Measuring β‐diversity with species abundance data

1. In 2003, 24 presence–absence β‐diversity metrics were reviewed and a number of trade‐offs and redundancies identified. We present a parallel investigation into the performance of abundance‐based metrics of β‐diversity. 2. β‐diversity is a multi‐faceted concept, central to spatial ecology. There are multiple metrics available to quantify it: the choice of metric is an important decision. 3. We test 16 conceptual properties and two sampling properties of a β‐diversity metric: metrics should be 1) independent of α‐diversity and 2) cumulative along a gradient of species turnover. Similarity should be 3) probabilistic when assemblages are independently and identically distributed. Metrics should have 4) a minimum of zero and increase monotonically with the degree of 5) species turnover, 6) decoupling of species ranks and 7) evenness differences. However, complete species turnover should always generate greater values of β than extreme 8) rank shifts or 9) evenness differences. Metrics should 10) have a fixed upper limit, 11) symmetry (β(A,B) = β(B,A)), 12) double‐zero asymmetry for double absences and double presences and 13) not decrease in a series of nested assemblages. Additionally, metrics should be independent of 14) species replication 15) the units of abundance and 16) differences in total abundance between sampling units. When samples are used to infer β‐diversity, metrics should be 1) independent of sample sizes and 2) independent of unequal sample sizes. We test 29 metrics for these properties and five ‘personality’ properties. 4. Thirteen metrics were outperformed or equalled across all conceptual and sampling properties. Differences in sensitivity to species’ abundance lead to a performance trade‐off between sample size bias and the ability to detect turnover among rare species. In general, abundance‐based metrics are substantially less biased in the face of undersampling, although the presence–absence metric, β(sim), performed well overall. Only β(Baselga R turn), β(Baselga B‐C turn) and β(sim) measured purely species turnover and were independent of nestedness. Among the other metrics, sensitivity to nestedness varied >4‐fold. 5. Our results indicate large amounts of redundancy among existing β‐diversity metrics, whilst the estimation of unseen shared and unshared species is lacking and should be addressed in the design of new abundance‐based metrics.