Gain Curves, Reproductive Efficiency, and Sex Allocation.

Reproductive efficiency reflects the gap between an organism's potential success and its actual achievement. Exploring how theoretical sex allocation models deal with reproductive efficiency reveals shortcomings in two fundamental elements of the theory, fitness gain curves and the Shaw-Mohler equation. Gain curves depict success but make no reference to the production of the entities that accrue fitness, so they imply nothing about efficiency in its common sense, the fraction of successful reproductive entities in relation to the number produced. Because the number of successful entities cannot exceed the number produced, a gain curve implies a minimum allowable production, but the implication itself exposes new problems. Gain curves are used to replace terms in the Shaw-Mohler equation that were meant to represent an individual's fair competitive share of total population fitness. If gain curves themselves represent individual fitness outcomes, the theoretical solutions can imply unequal aggregate success of male and female mating agents, a biological impossibility in a sexually reproducing population. If gain curves represent inputs to an arena of mating interactions, the theoretical solutions can imply misleading or biologically impossible patterns of reproductive efficiency. The relationship between pollination efficiency and pollen-ovule ratios in flowering plants is used as a window into the shortcomings of gain curves and the Shaw-Mohler equation. There are new modeling approaches to sex allocation that are more explicit about the processes that lead from production of male and female reproductive entities to their eventual fitness outcomes.