138 Follett et al.: New Approach to Quantify Growth Response to Pruning Statistical Analysis All statistical analysis was completed using R: A Language and Environment for Statistical Com- puting. Linear modeling was completed using the “lm” function in R, while ANOVA’s utilized the “aov” function, and Tukey’s tests were con- ducted with the “Tukey HSD” function. In the case of reporting R2 values, the adjusted R2 val- ues are reported whenever multiple variables are included in the linear regression analysis. Unless otherwise stated in the results, tests were initially done with the species pooled, then the model was fit to each species individually. In some cases, there was testing to investigate the differences between species, and this is specified in the results or figures. One-way ANOVA testing was used to test differences in means for all group tests, such as species, regrowth type, or trim type, where- as linear models were fit to all scalar variables. RESULTS Accuracy of TruPulse 360 for Branch Segment Length Measurements To assess how well the laser method captured branch growth, in-tree measurements made with a tape measure were compared to the laser de- rived measurements made from the ground; using linear regression and examining how close the slope was to unity, as well as the R 2 of the rela- tionship. For the 19 branch samples of F. penn- sylvanica, the laser derived measurements for annual pruning response growth were in close agreement with in-tree measurements [mean length = 0.52 m, SD = 0.354 m, R 2 = 0.98, F (1,92) = 4844, P < 0.001, slope = 0.948] (Figure 2). Results for the total branch length since the last pruning [mean length = 2.52 m, SD = 0.77 m, R 2 = 0.98, F (1,18) = 1223, P < 0.001, slope = 0.998] were similar to those for annual branch growth (total length data not shown in Figure 2). Branch Growth in Response to Pruning Using ANOVA testing (one-way), for all mea- sured years in this study, the documented mean annual branch response growth following prun- ing was highest in A. saccharinum, followed by F. pennsylvanica, while A. platanoides was the lowest (Figure 4). Acer platanoides was significantly dif- ©2016 International Society of Arboriculture Figure 4. Comparison of annual pruning response growth for three urban tree species since the last pruning epi- sode. The dark line of each boxplot represents the median, the upper and lower hinges are 75th and 25th percentiles, respectively, whiskers extend to highest and lowest values within the 1.5 inter-quartile range. Data points beyond the whiskers are outliers. Boxplots with same letters are not significantly different, Tukey’s honestly significant differ- ence HSD P < 0.001, N = 734. ferent from A. saccharinum, and F. pennsylvanica (P < 0.001), however there was no significant dif- ference between A. saccharinum and F. pennsyl- vanica (Figure 4, P < 0.001, Tukey’s HSD test). Linear regression analysis of the length of annual branch response growth showed a strong decline over time in A. platanoides and F. pennsylvanica, but only moderately in A. saccharinum (Figure 5). While the results were significant, there was a lot of variation, as can be seen by the relatively low R 2 values, particularly for A. saccharinum. Results are as follows; all species, R 2 = 734; F. pennsylvanica, R2 369; A. platanoides, R 2 A. saccharinum, R2 = 0.169, P < 0.001 N = 0.01, P < 0.05, N = = 0.05, P < 0.005, N = 278; = 0.005, P > 0.05, N = 252. Comparing species, the rate of decline was greatest for A. platanoides (slope = -0.07), followed by F. pennsylvanica (slope = -0.03), and then A. sac- charinum (slope = -0.02) (Figure 5). For all species, annual growth length of pruning response branches was much greater than unpruned (con- trol) branch growth (two sample t-test, mean annual response growth length = 0.66 m, mean control growth length = 0.15 m, P < 0.001). Maxi-
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