Bayesian Analysis

Explaining species distribution patterns through hierarchical modeling

Alan E. Gelfand, Mark Holder, Andrew Latimer, Paul O. Lewis, Anthony G. Rebelo, John A. Silander, and Shanshan Wu

Full-text: Open access

Abstract

Understanding spatial patterns of species diversity and the distributions of individual species is a consuming problem in biogeography and conservation. 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 biodiversity 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 flowering plant family Proteaceae (of about 330 in the CFR) for a defined subregion.

Using a Bayesian framework, we develop a two stage, spatially explicit, hierarchical 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 coefficients, and a spatial random effect. The second level of the hierarchy models, for each species, observed presence$/$absence at a sampling site through a conditional specification 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 disturbance. 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 different first and second stage specifications. This necessitates model comparison in a misaligned multilevel setting. All models are fitted using MCMC methods. A "best" model is selected. Parameter summaries offer 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 empirical "range of occupancy" displays. Summing yields the predicted species richness over the region. Summaries of the posterior for each environmental coefficient show which variables are most important in explaining species presence. Other biodiversity 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.

Article information

Source
Bayesian Anal. Volume 1, Number 1 (2006), 41-92.

Dates
First available in Project Euclid: 22 June 2012

Permanent link to this document
http://projecteuclid.org/euclid.ba/1340371072

Digital Object Identifier
doi:10.1214/06-BA102

Mathematical Reviews number (MathSciNet)
MR2227362

Citation

Gelfand, Alan E.; Silander, John A.; Wu, Shanshan; Latimer, Andrew; Lewis, Paul O.; Rebelo, Anthony G.; Holder, Mark. Explaining species distribution patterns through hierarchical modeling. Bayesian Analysis 1 (2006), no. 1, 41--92. doi:10.1214/06-BA102. http://projecteuclid.org/euclid.ba/1340371072.


