Trees, branches and (square) roots: why evolutionary relatedness is not linearly related to functional distance

An increasingly popular practice in community ecology is to use the evolutionary distance among interacting species as a proxy for their overall functional similarity. At the core of this approach is the implicit, yet poorly recognized, assumption that trait dissimilarity increases linearly with divergence time, that is all evolutionary time is considered equal. However, given a classic Brownian model of trait evolution, we show that the expected functional displacement of any two taxa is more appropriately represented as a linear function of time's square root. In light of this mismatch between theory and methodology, we argue that current methods at the interface of ecology and evolutionary biology often greatly overweight deep time relative to recent time. An easy solution to this weighting problem is a square root transformation of the phylogenetic distance matrix. Using simulated models of trait evolution and community assembly, we show that this transformation yields considerably higher statistical power, with improvements in 92% of trials. This methodological update is likely to improve our understanding of the connection between evolutionary relatedness and contemporary ecological processes.