Research Note No ISSN

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1 Research Note No ISSN Dose-response models for stand thinning with the Ezject herbicide injection system by W.A Bergerud Ministry of Forests and Lands

2 Dose -response models for stand thinning with the Ezject herbicide injection system by W.A. Bergerud B.C Ministry of Forests and lands Research Branch 31 Bastion Square Victoria, B.C. V8W 3E7 August 1988 Ministry of Forests and Lands

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4 SUMMARY This report analyzes mortality data collected to test the effectiveness of the Ezject herbicide lance developed by B. Dillistone. The lance injects a used.22 cartridge containing g of the herbicide glyphosate into a tree. This method is fairly safe for the person applying the treatment and for the environment, since the herbicide is contained. The lance can also treat a large number of trees quickly. Five trials were established in 1980 for western hemlock, Douglas-fir, and lodgepole pine. Initial doseresponse models have been developed for western hemlock and Douglas-fir. Models could not be fit for lodgepole pine, however, because not enough large trees were treated and the treatments were confounded with other factors. It is clear that the Ezject lance injector system is effective for killing trees. Increasing the number of capsules or placing them around the tree increased the size of tree which could be killed. Seasonal effects were small in the long run. It is recommended that in future trials, individual trees be randomly assigned one of a wide range of dosages. The range of dosages should be chosen so that about half the treated trees survive the treatments. From this, proper operational guidelines for dosage prescriptions may be developed. iii

5 ACKNOWLEDGEMENTS I am grateful to B. Dillistone, K. Bradley, M. Kovats, and H. Benskin for organizing this experiment; and to B. Dillistone and members of the Silviculture Branch for collecting the data. I received assistance and helpful suggestions from S. Omule, J. Boateng, G. Ackerman, and B. Dillistone for interpreting the results. I would also like to thank R.J. Mackay, J.G. Kalbfleisch, and S. Brown, professors of statistics at the University of Waterloo, for teaching me the basics of logistic regression. I am indebted to W.G. Roland for his support and editorial comments. iv

6 TABLE OF CONTENTS SUMMARY ACKNOWLEDGEMENTS iii iv 1 INTRODUCTION METHODS Study Design Preliminary Analysis Logistic Regression Analysis Development of operational guidelines RESULTS Preliminary Analysis Logistic Regression Analysis Western hemlock Douglas-fir Lodgepole pine Operational guidelines DISCUSSION Preliminary Analysis Logistic Regression Analysis CONCLUSIONS AND RECOMMENDATIONS REFERENCES

7 APPENDICES 1 Description of boxplots Preliminary analysis Counts of trees that improved at least once in the sequence of assessments Analysis of variance on initial dbh Percent dead by crown class at the 2nd-year assessmen Logistic regression analysis Models fitted to western hemlock data Tests for western hemlock data based on models in Table Models fitted to Douglas-fir data Tests for Douglas-fir data based on models in Table Ninety percent confidence limits for the predicted dbh of western hemlock (in cm) that can be killed with 50, 80, 90, 95, 97.5, and 99% mortality rates Ninety percent confidence limits for the predicted dbh of Douglas-fir (in cm) that can be killed with 50, 80, 90, 95, 97.5, and 99% mortality rates TABLES 1 Trials put in place in 1979 and Years of assessment collected for trials with data stored in LIBRARIAN Means of dbh (cm) for each tria Percent of trees killed for each treatment at each assessment for western hemlock at Youbou Percent of trees killed for each treatment at each assessment for Douglas-fir at Cowichan Lake Percent of trees killed for each treatment at each assessment for lodgepole pine at Cranbrook Percent of trees killed for each treatment at each assessment for lodgepole pine at Vanderhoof Percent of trees killed for each treatment at each assessment for lodgepole pine at 100 Mile House Parameters of the final predictive equations for western hemlock Parameters of the final predictive equations for Douglas-fir based on last year data, with small trees for treatment 32 presumed dead Percent of trees in each crown class category for each lodgepole pine block

