Minimal-Risk Seed Heteromorphism: Proportions of Seed Morphs for Optimal Risk-Averse Heteromorphic Strategies

Seed heteromorphism is the reproductive strategy characterized by the simultaneous production of multiple seed types. While comparing heteromorphic to monomorphic strategies is mathematically simple, there is no explicit test for assessing which ratio of seed morphs minimizes fitness variance, and hence offers a basis for comparing different heteromorphic strategies. Such a test may be particularly valuable when more than two distinct morphs are present, since many strategies may have equivalent geometric fitnesses. As noted by Gillespie (1974), in these cases avoiding rare but evolutionarily important instances of severe reductions in fitness involves the minimization of variation in fitness-i.e., risk. Here I compute the optimal proportions of two or more seed morphs for heteromorphic strategies that either: (1) minimize total fitness variance; or (2) maximize the fitness-risk ratio-i.e., the "extra" fitness accrued per unit of "extra" fitness variance. This work thereby provides a testable null hypothesis to estimate the optimal frequencies of seed morphs when multiple heteromorphic strategies have evolved in environments with severe fitness risks. Moreover, it also permits the calculation of expected seed morph frequencies when more than two seed morphs are produced.