A reformulation of Fisher's runaway identifies the heritability of mate choices as a key parameter and highlights limitations of the hypothesis.

Fisher proposed that female preference for mates with extreme traits could evolve as an essentially arbitrary outcome of a self-reinforcing process. Although Fisher's runaway has been shown to be a theoretical possibility, it is not clear whether it occurs in real populations, in part because existing models express the necessary conditions in terms of parameters that would be nearly impossible to estimate in the wild. Here, I reformulate models of the runaway in terms of two estimable parameters, the heritability and phenotypic variance of realized mate choices. Higher values of both quantities make the runaway more likely. In the most realistic model considered, in which mate choices are based on a mixture of absolute and relative criteria, a runaway cannot occur unless mate choice increases the variance of the male trait, which seems incompatible with the strong directional mating preferences typically observed in polygynous species. Even in the most favourable case for the runaway, purely relative preference without direct selection on preference, a substantial heritability of realized mate choices would be required if there is moderately strong stabilizing selection on the male trait. These results cast some doubt on whether the runaway is a plausible outcome in natural populations.