Export citation

References

  • Aspinall, R. (1992). "An Inductive Modeling Procedure Based on Bayes' Theorem for Analysis of Pattern in Spatial Data." International Journal of Geographic Information Systems, 6:105–121.
  • Aspinall, R. and Veitch, N. (1993). "Habitat Mapping from Satellite Imagery and Wildlife Survey using a Bayesian Modeling Procedure in a GIS". Photogrammetric Engineering and Remote Sensing, 59:537–543.
  • Augustin, N. H., Mugglestone, M. A., and Buckland, S. T. (1996). "The fate of clades in a world of recurrent climatic change: Milankovitch oscillations and evolution." Journal of Applied Ecology, 33:339–347.
  • Austin, M. P. and Meyers, J. A. (1996). "Current Approaches to Modelling the Environmental Niche of Eucalypts: implication for management of forest biodiversity." Forest Ecology and Management, 85:95–106.
  • –- (1996). "Current approaches to modelling the environmental niche of eucalypts: implication for management of forest biodiversity." Forest Ecology and Management, 85:95–106.
  • Austin, M. P., Nicholls, A. O., and Margules, C. R. (1990). "Measurement of the realized qualitative niche: environmental niches of five Eucalyptus species." Ecological Monographs, 60:161–177.
  • Besag, J. (1974). "Spatial Interaction and the Statistical Analysis of Lattice Systems." Journal of the Royal Statistical Society, Series B, 36:192–225.
  • Besag, J., Green, P., Higdon, D., and Mengersen, K. (1995). "Bayesian Computation and Stochastic Systems (with discussion)." Statistical Science, 10:3–66.
  • Brzeziecki, B., Kienast, F., and Wildi, O. (1993). "A Simulated Map of the Potential Natural Forest Vegetation of Switzerland." Journal of Vegetation Science, 4:499–508.
  • Clark, J. S., LaDeau, S., and Ibanez, I. (2003). "Fecundity of trees and the colonization-competition hypothesis." Ecological Monographs, (to appear).
  • Colwell, R. K. and Lees, D. C. (2000). "The Mid-Domain Effect: Geometric Constraints on the Geography of Species Richness." Trends in Ecology and Evolution, 15:70–76.
  • Cressie, N. A. C. (1993). Statistics for Spatial Data. Revised Edition. John Wiley & Sons, Inc.
  • Currie, D. J. (1991). "Energy and Large-scale Patterns of Animal and Plant Species Richness." American Naturalist, 137:27–49.
  • Darwin, C. (1872). On the Origin of Species by Means of Natural Selection or the Preservation of Favoured Races in the Struggle for Life. Sixth edition. John Murray, London, UK.
  • Dynesius, M. and Jansson, R. (2000). "Evolutionary consequences of changes in species' geographic distributions driven by Milankovitch climate oscillations." In Proceedings of the National Academy of Sciences, 9115–9120.
  • Ferrier, S., Drielsma, M., Manion, G., and Watson, G. (2002). "Extended Statistical Approaches to Modelling Spatial Pattern in Biodiversity in Northeast New South Wales. II". Community-level modeling. Biodiversity and Conservation, 11:2309–2338.
  • Ferrier, S., Watson, G., Pearce, J., and Drielsma, M. (2002). "Extended statistical approaches to modelling spatial pattern in biodiversity in northeast New South Wales. I. Species-level modeling." Biodiversity and Conservation, 11(2275-2307):Biodiversity and Conservation.
  • Fischer, H. S. (1990). "Simulating the distribution of plant communities in an alpine landscape." Coenoses, 5:37–43.
  • Gaston, K. J. (2003). The Structure and Dynamics of Geographic Ranges.. Oxford University Press, Oxford, UK.
  • Gelfand, A. E., Sahu, S. K., and Carlin, B. P. (1996). "Efficient Parametrizations for Generalised Linear Models." Bayesian Statistics 5: 227-246, Eds: Bernardo, J.M. et al., Oxford University Press: Oxford.
  • Gelfand, A. E., Schmidt, A. M., Wu, S., J. A. Silander, J., Latimer, A., and Rebelo, A. G. (2003). "Modelling Species Diversiy Through Species Level Hierarchical Modeling." Applied Statistics. forthcoming..
  • Gelfand, A. E. and Smith, A. F. M. (1990). "Sampling-Based Approaches to Calculating Marginal Densities." Journal of the American Statistical Association, 85:398–409.
  • Gilks, W. R., Best, N., and Tan, K. K. C. (1995). "Adaptive Rejection Metropolis Sampling within Gibbs Sampling." Applied Statistics, 44:455–472.
  • Gilks, W. R. and Wild, P. (1992). "Adaptive Rejection Sampling for Gibbs Sampling." Applied Statistics, 41(2):337–348.
  • Grant, V. (1981). Plant Speciation. 2nd. ed.. Columbia University Press, New York.
