Relative Homoplasy Index: A New Cross-comparable Metric for Quantifying Homoplasy in Discrete Character Datasets

Homoplasy is among the main hinderances to phylogenetic inference. However, investigating patterns of homoplasy can also improve our understanding of macroevolution, for instance by revealing evolutionary constraints on morphology, or highlighting convergent form-function relationships. Several methods have been proposed to quantify the extent of homoplasy in discrete character matrices, but the consistency index (CI) and retention index (RI) have remained the most widely used for decades, with little recent scrutiny of their function. Here, we test the performance of CI and RI using simulated and empirical datasets and investigate patterns of homoplasy with different matrix scenarios. In addition, we describe and test a new scaled metric, the relative homoplasy index (RHI), implemented in the R statistical environment. The results suggest that, unlike the RI, the CI does not constitute a direct measure of homoplasy. However, the RI consistently underestimates the extent of homoplasy in phylogenetic character-taxon matrices, particularly in datasets characterised by high levels of homoplasy. By contrast, RHI--the newly proposed metric--outperforms both methods in sensitivity to homoplasy levels, and is scaled between zero and one for comparison of values between different datasets. Using both simulated and empirical phylogenetic datasets, we show that relative levels of homoplasy remain constant with the addition of novel characters, and, in contrast to earlier work, decrease with the addition of taxa. Our results help illuminate the inherent properties of homoplasy in cladistic matrices, opening new potential avenues of research for investigating patterns of homoplasy in macroevolutionary studies.