Revealing patterns of homoplasy in discrete phylogenetic datasets with a cross-comparable index

Investigating patterns of homoplasy can improve our understanding of macroevolutionary processes by revealing evolutionary constraints on morphology and highlighting convergent form-function relationships. Here, we test the performance of several widely-used methods that provide measures of homoplasy, including the consistency (CI) and retention indices (RI), using simulated and empirical discrete morphological datasets. In addition, we describe and test a new method employing a novel randomisation protocol, which we term the relative homoplasy index (RHI). RHI outperforms other methods in a range of situations for measuring relative homoplasy and allows comparisons between different datasets. In line with some previous work, we show that relative levels of homoplasy remain constant with the addition of characters and decrease with the addition of taxa. We also show that the extent of homoplasy strongly influences the distribution of taxa in morphospace. Low homoplasy results in highly partitioned morphospace, while high homoplasy leads to clades overlapping in morphospace. Our results help illuminate the properties of relative homoplasy in morphological phylogenetic matrices, opening new potential avenues for research on homoplasy quantification in macroevolutionary studies.