Testing the accuracy of methods for reconstructing ancestral states of continuous characters

Many methods are available for estimating ancestral values of continuous characteristics, but little is known about how well these methods perform. Here we compare six methods: linear parsimony, squared-change parsimony, one-parameter maximum likelihood (Brownian motion), two-parameter maximum likelihood (Ornstein-Uhlenbeck process), and independent comparisons with and without branch-length information. We apply these methods to data from 20 morphospecies of Pleistocene planktic Foraminifera in order to estimate ancestral size and shape variables, and compare these estimates with measurements on fossils close to the phylogenetic position of 13 ancestors. No method produced accurate estimates for any variable: estimates were consistently less good as predictors of the observed values than were the averages of the observed values. The two-parameter maximum-likelihood model consistently produces the most accurate size estimates overall. Estimation of ancestral sizes is confounded by an evolutionary trend towards increasing size. Shape showed no trend but was still estimated very poorly: we consider possible reasons. We discuss the implications of our results for the use of estimates of ancestral characteristics.