DIGITALNA ARHIVA ŠUMARSKOG LISTA
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were measured on each leaf: leaf blade area (LA); leaf blade length (LL); maximum leaf blade width (MLW); leaf blade length, measured from the leaf base to the point of maximum leaf width (PMLW); leaf blade width at 50% of leaf blade length (LW1); leaf blade width at 90% of leaf blade length (LW2); angle closed by the main leaf vein and the line defined by the leaf blade base and a point on the leaf margin, at 10% of leaf blade length (LA1); angle closed by the main leaf vein and the line defined by leaf blade base and a point on the leaf margin, at 25% of leaf blade length (LA2); and petiole length (PL). Finally, a total of 2800 leaves, dried in a herbarium, were measured, and 25 200 simple data values were obtained. Statistical analyses – Statističke analize The measured morphological characteristics were described by standard descriptive statistical parameters: arithmetic mean, standard deviation, coefficient of variation (CV%), and the percentiles 0% (minimum), 5%, 25% (lower quartile), 50% (median), 75% (upper quartile), 95% and 100% (maximum). To assess the possibility of conducting multivariate statistical analyses and parametric tests, the symmetry, unimodality and homoscedasticity of data were verified (Sokal and Rohlf 2012). Assumptions of normality were checked using the Shapiro–Wilk test, and the assumption of homogeneity of variance using Levene’s test. A hierarchical analysis of variance (ANOVA) was performed to examine the partition of phenotypic variation between the continental and the Alpine-Dinaric regions, among populations within the regions, and within populations. The relationship between average values of morphological leaf characteristics and geographical longitude, latitude, and altitude (e.g. Krauze-Michalska and Boratyńska 2013) and the influence of climatic variables on leaf characteristics were tested using Spearman’s coefficient (Sokal and Rohlf 2012). Climate data were obtained from the WorldClim database with a spatial resolution close to a square km (Hijmans et al. 2005). To evaluate the correlation between multicharacter differences among populations, a Mantel test (Mantel 1967) was performed on the matrices of Euclidean distances. First, the correlations among all 19 WorldClim bioclimatic variables and topographic variables for all presence points were calculated to exclude the highly correlated ones, whilst keeping the variables useful in predicting the distribution limits of trees, such as climatic averages and extremes (Zimmermann et al. 2009; Temunović et al. 2012). We computed and tested the correlations between: (1) the matrix of the geographical distances between pairs of populations and the matrix of morphological differences among populations – “isolation by distance” (Wright 1943); and (2) the matrix of environmental distances and the matrix of morphological differences among populations – “isolation by environmental distance” (Mendez et al. 2010). The significance level was assessed after 10,000 permutations, and the Mantel test was performed with the R package “Vegan” (Oksanen et al. 2017). Multivariate statistical methods were used to identify the population differentiation (McGarigal et al. 2000). Pearson’s correlation coefficient was used to identify interactions between leaf traits and to detect potential redundant variables, i.e. highly correlated variables were excluded from the analyses. The conducted cluster analysis resulted in a hierarchical tree, where the unweighted pair-group method with arithmetic mean (UPGMA) was used to join the clusters, and the Euclidean distance to define the distance between the studied objects. The K-means method was applied to detect phenotypic structure and define the number of K-groups that best explained the morphological variation of populations (e.g Douaihy et al. 2012; Boratyński et al. 2013; Sobierajska et al. 2016). In addition, the biogeographical structure of the studied populations was further |