Explaining species distribution patterns through hierarchical modeling

Abstract

Understanding spatial patterns of species diversity and the distri-\nbutions of individual species is a consuming problem in biogeography and con-\nservation. The Cape Floristic Region (CFR) of South Africa is a global hotspot\nof diversity and endemism, and the Protea Atlas Project, with some 60,000 site\nrecords across the region, provides an extraordinarily rich data set to analyze bio-\ndiversity patterns. Analysis for the region is developed at the spatial scale of one\nminute grid-cells ( 37; 000 cells total for the region). We report on results for\n40 species of a \nowering plant family Proteaceae (of about 330 in the CFR) for a\nde ned subregion.\nUsing a Bayesian framework, we develop a two stage, spatially explicit, hierar-\nchical logistic regression. Stage one models the suitability or potential presence for\neach species at each cell, given species attributes along with grid cell (site-level)\nclimate, precipitation, topography and geology data using species-level coe cients,\nand a spatial random e ect. The second level of the hierarchy models, for each\nspecies, observed presence=absence at a sampling site through a conditional speci-\n cation of the probability of presence at an arbitrary location in the grid cell given\nthat the location is suitable. Because the atlas data are not evenly distributed\nacross the landscape, grid cells contain variable numbers of sampling localities.\nIndeed, some grid cells are entirely unsampled; others have been transformed by\nhuman intervention (agriculture, urbanization) such that none of the species are\nthere though some may have the potential to be present in the absence of distur-\nbance. Thus the modeling takes the sampling intensity at each site into account\nby assuming that the total number of times that a particular species was observed\nwithin a site follows a binomial distribution.In fact, a range of models can be examined incorporating di erent rst and\nsecond stage speci cations. This necessitates model comparison in a misaligned\nmultilevel setting. All models are tted using MCMC methods. A best" model\nis selected. Parameter summaries o er considerable insight. In addition, results are mapped as the model-estimated potential presence for each species across the\ndomain. This probability surface provides an alternative to customary empiri-\ncal \\range of occupancy" displays. Summing yields the predicted species richness\nover the region. Summaries of the posterior for each environmental coe cient show\nwhich variables are most important in explaining species presence. Other biodi-\nversity measures emerge as model unknowns. A considerable range of inference is\navailable. We illustrate with only a portion of the analyses we have conducted,\nnoting that these initial results describe biogeographical patterns over the modeled\nregion remarkably well.

Keywords

Affiliated Institutions

• Florida State University US
• Planta RU
• Clarion University US
• Duke University US

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