Adaptive differences among related bird species are often most evident in beak morphology, and large differences in beaks are clearly important influences on diet (Lack, 1947, 1971; Bock, 1970; Hespenheide, 1973; Lederer, 1975). Interspecific variation in other characters such as wing length and tarsus length also can influence foraging behavior and hence diet (Hespenheide, 1973). Modern evolutionary theory assumes that small differences in trophic characters are adaptive within species (Grant et al., 1976). A well-known theoretical formulation of this principle is Van Valen's (1965) 'niche-variation' hypothesis, which proposes that intraspecific variation in trophic characters is positively correlated with diet diversity. The status of this hypothesis is unclear. Several studies have failed to support it (Willson, 1969; Soule and Stewart, 1970; Lister, 1976), but other studies (Rothstein, 1973; Grant et al., 1976) have provided evidence for it. To evaluate the evolutionary significance of intraspecific morphological variation, we must investigate the heritability of quantitative traits. One way is to use the standard parent-offspring regression techniques of quantitative genetics (Falconer, 1960). This method has seldom been used in the field (but see Perrins and Jones, 1973), because it requires sedentary populations of organisms in relatively stable environments where breeding activities can be followed closely. Island popula-