Further statistical considerations for amino acid replacement data in protein sequences.

Gillespie (1986a) suggests a model of molecular evolution by natural selection. He has chosen this model to fit some statistical aspects of the sequence data that he examined. In the present letter I show that there may be more “wobble” in sequence data than the reader might suspect. The data for each protein sequence are taken to come from a star phylogeny and inference is for N,(t), the number of substitutions that occurred in the ith lineage of a radiation that occurred t years ago. Most of Gillespie’s discussion focuses on the estimation of the ratio R(t) = Var[Ni(t)]/E[Ni(t)]. The data available for estimation are the observed number of amino acids that differ between species i and j, Dw Gillespie (p. 140) writes: “As in other work, our results show that R(t) is always greater than one. The striking aspect of the estimates, however, is the narrow range of R(t) values: 1 .O < R(t) < 3.4.” However, the currently available data sets are sparse. First, it should be noted that the data on which Gillespie based his results are for just six protein sequences, four of which had counts of amino acid differences for six species and the other two of which had such counts for four species. The global number of species was 15, but only seven of these were considered in more than one sequence comparison. To demonstrate that even these data contain evidence that the range of R(t) may not be as narrow as Gillespie found, I consider the sequence comparison for the hemoglobin a-chain. The data are given in table 1, along with fictitious data for four