  • Green, P. J. and Richardson, S. (2002). "Hidden Markov Models and Disease Mapping." Journal of the American Statistical Association, 94:1055–1070.
  • Guisan, A., Edwards, J., T. C., and Hastie, T. (2002). "Generalized Linear and Generalized Additive Models in Studies of Species Distributions: Setting the Scene." Ecological Modelling, 157:89–100.
  • Guisan, A. and Zimmerman, N. E. (2000). "Predictive Habitat Distribution Models in Ecology." Ecological Modelling, 135:147–186.
  • Heegard, E. (2002). "The outer border and central border for species-environmental relationships estimated by non-parametric generalised additive models." Ecological Modelling, 157:131–139.
  • Heikkinen, J. and Högmander, H. (1994). "Fully Bayesian Approach to Image Restoration with an Application in Biogeography." Applied Statistics, 43:569–582.
  • Heikkinen, R. K. (1996). "Predicting Patterns of Vascular Plant Species Richness with Composite Variables: A Mesoscale Study in Finnish Lapland." Vegetation, 126:151–165.
  • Hoeting, J. A., Leecaster, M., and Bowden, D. (2000). "An Improved Model for Spatially Correlated Binary Responses." Journal of Agricultural, Biological and Environmental Statistics, 5(1):102–114.
  • Högmander, H. and Møller, J. (1995). "Estimating Distribution Maps from Atlas Data Using Methods of Statistical Image Analysis." Biometrics, 51:393–404.
  • Hooten, M. B., Larsen, D. R., and Wikle, C. K. (2003). Predicting the spatial distribution of ground flora on large domains using a hierarchical Bayesian model.. in review.
  • Hubbell, S. P. (2001). The Unified Neutral Theory of Biodiversity and Biogeography. Princeton University Press, Princeton, NJ, USA.
  • Huston, M. A. (1994). Biological Diversity. The Coexistence of Species on Changing Landscapes. Cambridge University Press, Cambridge, UK.
  • Jansson, R. and Dynesius, M. (2002). "The fate of clades in a world of recurrent climatic change: Milankovitch oscillations and evolution." Annual Review of Ecology and Systematics, 33:741–777.
  • Kempton, R. A. (2002). "Species Diversity." In A.H. El-shaarwari and W.A. Piegorsch, Eds. Encyclopedia of Environmentircs, 4:2086–2092.
  • Latham, R. E. and Ricklefs, R. E. (1993). "Global Patterns of Tree Species Richness in Moist Forests: Energy-Diversity Theory Does Not Account for Variation in Species Richness." Oikos, 67:325–333.
  • Leathwick, J. R. (2002). "Intra-generic Competition among Nothofagus in New Zealand's Primary Indiginous Forests." Biodiversity and Conservation, 11:2177–2187.
  • Lehmann, A. (1998). "GIS modeling of submerged macrophyte distribution using generalized additive models." Plant Ecology, 139:113–124.
  • Lehmann, A., Overton, J. M., and Leathwick, J. R. (2002). "GRASP": Generalized Regression Analysis and Spatial Prediction." Ecological Modelling, 159:189–207.
  • MacArthur, R. H., Recher, H. F., and Cody, M. (1966). "On the relation between habitat selection and species diversity." American Naturalist, 100:319–332.
  • Manel, S., Dias, J.-M., and Ormerod, S. J. (1999). "Comparing discriminant analysis, neural networks and logistic regression for predicting species distributions: a case study with a Himalayan river bird." Ecological Modelling, 120:337–347.
  • Mayr, E. (1942). Systematics and the Origin of Species.. Columbia University Press, New York.
  • Meyers, N., Mittermeier, R., Mittermeier, C. G., de Fonesca G. A. B., and Kent, J. (2000). "Biodiversity Hotspots for Conservation Priorities." Nature, 403:853–858.
  • Midgley, G. F., Hannah, L., Millar, D., Rutherford, M. C., and Powrie, L. W. (2002). "Assessing the Vulnerability of Species Richness to Anthropogenic Climate Change in a Biodiversity Hotspot." Global Ecology and Biogeography, 11:445–451.
  • Osborne, P. E. and Suarez-Seoane, S. (2000). "Should data be partitioned spatially before building large-scale distribution models?" Ecological Modelling, 157:249–259.
  • Owen, J. G. (1989). "Patterns of Herpetofaunal Species Richness:Relation to Temperature, Precipitation and Variance in Elevation." Journal of Biogeography, 16:141–150.
  • Palmer, M. W. (1996). "Variation in Species Richness: Towards a Unification of Hypotheses." Folia Geobotanica et Phytotaxonomica (Praha), 29:511–530.
  • Papaspiliopoulos, O., Roberts, G. O., and Skold, M. (2003). "Noncentered Parametrization for Hierarchical Models and Data Augmentation." Bayesian Statistics 7: 307-326, Eds: Bernardo, J.M. et al., Oxford University Press: Oxford.
