Using rarefaction to isolate the effects of patch size and sampling effort on beta diversity

Using rarefaction to isolate the effects of patch size and sampling effort on beta diversity A DRIAN C. S TIER , 1, ! B ENJAMIN M. B OLKER , 2 AND C RAIG W. O SENBERG3 Department of Ecology, Evolution and Marine Biology, University of California, Santa Barbara, California 93106 USA Departments of Mathematics & Statistics and Biology, McMaster University, Hamilton, Ontario L8S 4K1 Canada Odum School of Ecology, University of Georgia, Athens, Georgia 30602 USA Citation: Stier, A. C., B. M. Bolker, and C. W. Osenberg. 2016. Using rarefaction to isolate the effects of patch size and sampling effort on beta diversity. Ecosphere 7(12):e01612. 10.1002/ecs2.1612 Abstract. Beta diversity describes how species composition varies across space and through time. Current estimators of beta diversity typically ignore the effects of within-patch sample size, determined jointly by local abundance and sampling effort. Many ecological processes such as immigration, predation, or nutrient limitation affect abundance and asymptotic beta diversity concurrently; thus, existing metrics may confound changes in asymptotic beta diversity with changes that result from differences in abundance or sampling. Results from a stochastic simulation model illustrate how decreasing within-patch sample size may either increase or decrease observed beta diversity, depending on the type of metric, sample size, and community properties; these changes are easy to understand, and predict, by considering the effects of sampling on variance. A modified, patch-level form of rarefaction controls for variation in within-patch sample size; two case studies illustrate the utility of this approach. Studies seeking a mechanistic link between ecological process and beta diversity will continue to benefit from explicit consideration of sampling effects. Key words: beta diversity; biodiversity; rarefaction; sampling effects. Received 6 October 2016; accepted 10 October 2016. Corresponding Editor: Debra P. C. Peters. Copyright: © 2016 Stier et al. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. ! E-mail: adrian.stier@lifesci.ucsb.edu I NTRODUCTION resource managers to design reserve networks that maximize species complementarity across sites (Kattan et al. 2006). Similarly, beta diversity can be used to describe the rate at which species turn over through time in the presence of human impacts (Dornelas et al. 2014). Knowledge of the factors maintaining diversity among patches can also facilitate biodiversity preservation or recov- ery of diversity following the restoration of a degraded ecosystem (McKnight et al. 2007). Beta diversity is typically examined at two spatial scales: (1) large-scale variation in beta diversity that links species compositional differ- ences across gradients (e.g., with latitude or alti- tude) and encompasses multiple species pools (Condit et al. 2002, McKnight et al. 2007, He and Zhang 2009), and (2) local-scale variation in beta Within-patch (alpha) and among-patch (beta) diversities combine to produce regional patterns of diversity. Traditionally, ecologists have focused on local processes and their influence on alpha diversity. More recently, ecologists have turned to studying the drivers of beta diversity; patterns of beta diversity provide insight into the role of factors that generate species boundaries (Condit et al. 2002), facilitate regional diversity via environmental heterogeneity, and produce alternate community states (Fukami and Naka- jima 2011). From a conservation perspective, beta diversity is arguably as important as alpha diver- sity (Socolar et al. 2016): For example, quantify- ing the spatial scale of beta diversity can allow ❖ www.esajournals.org December 2016 ❖ Volume 7(12) ❖ Article e01612