Testing the Constant-Rate Neutral Allele Model With Protein Sequence Data

Abstract

ue of X 2 LF' With Omin determined, it is possible to test the constant-rate neutral allele model by checking the compatibility of observed levels of heterozygosity in extant populations with the levels expected with oequal to Omln. Omln for a-and ,B-hemoglobin are shown to be inconsistent with observed levels of heterozygosities at these loci in humans. There is apparently no value of 0 which is compatible with both the observed value of X 2 LF and the observed levels of heterozygosity at the aand ,B-hemoglobin loci of humans. It is concluded that the simple constant-rate neutral model can be regarded as highly improbable in the light of available data.To determine the distribution of X 2 LF under the neutral model, Monte Carlo simulations were used to produce sequences analogous to those analyzed by Langley and Fitch. These simulation-produced sequences were then analyzed in the same way that Langley and Fitch analyzed the actual sequence data. Their analysis is described in the next section. Following that section, the results of Gillespie and Langley are reviewed and extended approximately. Also discussed are the difficulties with applying these analytic results to estimate 0 or to test the neutral model directly. Next, the simulation algorithm is described and the results are presented and discussed. Langley-Fitch AnalysisThe analysis of Langley and Fitch consisted of three main steps. 1.) Inferring the numbers of substitutions occurring on each branch of the phylogenetic tree, for each protein, using a maximum parsimony procedure (Fitch, 1971;Fitch and Farris, 1974).2.) Finding maximum likelihood estimates of the substitution rate of each protein and of the times of each of the nodes of the phylogenetic tree. 3.) Calcu-203 ! Present address: Department of Genetics, University of California, Davis, California 95616. Fitch (1973, 1974) and Fitch and Langley (1976) statistically analyzed the pattern of nucleotide substitutions in seven proteins and 17 taxa and rejected the null hypothesis of a constantrate Poisson model of protein evolution, Their rejection of the constant-rate model was based on the extremely large observed value of a statistic (henceforth referred to as X 2 LF) , which has a standard Chi-squared distribution under their null hypothesis. Gillespie and Langley (1979) showed that under a constant-rate neutral allele model, X 2 L F is not Chi-squared distributed. Though they did not obtain the exact distribution of X 2 LF ' they were able to show that the expectation of X 2 LF is an increasing function of 0 = 4Nu, where N is the population size and u is the neutral mutation rate. Thus, the Langley and Fitch analysis does not constitute a test of the constant-rate neutral model. Evidently no test of the neutral model is possible using only the statistic X 2 LF ' since no matter how large the observed value of X 2 L F ' a sufficiently large value of 0 could account for the observation.If one knew the distribution of X 2 LF as a function of 0, one could use the observed value of X\F to estimate O....

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