because adult descendants are considerably larger than adult ancestors. If we standardize by size, we compare an adult ancestor with a juvenile descendant. Since coiling increases during ontogeny, ancestral adults are more coiled than juvenile descendants with incomplete growth. The criterion for standardization should be developmental stage, not size. When we compare adult ancestors with adult descendants, we note that descendants, as calculated by 5, have the same shape as ancestors when they are 1.2 times as large. Furthermore, adult descendants are actually 1.2 times as large as adult ancestors (Gould, 1972, p. 108). Coiling is retarded with respect to size but the biological result is not paedomorphosis. It is size increase with geometric similarity. Large descendants have the same shape as their smaller ancestors; retardation occurred in order to transpose the same shape to larger sizes attained in evolution. (This proviso does not disturb the conclusions of our previous example, Gryphaea gigantea. Here we had true paedomorphosis since the rate of phyletic size increase lagged far behind the value of 5. They must be equal for evolution to proceed in geometric similarity.) This example illustrates two important points: First, paedomorphosis and recapitulation are general results that depend upon a criterion of standardization and bear no ineluctable relation to any heterochronic process. The retardation that often leads to paedomorphosis can yield an equality of shape at corresponding developmental stages of ancestor and descendant. Second, all results must be considered at a biologically appropriate criterion of standardization. This may be size, age, or developmental stage.

Temporal Shift as a Mechanism of Dissociation

In the examples of the previous section, ancestral and descendant ontogenies followed the same slope and differed only in y-intercept. In this common situation, a temporal shift in development may often be identified as the mechanism of dissociation: an allometric feature grows at the same rate in descendants, but it begins to grow at smaller or larger body sizes. Consider, again, Gryphaea: Burnaby (1965) gives these equations for the periphery of the coiled valve versus the length of the flat valve (the ratio coiled/flat measures the amount of coiling—our measure of shape): C = .237F1.766 for ancestors, and C = 0.210F1.766 for descendants. Coiling begins when the coiled/flat ratio exceeds 1.0 (before that, the valves are of equal length and the shell is flat like an ordinary oyster—the equations apply only to the coiled portion of ontogeny). According to Burnaby's equations, the key ratio of 1.0 is reached at a size (flat valve length) of 6.5 mm in ancestors and 7.7 mm in descendants. The parallel regressions demon-