Partitioning of \(\alpha \) and \(\beta \) diversity using hierarchical Bayesian modeling of species distribution and abundance
 Jing Zhang,
 Thomas O. Crist,
 Peijie Hou
 … show all 3 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
Diversity partitioning is becoming widely used to decompose the total number of species recorded in an area or region \((\gamma )\) into the average number of species within samples \((\alpha )\) and the average difference in species composition \((\beta )\) among samples. Singlevalue metrics of \(\alpha \) and \(\beta \) diversity are popular because they may be applied at multiple scales and because of their ease in computation and interpretation. Studies thus far, however, have emphasized observed diversity components or comparisons to randomized, null distributions. In addition, prediction of \(\alpha \) and \(\beta \) components using environmental or spatial variables has been limited to more extensive data sets because multiple samples are required to estimate single \(\alpha \) and \(\beta \) components. Lastly, observed diversity components do not incorporate variation in detection probabilities among species or samples. In this study, we used hierarchical Bayesian models of species abundances to provide predictions of \(\alpha \) and \(\beta \) components in species richness and composition using environmental and spatial variables. We illustrate our approach using butterfly data collected from 26 grassland remnants to predict spatially nested patterns of \(\alpha \) and \(\beta \) based on the predicted counts of butterflies. Diversity partitioning using a Bayesian hierarchical model incorporated variation in detection probabilities by butterfly species and habitat patches, and provided prediction intervals for \(\alpha \) and \(\beta \) components using environmental and spatial variables.
 Anderson MJ, Crist TO, Chase JM, Vellend M, Inouye BD, Freestone AL, Sanders NJ, Cornell HV, Comita LS, Davies KF, Harrison SP, Kraft NJB, Stegen JC, Swenson NG (2011) Navigating the multiple meaning of beta diversity: a roadmap for the practicing ecologist. Ecol Lett 14:19–28
 Bliss, CI, Fisher, RA (1953) Fitting the negative binomial distribution to biological data. Biometrics 9: pp. 176200 CrossRef
 Brooks, SP, Gelman, A (1998) General methods for monitoring convergence of iterative simulations. J Comput Graph Stat 7: pp. 434455
 Caughley, G, Grice, D (1982) A correction factor for counting emus from the air, and its application to counts in western australia. Aust Wildl Res 9: pp. 253259 CrossRef
 Celeux, G, Forbes, F, Robert, C, Titterington, D (2006) Deviance information criteria for missing data models. Bayesian Anal 1: pp. 651674 CrossRef
 Clark, JS (2007) Models for ecological data. Princeton University Press, New Jersey
 Cressie, NAC (1993) Statistics for spatial data (revised edition). Wiley, New York
 Crist, TO, Veech, JA (2006) Additive partitioning of rarefaction curves and speciesarea relationships: unifying $$\alpha $$ α , $$\beta $$ β  and $$\gamma $$ γ diversity with sample size and habitat area. Ecol Lett 9: pp. 923932 CrossRef
 Crist, TO, Veech, JA, Gering, JC, Summerville, KS (2003) Partitioning species diversity across landscapes and regions: a hierarchical analysis of $$\alpha ,\,\beta $$ α , β , and $$\gamma $$ γ diversity. Am Nat 162: pp. 734743 CrossRef
 Dorazio, RM, Royle, JA, Soderstrom, B, Glimskar, A (2006) Estimating species richness and accumulation by modeling species occurrence and detectability. Ecology 87: pp. 842854 CrossRef
 Famoye, F (1993) Restricted generalized poisson regression model. Commun Stat Theory Methods 22: pp. 13351354 CrossRef
 Felix, F, Singh, KP (2006) Zeroinflated generalized poisson regression model with an application to domestic violence data. J Data Sci 4: pp. 117130
 Gelfand, AE, Silander, JA, Wu, S, Latimer, A, Lewis, P, Rebelo, AG, Holder, M (2006) Explaining species distribution patterns through hierarchical modeling. Bayesian Anal 1: pp. 4192 CrossRef
 Gelman A (2006) Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Anal 1:515–534
 Gelman, A, Rubin, DB (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7: pp. 457511 CrossRef
 Hall, DB, Zhang, Z (2004) Marginal models for zero inflated clustered data. Stat Model 4: pp. 161180 CrossRef
 Hofer G, Wagner HH, Herzog F, Edwards PJ (2008) Effects of topographic variability on the scaling of plant species richness in gradient dominated landscapes. Ecography 31:131–139
 Jost, L (2007) Partitioning diversity into independent alpha and beta components. Ecology 88: pp. 24272439 CrossRef
