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ŠUMARSKI LIST 3-4/2017 str. 36     <-- 36 -->        PDF

Using a sample of 240 plots in 120 1×1 kilometre cells scattered over a large portion of red deer range in Slovenia, we checked the relation between cull density and actual density calculated with pellet group counting. We built a generalised linear model that predicts actual local population density (based on pellet group counts) from different mortality causes (harvest, loss, traffic mortality) in different spatial windows (1×1 km, 3×3 km). Established predictive regression equations were extrapolated to the entire country (described in Stergar et al. (2012)).
Preparation of data on environmental factors – Priprema podataka o okolišnim čimbenicima
The study involved a broad range of environmental variables (Table 1) that could potentially (according to the results of previous studies) impact space use of red deer. The data on environmental variables were acquired from publicly available and our own databases.
Due to sex-specific dispersal, red deer spatially expands relatively slow and its expansion in Slovenia is not yet completed (Stergar et al. 2009). Population density at specific location may thus be affected by current habitat factors and management as well as by distance of this location from reintroduction site (and of habitat suitability in between). In addition to habitat variables, we therefore introduced the variable „cost distance”, which for any location within the population area represents the „cost” (difficulty) of migration from reintroduction/immigration site. Since there are four reintroduction/immigration macro-sites, Slovenia was divided into four areas (following Jerina (2006a)). Since it is more difficult for red deer to disperse through more fragmented space (space with lower habitat suitability), the difficulty of migration through each quadrant was arbitrarily assigned an index inversely proportional to the percentage of forest in the quadrant. Quadrants containing human settlements were by default designated as absolute obstacles to migration. Cost distance map was calculated with the CostGrow algorithm implemented in the GIS package Idrisi 17.00.
Baseline values of all environmental variables and variable cost distance were prepared in 1-km2 raster corresponding to the population density data. Actual values of variables used in the analysis were calculated for each cell as the average value of cell and eight neighbouring cells; each cell thus represents the value of the variable for a 3×3 km area. This size corresponds to the average home range size of red deer in Slovenia (Jerina 2006a).
Statistical analysis – Statistička analiza
Dependence between environmental factors, cost distance (independent variables) and population density (dependent variable) was analysed at the level of 1×1 km cells. Due to the specifics of the applied method for determining population densities (see Stergar et al. (2012)) and the averaging of independent variables in the 3×3 km grid, the data were spatially auto-correlated. Potential problems with spatial auto-correlation (Dormann et al. 2007) were avoided by systematically sampling only each central of the 9 neighbouring cells in the 3×3 km grid. Of the 19 746 quadrants entirely located within Slovenia, 2 197 were used for subsequent analysis.
Previous studies (Johnson 1980, Mayor et al. 2009) showed that habitat use is a hierarchical process, occurring at multiple spatial and temporal scales (multi-order habitat use): the first order represents global range of species, the second order local species densities, the third order space use within home range, and the fourth order selection of micro-locations for foraging and other activities. Our study separately examines the impacts of environmental factors on red deer space use of first and second order. In second-order analysis we included broad range of potentially relevant environmental variables, while in first-order analysis we omitted all variables that we assumed cannot impact the global range of the species (e.g. internal forest structure), and variables for which it is impossible to determine whether they are the cause or the consequence of red deer presence/absence (e.g. supplemental feeding).
First-order analysis involved all 2 197 sampled cells, of which 1 335 with red deer presence were used for second-order analysis. At both levels dependence between independent variables and the dependent variable was first checked with bivariate (Table 1) and then with multivariable analysis. At first order we used Point-biserial correlation (Tate 1954) and binary logistic regression (Hosmer et al. 2013) due to the binary dependent variable (red deer present/absent). At second order, where the dependent variable (red deer density) is continuous, we used Spearman correlation and generalised linear models (GLM) with gamma distribution of the dependent variable (Zuur et al. 2009), which corresponds to the distribution of red deer density.
All independent variables were first standardised. For both types of regression models we checked whether the relationships between the independent variables and the dependent variable were linear. The variable temperature was found to relate nonlinearly, thus square transformed temperature was additionally included in the model. To avoid multicollinearity, we: a) first calculated Spearman correlation for pairs of independent variables; if the absolute value of the correlation coefficient was > 0.6, the variable with the assumed ecologically less meaningful impact on red deer presence/density was excluded, and b) additionally excluded