Population Differences in Quantitative Characters as Opposed to Gene Frequencies

In a recent paper, Lewontin (1984) argued that no useful purpose can be served by comparing the variation of gene frequencies of local groups with variation of quantitative characters. He compared (a) the statistical significance of population differences in a quantitative character with (b) the significance of gene-frequency differences at individual loci contributing to variance in the quantitative character and showed that significance in one does not necessarily imply significance in the other. In view of this, Lewontin concluded that comparisons of these types of data serve no useful purpose. I argue here that this conclusion does not follow from his argument. Lewontin was able to construct examples in which significant differences in a quantitative character occur without significant gene-frequency differences (or the converse). The relevance of such examples depends on the frequency with which they occur in nature, that is, the frequency with which they are produced by evolution. Lewontin, however, took population differences in gene frequencies as givens rather than as random variables. Since his analysis proceeds from assumptions about the outcome of evolution, it tells nothing about the frequency with which such outcomes are produced by evolution. For example, it does not exclude the possibility that the examples he chose are events of negligible probability. Consequently, it provides no basis for conclusions conce tling the value of comparing differences in gene frequencies with those in quantitative characters. What, then, are the prospects for using such comparisons to test hypotheses about evolution? Inference is possible provided only that the results of such comparisons can be expected to differ under different evolutionary models. As I discuss below, models of genetic drift and migration seem particularly useful as a basis for generating testable hypotheses. Wright (1943, 1951) showed, using a model of additive gene effects at a single locus, that variation among populations in the value of a selectively neutral quantitative character is, in expectation, 2B = 2FST 20, where U2 is the genetic variance expected under panmixia with the same gene frequencies, and FST is the correlation among uniting gametes relative to the total population. Here, FST is a parameter of the evolutionary process (not a statistic) and depends on individual mobility and the sizes of local populations. Since it is nearly independent of the mean gene frequency for loci that are not near fixation (Rogers 1982), FST can be estimated from any sample of neutral loci. It is also possible to estimate abr using standard methods of quantitative genetics. Thus, the right-hand side of this equation can be estimated from genetic data, if some set of genetic markers is