correcting the bias of empirical frequency parameter estimators in codon models纠正偏差的经验频率参数估计在密码子模型.pdfVIP

Correcting the Bias of Empirical Frequency Parameter Estimators in Codon Models 1 2 3 4 Sergei Kosakovsky Pond *, Wayne Delport , Spencer V. Muse , Konrad Scheffler 1 Department of Medicine, University of California San Diego, San Diego, California, United States of America, 2 Department of Pathology, University of California San Diego, San Diego, California, United States of America, 3 Department of Statistics, North Carolina State University, Raleigh, North Carolina, United States of America, 4 Computer Science Division, Department of Mathematical Sciences, Stellenbosch University, Stellenbosch, South Africa Abstract Markov models of codon substitution are powerful inferential tools for studying biological processes such as natural selection and preferences in amino acid substitution. The equilibrium character distributions of these models are almost always estimated using nucleotide frequencies observed in a sequence alignment, primarily as a matter of historical convention. In this note, we demonstrate that a popular class of such estimators are biased, and that this bias has an adverse effect on goodness of fit and estimates of substitution rates. We propose a ‘‘corrected’’ empirical estimator that begins with observed nucleotide counts, but accounts for the nucleotide composition of stop codons. We show via simulation that the corrected estimates outperform the de facto standard F 3 |4 estimates not just by providing better estimates of the frequencies themselves, but also by leading to improved estimation of other parameters in the evolutionary models. On a curated collection of 856 sequence alignments, our estimators show a signi