56 model on the same data set. If this is the case, it is meaning- less to interpret the principal axes (Frisvad 1994). Therefore, to confirm or invalidate the relative superiority of a scenario over the random model, a delta value was computed by subtracting the broken-stick cumulated variance from the model cumulated variance after one, two, and three axes, per species and scenario. of the descriptors and their positions on the first axes, to esti- mate their relative contribution to variance. Spearman’s rs Appraisal of the Relationships Between Morpho- logical Variables and Their Contribution to the Growth Models Practitioners regularly try to identify a single tree parameter that would a) give an adequate representation of an urban tree population at any physiological stage, and b) allow for temporal or individual comparisons. To many professionals, this object- ive is a crucial step toward reducing the overall inventory costs. This part of the research was designed to test this intention. To do so, the 11 variables of scenario A (Table 1) were plotted on the first two axes of CA and the degree of association between variables was gauged by the angle formed by pairs or groups of descriptors in the biplot: the more acute the angle, the strong- er the association as the cosine of the angles in the biplot ap- proximate correlation between variables (Greenacre 2007). In addition, a Spearman’s statistic rs was computed between each is a nonparametric correlation coefficient computed from ranks. All multivariate statistical analyses indicated in the above sections were carried out using Statistica® (StatSoft, 2006) and the R package for multivariate analysis (Legendre and Casgrain 2006). RESULTS AND DISCUSSION Evaluation of the Explanatory Potential of Quali- tative and Quantitative Descriptors Two different projections were estimated with principal coordi- nate multidimensional analysis: quantitative and qualitative de- scriptors tested concurrently and quantitative inputs only. Table 2 shows the respective cumulative percentage of explained vari- ance for each model for the first three principal axes. The original work investigated more than ten axes for model differentiation but the outcome was identical with the three-dimension projection. In addition, it should be noted that cumulative variances expressed in Table 2 may seem low but this is inherent to Gower’s similar- ity coefficient. To confirm that these results were not erroneous nor an artefact of the analytical methodology and/or experimental protocol, quantitative descriptors were projected using a Euclid- ian coefficient that preserves the actual distance between objects in the multidimensional space. The results were satisfactory as the explained variance was over 93% for the first three axes. Clearly, conclusion to be drawn from PCO results is that there was a notable explanatory power decrease when qualitative in- dices (presence/absence of chlorosis; detection of parasites; presence and intensity of mechanical damages or sunscald/frost cracks; evaluation of crown density, crown development, and of general condition of trees) were included in the model. Rationale behind this conclusion can be explained with different possibil- ities. First, the classes that were defined for each variable were maybe inappropriate to express the complexity of urban tree con- dition. On the other hand, these results may have been influenced ©2009 International Society of Arboriculture honeylocust littleleaf linden Siberian elm Jutras et al.: Street Tree Inventory Parameters by the specific nature of qualitative indices. Most likely, despite appropriate calibration between the different observers dur- ing data collection, their intrinsic bias induced statistical noise. The objective of this section was to compare the significance of diverse qualitative and quantitative parameters. Both types have ad- vantages and disadvantages. Since many years, a debate has taken place on the respective superiority of qualitative or quantitative research and typically quantitative parameters were defined as ob- jective, reliable, transferable, and reproducible (Gelo et al. 2008). Based on our results, notwithstanding that qualitative indices are appealing in terms of inventory efficiency; it is proposed that quan- titative parameters might take precedence in urban tree inventory. Table 2. Percentage of explained variance per species for each of the first three principal axes. Species Norway maple silver maple common hackberry green ash Axis 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 Quantitative and qualitative descriptors 3.3% 1.4% 0.8% 4.3% 1.8% 1.0% 5.0% 2.3% 0.7% 3.8% 1.7% 1.1% 3.4% 1.5% 1.0% 6.8% 4.3% 3.1% 6.4% 3.2% 2.6% Quantitative descriptors only 9.8% 1.9% 1.2% 17.4% 3.3% 1.2% 19.0% 3.4% 1.7% 12.8% 3.0% 1.4% 9.7% 2.8% 1.5% 16.8% 6.7% 2.3% 17.0% 8.9% 1.9% Selection of the Most Important Quantitative Variables and Assessment of Model Integrity Results of the delta values that were computed between CA and broken-stick random model cumulated variances for each of the first three axes, per species and scenario are shown in Figure 2. For scenarios E and F, results for the third axis are not visible in the graph because the delta value is zero. Per- centages of cumulative variance for the first three axes of CA and the broken-stick model are presented in Table 3. Despite the fact that each of the species has its own canopy architecture, they showed remarkable similarity within scenar- ios. First, scenario E (annual DBH increment, crown volume in- crement, crown diameter increment, and height increment) and scenario F (DBH, crown volume, crown diameter, and height) rarely provided CA cumulated variances significantly greater than the broken-stick values. This result suggests low explana- tory power for these scenarios, close to a random model. There- fore, these variables might not be used as sole measurements to describe the complex reality of tree growth along sidewalks. Second, when ratio parameters were included in the analy- sis, tree growth model extraction was improved. For example, scenarios D and E were alike except for the inclusion of these
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