Identifying heterogeneity in rates of morphological evolution: discrete character change in the evolution of lungfish (Sarcopterygii; Dipnoi).

Quantifying rates of morphological evolution is important in many macroevolutionary studies, and critical when assessing possible adaptive radiations and episodes of punctuated equilibrium in the fossil record. However, studies of morphological rates of change have lagged behind those on taxonomic diversification, and most authors have focused on continuous characters and quantifying patterns of morphological rates over time. Here, we provide a phylogenetic approach, using discrete characters and three statistical tests to determine points on a cladogram (branches or entire clades) that are characterized by significantly high or low rates of change. These methods include a randomization approach that identifies branches with significantly high rates and likelihood ratio tests that pinpoint either branches or clades that have significantly higher or lower rates than the pooled rate of the remainder of the tree. As a test case for these methods, we analyze a discrete character dataset of lungfish, which have long been regarded as "living fossils" due to an apparent slowdown in rates since the Devonian. We find that morphological rates are highly heterogeneous across the phylogeny and recover a general pattern of decreasing rates along the phylogenetic backbone toward living taxa, from the Devonian until the present. Compared with previous work, we are able to report a more nuanced picture of lungfish evolution using these new methods.