Estimating divergence times in phylogenetic trees without a molecular clock.

were nonstationary at first positions for the ingroup at P = 0.01 using the chi-square test in PAUP*. The chi-square test in PAUP∗ appears to do a good job of identifying the worst offenders and although crude, is effective for a large data set when analyzing individual genes. We certainly anticipate that as more refined tests of stationarity are implemented (e.g., Foster, 2004), discrimination of genes that deviate from the stationary condition will improve. We note finally that although deviations from stationarity were detected at third positions, we are not suggesting that all misleading base compositional signal is at third positions. Since these nucleotides are linked as codons, we might expect that strong deviations at third positions would influence first and second positions of codons. Broadly speaking, accurate phylogenetic trees can be recovered from correctly aligned sequences when the inference model is consistent with the process that gave rise to the data. When processes are stationary over lineages and time, relatively straightforward models can be designed to yield accurate inferences, even from short sequences (Steel and Penny, 2000). When processes differ across or within lineages, models must explicitly accommodate the nonstationarity involved. This is generally not straightforward, and even if it could be done, would require many more parameters and associated error terms (but see Foster, 2004). As such, at a given data set size, stationary sequences will prove to be more effective for recovering phylogeny. Stationary sequences will be less prone to the grouping of taxa with convergent base compositions. Of course, when taxa share an atypical base composition in a gene sequence because of shared history, nonstationary sequences may outperform stationary sequences in recovering that branch when using models that assume stationarity. Such instances are cases of obtaining the right answer for the wrong reason (e.g. Swofford et al. 2001) and are a poor argument for use. The criterion of stationarity should prove useful in selecting genes for phylogenetic analysis from completely sequenced genomes, and to the extent that genes