8 FIGURES 1 Boxplots of dbh plot means for each trial Boxplots of dbh (cm) by crown class for Douglas-fir and lodgepole pine trials Percent dead by crown class at the 2nd-year assessment for Douglas-fir and lodgepole pine Predicted probabilities of death for western hemlock, plotted against dbh for the different treatments Observed proportion of Douglas-fir trees killed plotted against dbh class (2-cm classes) for each of the seasons/blocks (last year data Diameter at breast height of Douglas-fir with a predicted 90% chance of being killed Observed proportion of lodgepole pine trees killed at Cranbrook, plotted against dbh class for each season/block (from last year measured) Observed proportion of lodgepole pine trees killed at Vanderhoof, plotted against dbh class for each season/block (from last year measured) Observed proportion of lodgepole pine trees killed at 100 Mile House, plotted against dbh class for each season/block (from last year measured) The dbh of western hemlock with predicted probabilities of death for the various treatments The dbh of Douglas-fir with predicted probabilities of death for the various treatments: a) worst case season/block with lowest mortality rate; and b) best case winter with highest mortality rate

9 1 INTRODUCTION Improving yield by thinning stands of commercial timber is an important silvicultural management tool. B. Dillistone developed the Ezject 1 herbicide lance for this purpose. It selectively kills trees by injecting into the trunk a used.22 cartridge containing g isopropylamine salt of glyphosate. This method is fairly safe for the person applying the treatment and for the environment, since the herbicide is contained. The lance can also treat a large number of trees quickly. Several trials were established in 1979 and 1980 (Table 1) by B.C. Ministry of Forests staff and B. Dillistone, to study the effectiveness of the lances and to develop guidelines for operational use. Five of these trials were designed to study the number and arrangements (horizontal or vertical spacing) of capsules needed to kill trees of different species and size; and to determine the most effective season for application. Survival data were collected for up to 4 years after treatment. This report analyses the data from these five trials using logistic regression. 2.1 Study Design 2 METHODS A completely randomized design was originally proposed, using five lance treatments and four seasons of application. At each location (or trial), experimental units (plots) were to be randomly assigned a lance treatment and a season of application, with three or eight plots per treatment-season combination. Each plot contained many trees, 30 of which were selected for thinning and treatment with the lance. The trial for hemlock at Youbou was installed as designed. For the other trials all plots for one season were treated as a block, resulting in a randomized block design with season and blocks confounded. Some control plots were also established where trees were selected but not treated in any way. TABLE 1. Trials put in place in 1979 and The system was known as Wee-do when these studies were established.

10 The five lance treatments consisted of different numbers and arrangements of capsules of g isopropylamine salt of glyphosate injected into each tree: 00 = control 11 = 1 capsule 21 = 2 capsules arranged vertically 22 = 2 capsules on opposite sides of the tree 31 = 3 capsules arranged vertically 32 = 3 capsules arranged around the tree. (Please note the two-digit numbers. They will be used throughout the report to refer to the treatments.) The diameter at breast height and crown class 2 were recorded at the time of treatment; thereafter, assessment of the percent live crown of all trees was done yearly during the same season as the original treatment. A tree was considered dead only when 100% of the crown was dead. Crown class was not recorded at Youbou. Not all seasons were treated, nor were an equal number of years assessed for all trials and seasons (Table 2). TABLE 2. Years of assessment collected for trials with data stored in LIBRARIAN 2.2 Preliminary Analysis Data were checked for obvious errors and inconsistencies. Relationships between dbh, crown class, tree survival, treatments, and seasons of application were explored with plots, boxplots (see Appendix 1 for a description of a boxplot), and analysis of variance. In particular, the following patterns were expected and checked for: 1. trees dead one year should not be alive the next; 2. the percent live crown of treated trees should not increase with time; 3. the mean and range of initial tree diameter (dbh) should be similar for all treatment-season combinations within each trial; 4. the dbh for dominant trees should be larger than for suppressed trees; and 5. death of control trees should be rare. 2 Crown class was coded as: 1 Dominant 2 Co-dominant 3 Intermediate 4 Suppressed 5 Understory 2

