Arboriculture & Urban Forestry 45(1): January 2019 the corresponding likelihood of assessment subjectiv- ity among different researchers collecting data at the two time instances. Researchers first conducted a bivariate analysis to get an understanding of the influence of individual vulnerability indicators (i.e., exposure, sensitivity, and adaptive capacity indicators in Table 1) on the three ecological change variables, and insight into their utility for vulnerability framework refinement. The analysis included simple significance testing on rela- tionships between vulnerability indicators and mor- tality, condition, and growth, using the appropriate nonparametric statistical test based on data type. Spear- man’s Rho was used for tests between continuous variables and Pearson’s chi-squared (χ2 ) test was used for tests between categorical/binary variables. The Mann-Whitney U test was used for tests between con- tinuous and binary variables, while the Kruskal-Wallis rank test was used for tests between continuous and categorical variables with more than two groups. A subsequent multivariate analysis was conducted to evaluate the predictive capacity and explanatory power of the vulnerability indicators on urban forest ecological change in Harbord Village. Only those vulnerability indicators that were found to have sta- tistical significance at the α = 0.05 level in the bivari- ate analysis were included. Multiple linear (i.e., ordinary least squares) regression was used to predict the continuous tree condition and growth rate vari- ables. Condition and growth were used as dependent response variables in separate regression models using the reduced selection of vulnerability indicators as independent predictor variables. These two models were run on the 672 living trees only, as condition and growth cannot be measured on dead/removed trees. The site size (i.e., m2 of growing environment), height of nearest building, distance to nearest build- ing, distance to street, width of street, and width of sidewalk variables were log transformed to meet nor- mality assumptions for regression analysis. Tolerance values indicated no issues with multicollinearity (i.e., tolerance values above 0.1; Hair et al. 2010) for all variables except for some of the groups (i.e., dummy variables) of the land use and building type categori- cal variables. While this multicollinearity was to be expected to some degree, it does reduce the effective- ness of the models and is a source of uncertainty. Only the top five most abundant species were included in the analysis as dummy variables. 15 Lastly, to analyze the possible effects of the vul- nerability indicators on the binary variable describing tree mortality, researchers used a multilayer percep- tron neural network using IBM® SPSS® Statistics 24 (Hastie et al. 2009; Jutras et al. 2009). Multilayer perceptron neural networks are artificial neural net- works comprised of a collection of data structures and algorithms in a network meant to loosely mimic a biological brain. They fall within the discipline of machine learning that has been growing in impor- tance with the rise of computational power and large data sets (Hastie et al. 2009). The mixed structure, noisy, and highly variable nature of the vulnerability data—and of urban social-ecological systems in gen- eral—negate the use of many traditional inferential statistics. While logistic regression has been used to predict tree mortality in urban forests (e.g., Koeser et al. 2013), researchers opted not to use this approach because of the many categorical variables used in the analysis and comparatively small sample size (Hair et al. 2010). Neural networks have their origin in com- puter science and artificial intelligence, but have been applied successfully in tree mortality research in both rural (Guan and Gertner 1991; Hasenauer et al. 2011) and urban settings (Jutras et al. 2009). For example, Jutras et al. (2009) used them to investigate morpho- logical parameters of street trees in Montreal, Qué- bec, Canada. Multilayer perceptron neural networks use a number of neurons (i.e., units) in one or more layers, which communicate with each other via weighted connections, or links (Hastie et al. 2009). The independent variables (i.e., inputs) in the input layer communicate to neurons in one or more hidden Figure 1. Change in size-class distribution of measured trees between the 2007/2008 (N = 806) and 2014 (N = 672; N = 1,056 with newly planted trees) inventories in the Harbord Village neighborhood in Toronto, Ontario, Canada. ©2019 International Society of Arboriculture
January 2019
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