A cautionary note on quantitative measures of phenotypic convergence

Tests of phenotypic convergence can provide evidence of adaptive evolution, and the popularity of such studies has grown in recent years due to the development of novel, quantitative methods for identifying and/or measuring convergence. Two commonly used methods include (i) ‘distance-based’ methods that measure morphological distances between lineages in phylomorphospace and (ii) fitting evolutionary models to morphological datasets to test whether lineages have evolved toward adaptive peaks. Here, we demonstrate that both types of convergence measures are influenced by the position of putatively convergent taxa in morphospace such that morphological outliers are statistically more likely to exhibit convergence by chance. A more substantial issue is that some methods will often misidentify divergent lineages as being convergent. These issues likely influence the results of many studies, especially those that focus on morphological outliers. To help address these problems, we developed a new distance-based method for measuring convergence that incorporates distances between lineages through time and minimizes the possibility of divergent taxa being misidentified as convergent. We advocate the use of this method when the phylogenetic tips of putatively convergent lineages are of the same or similar geologic ages (e.g., extant taxa), meaning that convergence among the lineages is expected to be synchronous. We conclude by emphasizing that all available convergence measures are imperfect, and researchers should recognize the limitations of these methods and use multiple lines of evidence when inferring and measuring convergence.