11 2.3 Logistic Regression Analysis Logistic regression models were developed to examine the relationship between survival and dbh, lance treatment, and season of application. These models are conceptually similar to multiple regression and analysis of variance; however, the response variable has a binomial distribution, so that these models predict p, the probability of tree mortality. This analytical method is described in texts, such as Cox (1970), Dobson (1983), Feinberg (1980), and McCullagh and Nelder (1983). A good introductory text is Freeman (1987). Logistic regression analysis uses the logit transformation of p, denoted by θ, as the response variable where: θ = log (p/(1-p)) (1) The data were fit using the maximum likelihood methods available in the CATMOD procedure in SAS of the SAS Institute (1985). The models fitted had the following general form: θ = β o + β dbh + β1x + β 2 X 2 + (2) whereβ o, β, β 1, β 2,... are the parameters of the model, dbh is the covariate, and X 1, X 2,... are dummy variables for lance treatment and season. The final model was selected by first fitting a complicated model to the data. Then simpler versions were fitted to test terms in the complicated model. Terms or variables were dropped until it was not reasonable to drop any more. For example, the first model fitted for each of these trials allowed a different relationship between dbh and survival for each season by treatment combination (or cell). Then a second model was run, forcing the relationship (i.e., slope) between dbh and survival to be the same. If the change in deviance (see below) between the two models was not significant at a specified probability level, then it was deemed unnecessary to allow all the slopes to be different. In this way, the simplest model adequately describing or fitting the data was found. These different models were tested and compared using a transformation of the likelihood ratio statistic called the deviance. It is approximately c2-distributed, unlike the F-distribution of multiple regression. Changes in deviance were used to compare models just as changes in the Residual Sums of Squares are used in multiple regression to test if a variable should be included in the model. Where the predicted logit value, θ^, has been calculated, an estimate of the probability of success (i.e., death), p^, can be calculated by: p^ = exp ( θ^ ) / (1 + exp ( θ^ )) (3) Confidence limits for predicted probabilities and dbh were obtained by assuming multivariate normality for the model parameters. The plot structure was ignored in this analysis. Nevertheless, the datasets were too large for individual tree analysis, so trees were grouped into dbh classes with even-valued midpoints (dbh was measured in centimetres) Development of operational guidelines Operational guidelines were developed by rearranging the logistic regression models to obtain the largest size tree that could be killed with at least a specified probability given a specific treatment. These values were tabulated and plotted. 3.1 Preliminary Analysis 3 RESULTS The small number of trees whose percent live crown increased with time (including those that came back to life) are summarized in Table 2.1 of Appendix 2. 3

12 Boxplots of the dbh plot means are shown in Figure 1, while the means and Duncan s test are presented in Table 3 (corresponding ANOVA s are in Table 2.2, Appendix 2). There are seasonal differences in dbh for all trials except at Youbou (western hemlock) where the plots were randomly assigned treatments and season of application. The trees treated in the spring for Douglas-fir at Cowichan Lake were larger than those for the other seasons. The dbh differences between seasons were large for the lodgepole pine, with the fall trees at Cranbrook being especially small. FIGURE 1. Boxplots of dbh plot means for each trial. 4

13 TABLE 3. Means of dbh (cm) for each trial Boxplots of individual tree dbh for the different crown classes at all sites (except Youbou where crown class data were not collected) are plotted in Figure 2. Dominant and co-dominant trees have larger dbh than do the suppressed trees. The boxplots were split up by season (plots not presented), but showed little difference between seasons for a given crown class except for the small fall lodgepole pine at Cranbrook. The percent of trees that died are summarized in Tables 4-8 and are arranged by treatment, season of application, and year of assessment. A few control trees were included in the Cranbrook and Vanderhoof trials. The coding forms indicate that the control trees at Vanderhoof died in the 2nd year, but a recent inspection found that most are alive (G. Ackerman, Silviculture Branch, pers. comm.). The simple effect of crown class on mortality is illustrated in Figure 3 (and tabulated in Appendix 2, Table 2.3). There does not appear to be large seasonal differences in mortality, except in Cranbrook. 3.2 Logistic Regression Analysis Western hemlock Logistic regression models were fitted to data collected in the 2nd year, since these were available for all seasons, and also to the last year data were collected: in the 2nd year for fall and winter and the 3rd year for spring and summer. The models fitted and tests conducted are summarized in Appendix 3, Tables 3.1 and

14 All models adequately fit the data. The tests suggest that the shape of the response to dbh is constant regardless of treatments, and that there is no season-by-treatment interaction. There were treatment differences, although two capsules applied horizontally (22) produced a similar response as three capsules applied vertically (31). For the 2nd-year data, the fall and winter seasons had similar responses and were more effective than the spring and summer applications. Seasonal differences became slight when the 3rd-year spring and summer data were compared with the 2nd-year fall and winter data. Thus, final seasonal differences were small. FIGURE 2. Boxplots of dbh (cm) by crown class for Douglas-fir and lodgepole pine trials. 6

15 TABLE 4. Percent of trees killed for each treatment at each assessment for western hemlock at Youbou TABLE 5. Percent of trees killed for each treatment at each assessment for Douglas-fir at Cowichan Lake TABLE 6. Percent of trees killed for each treatment at each assessment for lodgepole pine at Cranbrook 7

