CHARACTER VARIABILITY AND EVOLUTIONARY RATE IN MENIDIA.

Johnson and Mickevich (1977) claimed to demonstrate an association between within-population variability and evolutionary rate for both allozyme loci and morphological characters in the atherinid fish genus Menidia. Their paper is extremely interesting for at least two reasons. First, it purports to demonstrate an evolutionary phenomenon exhibited by both electrophoretic and morphological characters; second, if their conclusions are correct it should be possible to estimate the relative likelihood of future evolutionary change for different characters within a lineage based solely upon measurements of present-day variability of those characters within that lineage. Johnson and Mickevich used two data sets: 24 allozyme loci sampled from 22 populations in five species of Menidia, and 22 morphological characters from a partly different set of 22 populations. For the 16 populations that were represented in both of these data sets, phylogenetic trees constructed separately from the two different types of data provide ". . . nearly perfect congruence. The differences between the two trees are slight rearrangements within species. ... (Mickevich and Johnson, 1976). Two measures of evolutionary change were used: phenetic distance, or range of divergence, and patristic distance, the amount of change over a phylogenetic tree. For the allozyme loci, these quantities were based upon frequency differences between populations for each allele at a locus; the sum over these alleles was used as the measure of evolutionary change for the locus. By subtracting the phenetic from the patristic distance, an estimate of the repetitive portion of evolutionary change was also obtained. This represents reversals and parallel and convergent evolution, all of which contribute to the patristic but not to the phenetic distance. For both data sets, this repetitive component gives the highest correlation with intrapopulation variability, and the phenetic gives the lowest. Within-population variability was measured by the information statistic, H, for the allozyme data. For the morphometric characters, within-population variability was measured by the average standard deviation (divided by the grand mean) and measures of evolutionary change were computed between population means (also divided by the grand mean for that character). The point that I hope to make in this note is that there were several potential biases in the analyses performed by Johnson and Mickevich. First, they did not adequately correct for the possible contribution of sampling variance to their correlations. This bias applies to both the morphological and the allozyme data and is especially important for the repetitive component of the patristic distance. Second, their measures of variability and evolutionary change for the allozyme loci are not entirely free to vary independently, and a correlation between them, for certain frequency ranges, is unsurprising. This, too, is especially important for the repetitive component. Third, their measures of variability and change for the allozyme loci are both the result of summation processes across the number of alleles per locus. A correlation could result because different loci have different numbers of alleles. When this effect is removed, the correlation is primarily a function of the repetitive component for "essentially invariant" loci. Fourth, the gap-coding used for the morphological characters could introduce circular logic by giving relatively less-variable characters more weight in the construction of the phylogenetic tree. Since tree construction techniques minimize repetitive evolution, this weighting could result in a correlation between variability and apparent repetitive evolution. I do not claim that Johnson and Mickevich's conclusions are incorrect; only that they have presented no convincing evidence for those conclusions. Hopefully, future attempts to examine the relationship between variability and evolutionary rate will take some of these potential sources of bias into consideration. Are the correlations artifacts of sampling error? Sokal (1976) observed that in the absence of amonggroup differences the range of divergence among sample means should be correlated with the withingroup standard deviation. This is because the sampling variance of the mean is then proportional to the within-group variance. Johnson and Mickevich attempted to correct for this effect in the morphological data by omitting two characters that show no statistically significant differences ". . . between any pair of populations." Even though this procedure should reduce the bias, the fact that the amonggroup variance is partly composed of the withingroup variance (Sokal and Rohlf, 1969, p. 193) should still cause some correlation between the withinand among-group variability. A more appropriate method of analysis, at least for the phenetic component, would be to estimate variance components at the two levels as was done by Sokal (1976). Dr. Johnson informs me that he believes the in-