Counting mutations by parsimony and estimation of mutation rate variation across nucleotide sites —a simulation study

Under variable mutation rates across sites/phylogenetic lineages, we use computer simulation to investigate counting mutations by parsimony for a sample of DNA sequences from different species. We also investigate several new and existing parsimony-based methods for estimating α, the gamma shape parameter which models mutation rate variation across nucleotide sites within a DNA sequence. We found that the performance of parsimony counting is not significantly affected by random variable mutation rates across phylogenetic lineages, and is consistently better under UPGMA reconstructed topologies than under true ones. If all the mutation and phylogenetic information is known, all α-estimating methods investigated are unbiased. If mutations are inferred by parsimony, α is often but not always overestimated. The magnitude of overestimation depends on the number of species in analysis, time distribution for speciation to occur, transition/transversion bias, and true α itself. With a large number of DNA sequences (> 20), α can be estimated with little bias and small sampling error. Interestingly, the estimation is often more accurate if mutations inferred by parsimony are based on UPGMA reconstructed topologies than on true ones. Our newly developed mean-zero-class method, together with the maximum-likelihood method, performs best statistically. Finally, several statistical problems awaiting solutions are presented. Some terminologies from molecular evolution used in this paper are summarized in the Appendix.