 Kraft, NJB, Comita, LS, Chase, JM, Sanders, NJ, Swenson, NG, Crist, TO, Stegen, JC, Vellend, M, Boyle, B, Anderson, MJ, Cornell, HV, Davies, KF, Freestone, AL, Inouye, BD, Harrison, SP, Myers, JA (2011) Disentangling the drivers of betadiversity along latitudinal and elevational gradients. Science 333: pp. 17551758 CrossRef
 Lambert, D (1992) Zeroinflated poisson regression, with an application to defects in manufacturing. Technometrics 34: pp. 114 CrossRef
 Lande, R (1996) Statistics and partitioning of species diversity, and similarity among multiple communities. Oikos 76: pp. 513 CrossRef
 Lee, AH, Wang, K, Yau, KKW (2001) Analysis of zeroinflated poisson data incorporating extent of exposure. Biometrical J 43: pp. 963975 CrossRef
 PeresNeto PR, Legendre P, Dary S, Borcard D (2006) Variation partitioning of species data matrices: estimation and comparison of fractions. Ecology 87:2614–2625
 Potts, JM, Elith, J (2006) Comparing species abundance models. Ecol Model 199: pp. 153163 CrossRef
 Ridout MDCGB, Hinde J (1998) Models for count data with many zeros. In: Invited paper presented at the nineteenth international biometric conference, Cape Town, South Africa, pp 179–190
 Ridout, M, Hinde, J, Demétrio, CGB (2001) A score test for testing a zeroinflated poisson regression model against zeroinflated negative binomial alternatives. Biometrics 57: pp. 219223 CrossRef
 Roschewitz, I, Gabriel, D, Tscharntke, T, Thies, C (2005) The effects of landscape complexity on arable weed species in organic and conventional farming. J Appl Ecol 42: pp. 873882 CrossRef
 Sandland, RL, Cormack, RM (1984) Statistical inference for poisson and multinomial models for capture–recapture experiments. Biometrika 71: pp. 2733
 Sturtz S, Ligges U, Gelman A (2005) R2winbugs: a package for running winbugs from R. J Stat Softw 12:1–16
 Stegen JC, Freestone AL, Crist TO, Anderson MJ, Chase JM, Comita LS, Cornell HV, Davies KF, Harrison SP, Hurlbert AH, Inouye BD, Kraft NJB, Myers JA, Sanders NJ, Swenson NG, Vellend M (2013) Stochastic and deterministic drivers of spatial and temporal turnover in breeding bird communities. Glob Ecol Biogeogr 22:202–212
 Tuomisto, H (2010) A diversity of beta diversities: straightening up a concept gone awry. part 1. Defining beta diversity as a function of alpha and gamma diversity. Ecography 33: pp. 222 CrossRef
 Linde, A (2005) Dic in variable selection. Statistica Neerlandica 59: pp. 4556 CrossRef
 Veech, JA, Crist, TO (2007) Habitat and climate heterogeneity maintain betadiversity of birds among landscapes within ecoregions. Glob Ecol Biogeogr 16: pp. 650656 CrossRef
 Veech, JA, Summerville, KS, Crist, TO, Gering, JC (2002) The additive partitioning of diversity: recent revival of an old idea. Oikos 99: pp. 39 CrossRef
 Wagner, HH (2004) Direct multiscale ordination with canonical correspondence analysis. Ecology 85: pp. 342351 CrossRef
 Wagner, HH, Wildi, O, Ewald, KC (2000) Additive partitioning of plant species diversity in an agricultural mosaic landscape. Landsc Ecol 15: pp. 219227 CrossRef
 Wang, L (2010) Irtzip modeling for multivariate zeroinflated count data. J Educ Behav Stat 35: pp. 671692 CrossRef
 Wang, W, Famoye, F (1997) Modeling household fertility decisions with generalized poisson regression. J Popul Econ 10: pp. 273283 CrossRef
 Wang W, Gelman A (2013) A problem with the use of crossvalidation for selecting among multilevel models. http://www.stat.columbia.edu/~gelman/research/unpublished/xval.pdf. Accessed 24 Dec 2013
 Wulu, JT, Singh, KP, Famoye, F, McGwin, G (2002) Regression analysis of count data. J Indian Soc Agric Stat 55: pp. 220231
 Title
 Partitioning of \(\alpha \) and \(\beta \) diversity using hierarchical Bayesian modeling of species distribution and abundance
 Journal

Environmental and Ecological Statistics
Volume 21, Issue 4 , pp 611625
 Cover Date
 20141201
 DOI
 10.1007/s1065101302712
 Print ISSN
 13528505
 Online ISSN
 15733009
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Bayesian hierarchical modeling
 Butterflies
 Diversity partitioning
 Multiple scales
 Markov chain Monte Carlo (MCMC)
 Zeroinflated Poisson distribution
 Authors

 Jing Zhang ^{(1)}
 Thomas O. Crist ^{(2)}
 Peijie Hou ^{(3)}
 Author Affiliations

 1. Department of Statistics, Miami University, Oxford, OH, 45056, USA
 2. Department of Biology, Institute for the Environment and Sustainability, Miami University, Oxford, OH, 45056, USA
 3. Department of Statistics, University of South Carolina, Columbia, SC, 29201, USA