A Comment on the Comments of Rogers and Felsenstein

Rogers' suggestion (1986) that the formula B = FST Cro helps us to decide whether between-population differences (Cr2 ) are what we expect from withinpopulation differences (cr2) will not work because it is circular. The only way to relate Cr2 to Cr2 is to have an estimate of FST based on neutral genes. But the only way to estimate FST is by the relationship between cr2 and Cr2 for such genes. That is, we would have to know that the genes were neutral in the first place, which is precisely what we wanted to find out from the test! As a matter of fact, we can solve the problem in the future by using, say, third-position or intron polymorphism in DNA sequences. If we first estimate FST from such data, we could then later apply that estimate to quantitative characters or enzyme polymorphisms. Note, however, that this involves ancillary information from other data and cannot be judged simply from the comparison of quantitative characters and isozyme polymorphisms, which is what the whole discussion is about. Felsenstein (1986) has made a substantive contribution to the problem. He points out that, if the drift variance is substituted into my equation (14) (1984, p. 121), we get a strong result: if isozyme and quantitative characters are both purely neutral, isozyme difference is statistically significant more often than quantitative characters, except in the biologically unrealistic case of perfect heritability. Indeed, for heritabilities of the order of 50%, isozyme differences are much more powerful than quantitative differences in detecting population differentiation. On the one hand, this illustrates my general point that the two kinds of characters have different powers to detect the same force of differentiation. On the other, it shows that I was wrong in saying that no information exists in the comparison. What Felsenstein's calculation shows is that, if quantitativecharacter differences are significant while isozyme differences are not (a common observation), we can reject the hypothesis that both are neutral. This is not much, but it is better than nothing. One cannot, alas, make any stronger statement. One could not, for example, say that the quantitative characters were under selection while the isozymes were neutral, a temptation to which many have succumbed. Nor could one even say that differentiating selection was stronger for quantitative characters than for isozymes, since Felsenstein's demonstration depends critically on the pure drift variance being the dominant term. If drift is weak, compared with selection, then we have no way of predicting what the variance of gene-frequency differences, (r , will be, and it is this quantity that is critical in equation (14). Finally, if isozyme differences are significant while quantitative differences are not, or if they are both nonsignificant, there is no information about anything.