Estimation of Ancestral States of Continuous Characters: A Computer Simulation Study

In systematics, we usually estimate ancestral phenotypes of morphological and molecular characters measured as categorical or " state " variables. Ancestral estimation has also been important in the studies of animal behavior, physiology, ecology, and other areas of biology, where the characters are usually measured as continuous rather than categorical variables. In the past, the most common way of estimating the ancestral states of continuous characters was to use a parsimony algorithm have been developed for estimating the ancestral states of continuous characters on a phy-logeny. For several reasons, the theory underlying these methods provides a major leap forward from the traditional parsimony methods. In the current study, I use computer simulation to examine the statistical properties of these methods and to determine how much of an improvement these methods actually provide when applied to realistic data. estimates the phenotype of each ancestor as a weighted average of all the phenotypes measured for extant taxa. The weights used in calculating averages correspond to the phylogenetic distance between each ex-tant taxon and the ancestor being estimated. Huey and Bennett (1987) applied this approach , iteratively calculating each ancestral state as the average of its three nearest neighbors until estimates converged on stable solutions. Maddison (1991) provided a recur-sive equation for getting the estimates and explored the assumptions of the method. Specically, he showed that SSP is a statistically reasonable approach very similar to using least-squares regression to estimate ancestral states. McArdle and Rodrigo (1994) showed how SSP could be described as a system of linear equations and thus provided a direct algorithm that can be used to reduce computational time. Linear or Wagner parsimony (Farris, 1970; Swofford and Maddison, 1987) is a similar method that lacks the above statistical development and justication. Instead of minimizing the sum of squared evolutionary changes on the phylogeny, it minimizes the simple sum of changes. In a computer simulation study, Butler and Losos (1997) found that the two methods produce rather different results and that linear parsimony gave worse estimates under the type of phe-notypic evolution (Brownian motion) considered in their simulation procedure. I do not consider linear parsimony in the current study. One weakness of SSP is that it does not include any measure of estimation accuracy. For example, the state at the root of a phy-logeny is known with less accuracy than a state nearer the tips, simply because the longer time since …