16 TABLE 7. Percent of trees killed for each treatment at each assessment for lodgepole pine at Vanderhoof TABLE 8. Percent of trees killed for each treatment at each assessment for lodgepole pine at 100 Mile House FIGURE 3. Percent dead by crown class at the 2nd-year assessment for Douglas-fir and lodgepole pine. 8

17 The parameters for the final predictive equations are in Table 9. Using the last year data, the equation for the one capsule treatment is: θ^ = log ( p^ /(1-p^ )) = dbh class. The equations for the last year data are plotted in Figure 4. Notice that the shapes of the logistic curves are the same and that the treatment effect is to shift the curve along the horizontal axis. These equations are used to predict the probability of killing trees of a given size and the size of tree that can be killed with a certain probability (see Section 3.2.4, Operational Guidelines ) Douglas-fir Logistic regression models were fitted to data collected in the 2nd year, since this was available for all seasons, and also to the last year data were collected: in the 2nd year for fall and winter and the 3rd year for spring and summer. The models fitted and tests conducted are summarized in Appendix 3, Tables 3.3 and 3.4. Although most of the models provided an adequate fit, a fairly complicated model (#3) was required for both 2nd- and last year data. The dbh class parameter for treatment 32 is smaller (-0.53, SE= 0.04) than the other treatments (-0.79, SE = 0.03). There are also indications of a season-by-treatment interaction. To investigate these interactions, the data were plotted in Figure 5. The shapes of the curves are very similar, but there are an unusually high number of small trees surviving the 32 treatments in all seasons. When these small trees (with dbh class less than 10 cm) are assumed dead, the evidence for slope parameter differences becomes very weak. If the survival of these small trees is an anomaly, then the dbh parameter can be assumed constant for all treatments and seasons. The parameter estimates are presented in Table 10. TABLE 9. Parameters of the final predictive equations for western hemlock TABLE 10. Parameters of the final pridictive equations for Douglas-fir based on last year data, with small trees for treatment 32 presumed dead a SE of parameter estimate in brackets. 9

18 FIGURE 4. Predicted probabilities of death for western hemlock, plotted against dbh for the different treatments. 10

19 FIGURE 5. Observed percent dead for Douglas-fir, plotted against dbh class (2-cm classes) for each of the seasons/blocks (last year data). 11

20 To show the season-by-treatment interaction, the dbh with a predicted 90% mortality rate was plotted in Figure 6. The interaction, indicated by the non-parallelism of the lines, results from the unusual success of treatment 21 in the fall and the greater success of treatment 32 to that of 31 in the fall and summer. Thus, there is no difference between treatments 31 and 32 except in the summer (and maybe in the fall), and treatments 21 and 22 are widely separated except for the fall applications. For all treatments, the winter application (in March 1981) had the greatest success rate Lodgepole pine Three installations of lodgepole pine were established at Cranbrook, Vanderhoof, and 100 Mile House. The mortality for the last year observed is plotted in Figures 7-9. Some of the plots have the expected S-shape, indicating decreasing mortality with increasing tree size. Other plots are quite flat at 100% mortality, since most of the trees treated were small and died. Many of the curves are erratic at higher dbh. This is largely due to the small number of large trees treated: one tree s response strongly influences the observed percentage. Logistic regression analysis was not conducted. Such models could not be fitted, since most of the trees died and the response of the larger trees was erratic. It follows that it was not possible to develop dose-response curves for lodgepole pine. FIGURE 6. Diameter at breast height of Douglas-fir with a predicted 90% chance of being killed. 12

21 FIGURE 7. Observed proportion of lodgepole pine trees killed at Cranbrook, plotted against dbh class for each season/block (from last year measured). 13

22 FIGURE 8. Observed proportion of lodgepole pine trees killed at Vanderhoof, plotted against dbh slass for each season/block (from last year measured). 14

23 FIGURE 9. Observed proportion of lodgepole pine trees killed at 100 Mile House, plotted against dbh class for each season/block (from last year measured) Operational guidelines The logistic regressions fitted to the western hemlock and Douglas-fir data were rearranged to obtain the predicted size of tree that could be killed with a 50, 80, 90, 95, 97.5, and 99% certainty. These values are plotted in Figures 10 and 11. The season-by-treatment interaction complicates the results for Douglas-fir, such that two sets of values were plotted: the worst season (usually fall) and the best season (always winter) for each treatment. Confidence limits for the plotted values are tabulated in Appendix 3, Tables 3.5 and 3.6. The lower number of each pair in these tables is the one-tailed 95% confidence limit which could be used as operational guidelines. 15

