Toward a General Theory of Heteromorphic Reproduction

P. William Hughes

Organisms often divide reproductive investment among outputs that differ in morphology, timing, or reproductive mechanism. In this paper I extend the minimum-risk treatment of seed heteromorphism to the more general question of organisms with ‘portfolios’ of biologically distinct reproductive outputs. The resulting framework specifies a common investment and fitness currency, calculates returns and covariances across shared environmental states, and compares minimum variance at fixed expected fitness with maximization of long-run geometric growth.
I then derive general inclusion criterion for an additional output and provide an analysis of two seed morphs and a clonal propagule present in four hypothetical environments. For this result, an expected return of three results in the clone reduces minimum variance by 83.6%. When both systems are optimized independently for geometric growth, the clone enters despite lower standalone arithmetic and geometric returns than the optimized seed-only portfolio, with the geometric mean growth rising by 5.2% even as arithmetic mean return falls. Overall, these illustrative calculations demonstrate the usefulness of this framework, since it provides an explicit procedure for showing how different reproductive outputs must perform as one portfolio, illustrates how to compare portfolios, and can be used to develop allocation predictions.