| The accurate description of spatial patterns of species richness and proper modeling of the species-environment relationships are important focuses in biogeography, ecology and biology. In this study, the New York State Breeding Bird Atlas (BBA) conducted from 1980 to 1985 and from 2000 to 2005 were used with a total of 5,332 spatially-referenced blocks (5 x 5 km in size) covering the entirety of New York State (125,384 km2). The spatial patterns and variations of bird species richness were investigated in multi-scales using localized statistics, spatial Poisson regressions and wavelet transform methods. In the first manuscript, I focused on the description and exploratory analysis of the patterns and variations of bird species richness. The results of localized mean and standard deviation indicated that the spatial distribution and variations of bird species richness were heterogeneous and scale-dependent. In the second manuscript, spatial Poisson models including auto-Poisson regression (AP), generalized linear mixed Poisson regression (GLMP) and geographically weighted Poisson regression (GWPR) were used to predict the bird species richness from environmental variables. The AP and GLMP models produced better model predictions, significantly reduced spatial autocorrelations in the model residuals, and generated more desirable spatial pattern of model residuals than the global Poisson model. However, AP and GLMP were ineffective in explaining the spatial heterogeneity of the spatial relationships between bird species richness and environmental variables. In contrast, the GWPR model was more effective in reducing spatial autocorrelation of model residuals and incorporating spatial heterogeneity at different spatial scales, especially at small spatial scales. In the third manuscript, the two dimensional discrete wavelet transform method was used to explore the issue of isotropy in building species distribution models. The wavelet variances and local wavelet variances indicated that the distributions of spatial variations in the relationships between bird species richness and environmental variables were direction-dependent, in addition to being spatially non-stationary and scale-dependent. The wavelet regression demonstrated that the predictive powers of environmental variables such as temperature and precipitation were not only scale-dependent but also direction-dependent. Our results indicated that spatial anisotropy may be a very common phenomenon in some spatial processes.;Key words: spatial autocorrelation, spatial stationarity, spatial isotropy, localized descriptive statistics, spatial scale, bird species richness, auto-Poisson model, generalized linear mixed Poisson model, geographically weighted Poisson model, discrete wavelet transform, wavelet regression. |
