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Assessing adequacy of models of phyletic evolution in the fossil record

Comparing relative fit of different models of evolutionary dynamics to time series of phyletic change is a common tool when interpreting the fossil record. However, a measure of relative fit is no guarantee the preferred model describes the data well. Selecting a good model is essential for robust inferences, but we are currently lacking tools to investigate if a model of phyletic evolution represents an adequate description of trait dynamics in fossil data. This study develops a general statistical framework implemented in R for assessing the adequacy of the three most commonly used models of evolution in the fossil record; stasis, directional change and random walk. The statistical framework is applied to 300 fossil time series in order to assess how often the three models represent adequate descriptions of evolutionary dynamics in the fossil record. The model that showed the best relative fit to a particular fossil time series (using AICc) passed all adequacy tests in 219 out of 300 cases (73%, directional trend = 76%, stasis = 64%, random walk = 81%). It is therefore not uncommon that the best model according to AICc does not adequately describe the trait dynamics in a fossil time series. Statistical tests of model adequacy ease evaluation of whether a particular model is a good descriptor of phyletic evolution and can assist in making meaningful inferences of model parameters (e.g., as rates of evolution) and interpretations of evolution in the fossil record.