TESTING THE CONSTANT-RATE NEUTRAL ALLELE MODEL WITH PROTEIN SEQUENCE DATA.

Abstract

Langley and 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 X2LF), which has a standard Chi-squared distribution under their null hypothesis. Gillespie and Langley (1979) showed that under a constant-rate neutral allele model, X2LF is not Chi-squared distributed. Though they did not obtain the exact distribution Of X2LF, they were able to show that the expectation Of X2LF 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 X2LF, since no matter how large the observed value Of X2LF, a sufficiently large value of 0 could account for the observation. If one knew the distribution Of X2LF as a function of 0, one could use the observed value Of X2LF to estimate 0. I report here the results of Monte Carlo simulations that were used to characterize the distribution Of X2LF for several values of 0. The simulations were used to determine 0, the value of 0 for which the mean value Of X2LF over many simulation trials equals the observed value Of X2LF. The simulations were also used to determine Omil, the value of 6 for which approximately 5% of the simulation trials produced values Of X2LF greater than or equal to the observed val-