Using state space models to understand trait evolution in fossil lineages

Linear state space models provide a useful framework for investigating phenotypic evolution in fossil lineages for a wide variety of models representing Brownian motion, Ornstein-Uhlenbeck processes, and the potential influence of environmental covariates. A state space framework also provides access to residuals for the predicted and observed values at each time point as well as improved numerical stability. We illustrate the value of the state space approach by reanalyzing a classic dataset of trait evolution in the diatom lineage Stephanodiscus yellowstonensis. A series of increasingly complex models were fit to these data, including a novel modification of an Ornstein-Uhlenbeck model in which a trait tracks an exogenous covariate. These model results suggest that the number of spines on the periphery of the diatom is best explained by adaptation to changing solar insolation over time.