24 FIGURE 10. The dbh of western hemlock with predicted probabilities of death for the various treatments. 16

25 FIGURE 11. The dbh of Douglas-fir with predicted probabilities of death for the various treatments: a)worst case season/block with lowest mortality rate; and b) best winter with highest mortality rate. 17

26 4 DISCUSSION 4.1 Preliminary Analysis The reason that the percent live crown of a few treated trees increased with time may have been due to observational problems in the field (G. Ackerman, Silviculture Branch, pers. comm.). The seasonal differences in initial dbh for the Douglas-fir and lodgepole pine trials were due to the confounding of seasons with blocks. The spring block for the Douglas-fir was physically separate from the other three blocks, which were close together. The lodgepole pine blocks at Cranbrook had different initial densities, with the fall block being the most dense (4950 stems per hectare) and the summer the least dense (2800 stems per hectare). The winter block had 3335 stems per hectare (reported by G. Ackerman, Silviculture Branch, Victoria). 4.2 Logistic Regression Analysis The plot structure of the design was ignored in this analysis. This would not be reasonable if the usual normal regression models were used, since the plots were the experimental units and their variation would be an important part of the analysis. Although the logistic regression analysis could be done this way, the mean dbh of 30 trees in each plot would be the covariate. This is meaningless, since treatment dosages are determined individually for each tree. Logistic regression analysis uses the binomial distribution to model the data. This requires the following assumptions: 1) plot responses are independent; 2) tree responses within plots are independent; 3) the probability of success is the same for all plots, given the same treatment and stand characteristics; and 4) the probability of success is the same for all trees within a plot, given the same dbh. If these assumptions are reasonable, then the plot structure is irrelevant since each tree responds independently of any other tree and, given the same dbh and treatment, has the same probability of death as any other tree whether that tree is nearby, in the same plot, or in a different plot. Logistic regression models successfully fit the mortality data collected for western hemlock and Douglasfir. The final equations predict the proportion of trees with a certain dbh that would die as a result of treatment. This can also be thought of as the probability of a tree with a specific dbh dying as a result of the treatment. The interpretation of the model is straightforward for western hemlock, as there are replicates for each season and treatment. It was found that larger trees could be killed if they were injected with more capsules or the capsules were placed horizontally around the tree. Interpretation of the Douglas-fir and lodgepole pine data was complicated by a number of problems. For both species, blocks and seasons were confounded so that their effects can not be reliably separated during interpretation. For instance, because the lodgepole pine blocks had different stand densities, any season differences found may, in fact, be due to the different densities, or to any other factor associated with the blocks. Another complicating factor for the lodgepole pine was that the treated trees at Cranbrook had a very different crown class representation than at Vanderhoof and 100 Mile House. The trees at Cranbrook took from 3 to 4 years to die, while most of those at Vanderhoof and 100 Mile House were dead in only 1 or 2 years. The winter and summer trees at Cranbrook tended to be somewhat larger (Figure 1) than other lodgepole pine blocks, which may partly explain their resistance to the herbicide. On the other hand, the fall trees were quite small but still took 2 years to reach 90% mortality (Table 6). Crown class may partly explain this. At Cranbrook, 83% of the treated trees had a dominant or co-dominant crown class as opposed to only 17 and 13% at Vanderhoof and 100 Mile House, respectively (Table 11). The observed results, then, are not surprising if dominant and co-dominant trees can better resist the herbicide than can the intermediate and suppressed trees. 18

27 TABLE 11. Percent of trees in each crown class category for each lodgepole pine block Interpretation of Douglas-fir data was more successful. An interesting anomaly in the data was that a number of small Douglas-fir survived the heaviest dose used in these trials (i.e., three capsules applied horizontally around the tree). This could be due to an overdose response, in which the area right around the injected capsules died so quickly that the herbicide was not translocated throughout the tree (J. Boateng, Silviculture Branch, pers. comm.). Treatment differences were similar to those for western hemlock, wherein larger trees could be killed when injected with more cpsules of the capsules were applied around the tree instead of vertically up one side. It is not clear how to interpret the season-by-treatment interaction, especially as any seasonal effects may be block effects. It would be prudent, therefore, to develop operational guidelines on the basis of the least successful season of block observed. Crown class was, by and large, ignored while these models were fitted. This was particularly true for western hemlock, for which this information was unavailable. Douglas-fir had the best set of data for examining crown class effects Models fitted with crown class instead of dbh class were found to fit poorly, and models with both has such large standard errors for many of the parameter estimates that they were considered unsuitable. Lodgepole pine results were confounded by large differences in the proportions of trees in different crown class for the various trials. 19

