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Explaining species distribution patterns through hierarchical modeling
Gelfand, Alan E. Silander, John A., Jr. Wu, Shanshan Latimer, Andrew Lewis, Paul O. Rebelo, Anthony G. Holder, Mark T.
Gelfand, Alan E.
Silander, John A., Jr.
Wu, Shanshan
Latimer, Andrew
Lewis, Paul O.
Rebelo, Anthony G.
Holder, Mark T.
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Abstract
Understanding spatial patterns of species diversity and the distri-
butions of individual species is a consuming problem in biogeography and con-
servation. The Cape Floristic Region (CFR) of South Africa is a global hotspot
of diversity and endemism, and the Protea Atlas Project, with some 60,000 site
records across the region, provides an extraordinarily rich data set to analyze bio-
diversity patterns. Analysis for the region is developed at the spatial scale of one
minute grid-cells ( 37; 000 cells total for the region). We report on results for
40 species of a
owering plant family Proteaceae (of about 330 in the CFR) for a
de ned subregion.
Using a Bayesian framework, we develop a two stage, spatially explicit, hierar-
chical logistic regression. Stage one models the suitability or potential presence for
each species at each cell, given species attributes along with grid cell (site-level)
climate, precipitation, topography and geology data using species-level coe cients,
and a spatial random e ect. The second level of the hierarchy models, for each
species, observed presence=absence at a sampling site through a conditional speci-
cation of the probability of presence at an arbitrary location in the grid cell given
that the location is suitable. Because the atlas data are not evenly distributed
across the landscape, grid cells contain variable numbers of sampling localities.
Indeed, some grid cells are entirely unsampled; others have been transformed by
human intervention (agriculture, urbanization) such that none of the species are
there though some may have the potential to be present in the absence of distur-
bance. Thus the modeling takes the sampling intensity at each site into account
by assuming that the total number of times that a particular species was observed
within a site follows a binomial distribution.In fact, a range of models can be examined incorporating di erent rst and
second stage speci cations. This necessitates model comparison in a misaligned
multilevel setting. All models are tted using MCMC methods. A best" model
is selected. Parameter summaries o er considerable insight. In addition, results are mapped as the model-estimated potential presence for each species across the
domain. This probability surface provides an alternative to customary empiri-
cal \range of occupancy" displays. Summing yields the predicted species richness
over the region. Summaries of the posterior for each environmental coe cient show
which variables are most important in explaining species presence. Other biodi-
versity measures emerge as model unknowns. A considerable range of inference is
available. We illustrate with only a portion of the analyses we have conducted,
noting that these initial results describe biogeographical patterns over the modeled
region remarkably well.
Description
Date
2006
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Volume Title
Publisher
International Society for Bayesian Analysis
Research Projects
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Keywords
adaptive rejection method, Markov random field, spatial logistic regression, species range, species richness
Citation
Gelfand, Alan E, John A. Silander, Jr., Shan-shan Wu, Andrew M. Latimer, Paul O.
Lewis, Anthony G. Rebelo, and Mark Holder. Explaining species distribution patterns through hierarchical modeling. Bayesian Analysis, 1:41{92, 2006.