Modelling rate distributions using character compatibility: implications for morphological evolution among fossil invertebrates
Peter J. Wagner*
National Museum of Natural History, Smithsonian Institution,Washington DC 20013, USA
Rate distributions are important considerations when testing hypotheses about morphological evolution or phylogeny. They also have implications about general processes underlying character evolution. Molecular systematists often assume that rates are Poisson processes with gamma distributions. However, morphological change is the product of multiple probabilistic processes and should theoretically be affected by hierarchical integration of characters. Both factors predict lognormal rate distributions. Here, a simple inverse modelling approach assesses the best single-rate, gamma and lognormal models given observed character compatibility for 115 invertebrate groups. Tests reject the single-rate model for nearly all cases. Moreover, the lognormal outperforms the gamma for character change rates and (especially) state derivation rates. The latter in particular is consistent with integration affecting morphological character evolution.
character evolution, compatibility, lognormal distribution, gamma distribution, information theory
One contribution of 12 to a Special Feature on ‘Models in palaeontology’.
Received May 20, 2011.
Accepted July 7, 2011.
This journal is © 2011 The Royal Society