28 Crown class will be an important variable to consider when these results are applied to other stands, since the trees may be generally larger or smaller. Although the high correlation between dbh and crown class may not change in these other stands, if a stand has generally larger trees, then those of the same size are more likely to have a weaker crown class than in the studied stand. Thus, it may be easier to kill trees of a certain dbh than is suggested by this study. Alternatively, if the other stand has generally smaller trees, it may be more difficult to kill trees than would be expected from the present results. Of course, crown class will not be a problem if these results are applied to stands of similar tree size and stand structure as those considered in this report. 5 CONCLUSIONS AND RECOMMENDATIONS It is clear that the Ezject lance injector system is effective for killing trees. Initial dose-response models have been developed for western hemlock and Douglas-fir. Models could not be fit for lodgepole pine, however, as too few large trees were treated and the treatments were confounded with other factors. Comprehensive dose-response models for the Ezject lance injector system require data from more trials in different stands for each target species. The design should be somewhat different from that used in this study. Within each stand, trees should be individually and randomly assigned treatments, with an increased number of doses used. Several stands with different average tree size and stand structure should be tested so that each dose would be tested on a wide range of dbh and crown class. The trial should also be designed so that about half the trees will survive treatment. In this way, guidelines for the efficient use of the lance can be generated. 20

29 6 REFERENCES Cox, D.R Analysis of binary data. Methuen & Co. Ltd., London. Dobson, A.J An introduction to statistical modelling. Chapman & Hall, London. Feinberg, S The analysis of cross-classified data. 2nd ed. The MIT Press, Cambridge, Mass. Freeman, D.H Applied categorical data analysis. Marcel Dekker Inc., New York, N.Y. McCullagh, P. and J.A. Nelder Generalized linear models. Chapman & Hall, London, pp Pregibon, D Logistic regression diagnostics. Annals of Statistics 9: SAS Institute SAS user s guide: statistics. Cary, N.C. 21

30 APPENDIX 1. Description of boxplots Middle Bar = MEDIAN + in middle of box = MEAN Ends of box = 25 & 75 PERCENTILES (i.e., QUARTILES) Length of box = Interquartile Distance (IQD) Whiskers extend an IQD beyond box. If the lowest or highest value in the data falls within the length of the whisker, then the whisker will stop at that value. 0 indicates points within 3/2 IQD of end of box (i.e., within 2 IQD from median). * indicates points beyond 3/2 IQD of end of box (i.e., beyond 2 IQD from median). NOTE: 1. If data are normally distributed, then about 1 out of 20 observations should fall outside the whiskers, and an asterisk should occur about once for every 200 observations. 2. If data are symmetrically distributed, then the + (MEAN) and the middle bar (MEDIAN) should be close together. PROOF OF NOTE 1: By definition, 50% of the data are between the quartiles. This occurs at Z = ±.675 (for a normal distribution), so IQD = Hence, 3/2 IQD from median is at The area between ± is So about 1/25 or 1/20 values should be beyond 3/2 IQD from median, i.e., beyond whiskers. 22

31 APPENDIX 2. TABLE 2.1. Preliminary analysis Counts of trees that improved at least once in the sequence of assessments 23

32 TABLE 2.2. Analysis of variance on initial dbh 24

33 TABLE 2.3. Percent dead by crown class at the 2nd-year assessment (of treated trees only). (Sample sizes in brackets below percentage.) 25

34 APPENDIX 3. Logistic regression analysis TABLE 3.1. Models fitted to western hemlock data TABLE 3.2. Tests for western hemlock data based on models in Table

35 TABLE 3.3. Models fitted to Douglas-fir data TABLE 3.4. Tests for Douglas-fir data based on models in Table

36 TABLE 3.5. Ninety percent confidence limits for the predicted dbh of western hemlock (in cm) that can be killed with 50, 80, 90 95, 97.5 and 99% mortality rates TABLE 3.6. Ninety percent confidence limits for the predicted dbh of Douglas-fir (in cm) that can be killed with 50, 80, 90, 95, and 99% mortality rates 28