Inference of gene sequences in ancestral species has been widely used to test hypotheses concerning the process of molecular sequence evolution. However, the approach may produce spurious results, mainly because using the single best reconstruction while ignoring the suboptimal ones creates systematic biases. Here we implement methods to correct for such biases and use computer simulation to evaluate their performance when the substitution process is nonstationary. The methods we evaluated include parsimony and likelihood using the single best reconstruction (SBR), averaging over reconstructions weighted by the posterior probabilities (AWP), and a new method called expected Markov counting (EMC) that produces maximum-likelihood estimates of substitution counts for any branch under a nonstationary Markov model. We simulated base composition evolution on a phylogeny for six species, with different selective pressures on G+C content among lineages, and compared the counts of nucleotide substitutions recorded during simulation with the inference by different methods. We found that large systematic biases resulted from (i) the use of parsimony or likelihood with SBR, (ii) the use of a stationary model when the substitution process is nonstationary, and (iii) the use of the Hasegawa-Kishino-Yano (HKY) model, which is too simple to adequately describe the substitution process. The nonstationary general time reversible (GTR) model, used with AWP or EMC, accurately recovered the substitution counts, even in cases of complex parameter fluctuations. We discuss model complexity and the compromise between bias and variance and suggest that the new methods may be useful for studying complex patterns of nucleotide substitution in large genomic data sets.
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