Rarefaction of beta diversity

Beta diversity has long been used to summarize the amount of variation in species composition among a set of N sampling units. However, while classical beta diversity provides an estimate of multiple-site dissimilarity among all sampling units, it is not informative on the changes of multiple-site dissimilarity as a function of sampling effort. For gamma diversity, this pattern is usually represented as a species accumulation curve, which is the graph of the number of observed species when the number of plots varies from 1 to N. Here, we will show that species accumulation curves may also be used to summarize directional and non-directional beta diversity as a function of sampling effort. The behavior of the proposed measures of beta diversity is illustrated with one worked example on plant species in Mediterranean coastal vegetation. We believe this approach to the measurement of beta diversity provides a relevant contribution to summarize multiple-site dissimilarity as the result of a species turnover process, rather than as a static indicator. For directional species accumulation curves, the method, for which we provide a custom R function, further allows summarizing the spatial autocorrelation in species composition among plots along an a-priori defined spatial, temporal or environmental gradient.