ORIGINAL ARTICLE doi:10.1111/j.1558-5646.2011.01460.x IDENTIFYING HETEROGENEITY IN RATES OF MORPHOLOGICAL EVOLUTION: DISCRETE CHARACTER CHANGE IN THE EVOLUTION OF LUNGFISH (SARCOPTERYGII; DIPNOI) Graeme T. Lloyd,1,2 Steve C. Wang,3 and Stephen L. Brusatte4,5 1Department of Palaeontology, Natural History Museum, Cromwell Road, London SW7 5BD, United Kingdom 2E-mail:
[email protected] 3Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081 4Division of Paleontology, American Museum of Natural History, Central Park West at 79th Street, New York, New York 10024 5Department of Earth and Environmental Sciences, Columbia University, New York, New York 10025 Received February 9, 2010 Accepted August 15, 2011 Data Archived: Dryad: doi:10.5061/dryad.pg46f 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.