A cautionary note on quantitative measures of phenotypic convergence

Abstract

ABSTRACTTests 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 measuring convergence. These methods include the commonly appliedC1–C4 measures of Stayton (2015), which measure morphological distances between lineages in phylomorphospace, and Ornstein-Uhlenbeck evolutionary model-fitting analyses to test whether lineages have convergently evolved toward adaptive peaks.We test the performance ofC-measures and other convergence measures under various evolutionary scenarios. We reveal critical issues withC-measures, which we help to address by developing novel convergence measures (Ct1–Ct4-measures) that measure distances between lineages at specific points in time.The most substantial issue withC-measures is that they will often misidentify divergent lineages as convergent; this is most common when focal taxa are morphological outliers. In contrast, our newCt-measures minimize the possibility of misidentifying divergent taxa as convergent.Ct-measures are most appropriate when putatively convergent lineages are of the same or similar geologic ages (e.g., extant taxa), meaning that all or most of the evolutionary histories of the lineages overlap in time. BeyondC-measures, we demonstrate issues with other convergence measures. We find that all distance-based convergence measures are influenced by the position of putatively convergent taxa in morphospace, with morphological outliers often statistically more likely to be categorized as convergent by chance. Further, we demonstrate that multiple-regime Ornstein-Uhlenbeck models often outperform simpler models when fit to divergent lineages, highlighting that model support for multiple-regime models should not always be assumed to reflect convergence among focal lineages.The issues with convergence measures highlighted here are especially relevant because they influence the degree of inferred convergence in many past studies, raising the concern that many lineages have been mistakenly identified as convergent. Our new convergence measures provide researchers with an improved comparative tool for future studies. Nonetheless, we emphasize 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.