54 Multivariate algorithms are predominantly supported by ma- trix algebra and statistical theory around the concept of multi- dimensional space: each of n trees is considered a vector in a p-dimensional space, where p is the number of recorded vari- ables. The axes can be rotated so as to maximize the percent- age of variance explained (Legendre and Legendre 1998). This reduces the data set dimensions into a small number of readily interpretable independent axes, and significant variables can thus be identified. Applied research problems were successfully stud- ied with these methods. Plant growth models elaborated by Jutras (1989) made use of cluster analysis, parametric and nonparamet- ric discriminant analysis, and contingency analysis. Savva et al. (2002) compared tree-ring characteristics using cluster analysis. Matyas (1994) developed a growth-response model to predict the effects of climate change on tree growth and survival with princi- pal component analysis. Leclerc et al. (2001) also used principal component analysis for a study on grouping soils of the Mont- real lowlands. Hammitt (2002) used factor analysis involving principal components to determine common functions of urban forest and park refuges. Hence, it can be inferred that multivari- ate methods might be powerful analytical tools to unveil eco- logical structures related to complex street tree growth patterns. The main objective of this paper is to assess the relevance of several low-technology parameters and to identify key vari- ables that might be used within a reliable street tree inventory procedure. In view of that, a multivariate statistical analysis scheme was designed and tested on growth models of seven urban tree species. Three primordial and successive steps com- posed this scheme. The first one aimed at comparing the sig- nificance of diverse qualitative and quantitative parameters (section: evaluation of the explanatory potential of qualitative and quantitative variables); the second one explored the likeli- hood of reducing the volume of information needed for urban tree growth estimation (section: selection of the most important quantitative variables and assessment of model integrity); and the last one looked for the identification of an inventory param- eter that could be used to assess any urban tree physiological stage (section: appraisal of the relationships between morpho- logical descriptors and their contribution to growth models). MATERIALS AND METHODS The City of Montreal (Quebec, Canada) is located at 45°30’N and 73°34’W. There are over 220,000 trees transplanted along 4,460 km (2,770 miles) of roads, boulevards, and streets. To define the experimentation strategy and sample size, exploratory field work was carried out in 1999 and 2000 in downtown, institutional, commercial (outside the downtown core), and residential zones. Representative streets were selected according to the following criteria: height of buildings and geographic orientation (variable irradiance conditions), importance of vehicular and pedestrian use, size of tree pits, and width of street since trees beside a wide, heavily traveled city street may be subjected to higher salt level and winds than narrower, less traveled streets (Berrang et al. 1985). Sampled tree species were restricted to the most important ones found on Montreal’s streets. The final data collection took place in 2001 and was composed of the following species: Norway maple (Acer platanoides – 312 trees), silver maple (Acer saccharinum – 224 trees), common hackberry (Celtis occidentalis – 187 trees), green ash (Fraxinus pennsylvanica – 245 trees), honeylocust ©2009 International Society of Arboriculture Jutras et al.: Street Tree Inventory Parameters (Gleditsia triacanthos – 301 trees), littleleaf linden (Tilia cordata – 116 trees), and Siberian elm (Ulmus pumila – 147 trees). The age class distribution of sampled trees is represented in Figure 1. The variables recorded were: genus and species; number of years after transplantation; diameter at breast height (1.35 m/4.4 ft); width of crown (Coombes 1994); total height and crown base Figure 1. Distribution of age classes per species in experimental design. elevation. Crown volumes were calculated by means of the up- per-half spheroid model (Ludwig et al. 1975). Qualitative par- ameters were also assessed: presence or absence of chlorosis; detection and general identification of parasites to characterize the phytopathological condition of trees; presence and intensity of mechanical damages or sunscald/frost cracks (scale: 1: no damage, 2: presence of a few small healed damages, 3: numer- ous damages partially healed, 4: numerous damages unhealed, 5: very numerous severe damages); evaluation of crown density, from dense foliage to dying trees (scale: 1: 100%, 2: 75%, 3: 50%, 4: 25%, 5: 0%); crown development on the basis of an- nual shoot growth (scale: 1: vigorous, 2: moderate, 3: fair, 4: poor, 5: dying or dead); general condition of trees (scale: 1: vig- orous tree, no dying branches, no insect infestation, no mech- anical damage, 2: moderate growing tree, must not have more than three dying main branches, insect infestation if present must be benign, mechanical damages if present must be healed, 3: fair growing tree, may have up to one-third dying branches, insect infestation important but not detrimental, mechanical dam- ages may be numerous but must be partly or entirely healed, 4: poor growing individuals, with one-third to two-thirds dying branches, insect infestation may cause severe defoliation, mech- anical damages are unhealed and there is presence of large sun- scald cracks, 5: dying trees, severely damaged or infested, with a very low number of poorly growing branches, or dead trees). In order to possibly improve the growth model precision, combinations of morphological parameters were built up to form composite variables: ratios of crown diameter/diameter at breast height (DBH); crown volume/DBH; total height/DBH; an- nual DBH increment, crown volume increment, crown diameter increment, and height increment. The last four composite vari- ables are associated with size measurements. An annual crown volume increment was calculated as the difference between measured crown volume and crown volume at transplantation, divided by the number of years since transplantation. To obtain
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