  • Rahbek, C. and Graves, G. R. (2001). "Multiscale assessment of patterns of avian species richness." In Proceedings of the National Academy of Sciences 89(8), 4534–4539.
  • Rebelo, A. G. (1991). Protea Atlas Manual: Instruction Booklet to the Protea Atlas Project. Protea Atlas Project, Cape Town.
  • –- (2001). Proteas: A Field Guide to the Proteas of Southern Africa. Fernwood Press, Vlaeberg, South Africa (2nd Edition).
  • –- (2002). "The Protea Atlas Project." Technical report, Retrieved on-line 12 May, 2002 from: http://protea.worldonline.co.za/default.htm.
  • –- (2002). "The State of Plants in the Cape Flora." In Proceedings of a conference held at the Rosebank Hotel in Johannesburg, 18–43. G.H. Verdoorn and J. Le Roux (editors) The State of South Africa's Species. Endangered Wildlife Trust.
  • Ritchie, M. E. and Olff, H. (1999). "Spatial Scaling Laws Yield a Synthetic Theory of Biodiversity." Nature, 400:557–560.
  • Rohde, K. (1992). "Latitudinal Gradients in Species Diversity: the Search for the Primary Cause." Oikos, 65:514–527.
  • Rosenzweig, M. L. (1995). Species Diversity in Space and Time. Cambridge University Press, Cambridge, UK.
  • Rouget, M., Richardson, D. M., Cowling, R. M., Lloyd, J. W., and Lombard, A. T. (2003). "Current Patterns of Habitat Transformation and Future Threats to Biodiversity in Terrestrial Ecosystems of the Cape Floristic Region, South Africa." Biological Conservation, 112:63–83.
  • Royle, J. A., Link, W. A., and Sauer, J. R. (2002). Statistical mapping of count survey data. In J.M. Scott, P.J. Heglund, M.L. Morrison, J.B. Haufler, M.G. Raphael, W.Q. Wall and F.B. Samson (Eds.) Predicting Species Occurrences - Issues of Accuracy and Scale.. Island Press, Washington, DC.
  • Schultze, R. E. (1997). "South African Atlas of Agrohyrdology and Climatology." Technical report, Report TT82/96. Water Research Commission, Pretoria, South Africa.
  • Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and Van Der Linde, A. (2002). "Bayesian Measures of Model Complexity and Fit." Journal of the Royal Statistical Society, Series B, 64:1–34.
  • Takhtajan, A. (1986). Floristic Regions of the World. University of California Press, Berkeley, CA, USA.
  • Venables, W. and Ripley, B. (1999). Modern Applied Statistics with S-PLUS (3rd edition).. Springer-Verlag, New York.
  • Wallace, A. R. (1895). Natural Selection and Tropical Nature: Essays on Descriptive and Theoretical Biology.. Macmillan, London.
  • Whittaker, R. J., Willis, K. J., and Field, R. (2001). "Scale and species richness: towards a general, hierachical theory of species diversity." Journal of Biogeography, 28:453–470.
  • Wikle, C. K. (2002). Spatial modeling of count data: A case study in modelling breeding bird survey data on large spatial domains. In: A. Lawson and D. Denison (eds). Spatial Cluster Modelling.. CRC Press, Boca Raton, FL.
  • –- (2003). "Hierarchical Bayesian models for predicting the spread of ecological processes." Ecology (to appear).
  • Wikle, C. K. and Royle, J. A. (2002). Spatial statistical modeling in biology. In: Encyclopedia of Life Support Systems.. Publishers, Oxford, UK.
  • Wiley, E. O. (1981). Phylogenetics: the theory and practice of phylogenetic systematics.. John Wiley and Sons, New York.
  • Woodward, F. I., Smith, T. M., and Emanuel, W. R. (1995). "A global land primary productivity and phytogeography model." Global Biogeochemical Cycles, 9(4):471–490.
  • Wu, S., Lewis, P., Holder, M., Silander, J. J., and Gelfand, A. E. (2004). "A Hierarchical Allopatry Model for Interspecies Range Dependence." Submitted.
  • Yee, T. W. and Mitchell, N. D. (1991). "Generalised additive models in plant ecology." Journal of Vegetation Science, 2:587–602.
  • Zaniewski, A. E., Lehmann, A., and Overton, J. M. (2002). "Predicting species spatial distributions using presence-only data: a case study of New Zealand ferns." Ecological Modelling, 157:261–280.

See also

  • Related item: Jennifer A. Hoeting. Some perspectives on modeling species distributions (comment on article by Gelfand et al. Bayesian Anal., Vol. 1, Iss. 1 (2006), 93-97.
  • Related item: Jay M. Ver Hoef. Comment on article by Gelfand et al. Bayesian Anal., Vol. 1, Iss. 1 (2006), 99-101.
  • Related item: Alan E. Gelfand, John A. Silander, Shanshan Wu, Andrew Latimer, Paul O. Lewis, Anthony G. Rebelo, Mark Holder. Rejoinder. Bayesian Anal., Vol. 1, Iss. 1 (2006), 103-104.