Continuous Ancestral Character Estimation

Introduction

An ancestral character is a biological trait that is present in a group of related organisms and is thus inferred to have been present in the most recent common ancestor of these organisms. Traits of interest, for example fruit size or the presence of parasite resistance, can therefore be traced back in time along a known phylogeny.

Estimating ancestral character values is a phylogenetic analysis that can be used to test evolutionary hypotheses, such as the temporal sequence of evolutionary events or the appearance of adaptive traits. Because ancestral character values are not observed, it is more rational to consider them as parameters in a model where the character values of recent species are the observed values.

Continuous Ancestral Character Estimation (CACE) assumes that traits evolve according to a Brownian motion process. Under this model, the expected difference between two taxa can be computed as a function of the time separating the taxa from their most recent common ancestor, which is obtained from the phylogenetic tree. Maximum Likelihood is then used to obtain the ancestors' trait values, which minimizes the sum of squared changes along the branches. The output is a table of ancestral trait values and the corresponding 95% confidence intervals. These value estimates can be plotted on the phylogenetic tree using a color gradient. Additionally, the function outputs an estimate of the Brownian motion parameter ?² and the log likelihood of the model.

Implementation

CACE uses Analysis of Phylogenetics and Evolution (ape) which is a module for the R Language and Environment and provides functions for reading, writing, plotting, and manipulating phylogenetic trees.

ace(x, phy, type = "continuous", method = "ML", CI = TRUE, model = "BM", scaled = TRUE, kappa = 1, corStruct = NULL, ip = 0.1)

Question

Given a set of observations for a continuous trait (e.g. height, weight, yield,...) for a set of taxa with a known phylogenetic relationship, how can we estimate the value of the trait (and its confidence intervals) in the ancestors of these taxa?

Method

The trait is assumed to evolve according to a Brownian motion process. Under this model, the expected difference between two taxa can be computed as a function of the time separating the taxa from their most recent common ancestor, which is obtained from the phylogenetic tree. Maximum Likelihood is then used to obtain the ancestors' trait values which minimize the sum of squared changes along the branches.

Output

The output is a table of ancestral trait values and the corresponding 95% confidence intervals. These value estimates can be plotted on the phylogenetic tree using a color gradient.

Additionally, the function outputs an estimate of the Brownian motion parameter ?² and the log likelihood of the model.

References

Schluter, D., Price, T., Mooers, A. O. and Ludwig, D. (1997) Likelihood of ancestor states in adaptive radiation. Evolution, 51, 1699-1711.

Paradis, E., Claude, J. and Strimmer, K. (2004) APE: analyses of phylogenetics and evolution in R language. Bioinformatics, 20, 289-290.