 69 04 72 NE 28 Middle 172 Mecha. 10 05 38 E 45 Plateau 14 None 159 06 7 SE 28 Upper 32 07 10 S 47 08 2 SW 48 w 25 NW 14 Target 9 Bbrush . 1 01 1 Flat 0 1220 27 Level 0 1050 8 39 (4plots) Brush 0 03 2 N 1 Lower 0 Burn 0 04 1 NE 0 Middle 3 Mecha. 3 05 0 E 1 Plateau 0 None 06 0 SE 0 Upper 1 07 0 S 1 08 0 SW 0 W 1 NW 0 Yrsince: time-since-disturbance, Siteprep: site preparation, SS: site series, Slposit: slope position, TPH: number of residual trees per ha, BA: residual basal area per ha, CCF: crown competition factor. 114 Table VIII.3. Average values of the auxiliary variables of the reference and outlier target plots for M S N Run 4. Plot Type Yrsince Siteprep #. SS # Aspect # Elevation Slope SIposit # TPH BA CCF Reference 12 Bbrush 15 01 39 Flat 5 1120 27 Level 10 1033 10 48 (269 plots) Brush 19 03 97 N 30 Lower 37 Burn 71 04 67 NE 23 Middle 176 Mecha. 11 05 46 E 44 Plateau 12 None 153 06 5 SE 31 Upper 34 07 13 S 47 08 2 SW 46 W 26 NW 17 Target 9 Bbrush 0 01 5 Flat 0 894 29 Level 1 1186 16 74 (9 plots) Brush 1 03 1 N 2 Lower 0 Burn 1 04 3 NE 2 Middle 7 Mecha. 0 05 0 E 1 Plateau 0 None 7 06 0 SE 1 Upper 0 07 0 S 1 1 08 0 SW 2 w 0 NW 0 Yrsince: time-since-disturbance, Siteprep: site preparation, SS: site series, SIposit: slope position, TPH: number of residual trees per ha, BA: residual basal area per ha, CCF: crown competition factor. Table VIII.4. Average values of the auxiliary variables of the reference and outlier target plots for M S N Run 5. Plot Yrsince Siteprep #. SS # Aspect # Elevation Slope SIposit # TPH BA CCF Type Reference 12 Bbrush 13 01 43 Flat 4 1111 28 Level 7 976 10 49 (262 Brush 16 03 88 N 25 Lower 41 plots) Burn 73 04 66 NE 22 Middle 171 Mecha. 12 05 46 E 48 Plateau 13 None 148 06 07 08 7 10 2 SE S SW W NW 27 46 47 22 21 Upper Depression 30 0 Target 10 Bbrush 0 01 1 Flat 0 884 27 Level 0 1364 19 96 (7 plots) Brush 1 03 3 N 2 Lower 1 Burn 0 04 3 NE 1 Middle 6 Mecha. 0 05 0 E 2 Plateau 0 None 6 06 07 08 0 0 0 SE S SW w NW 1 0 1 0 Upper 0 Yrsince: time-since-disturbance, Siteprep: site preparation, SS: site series, SIposit: slope position, TPH: number of residual trees per ha, BA: residual basal area per ha, CCF: crown competition factor. 115 

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