Pollination efficiency and the evolution of sex allocation - diminishing returns matter.

Immobility of flowering plants requires them to engage pollen vectors to outcross, introducing considerable inefficiency in the conversion of pollen production into sired seeds. Whether inefficiencies influence the evolution of the relative resource allocation to female and male functions has been debated for more than 40 years. Whereas early models suggested no effect, negative interspecific relations of mean pollen production and pollen : ovule ratios to the proportion of removed pollen that is exported to stigmas (pollen-transfer efficiency) indicate otherwise. Here, we consider theoretically a key condition that determines whether the efficiencies of processes (first derivative of process output with respect to input) affect the evolutionarily stable sex (ESS) allocation. No effect arises if all individuals experience the same efficiency. By contrast, a decline in process efficiency with increasing allocation (diminishing returns) generally reduces the ESS male allocation for a population. Furthermore, differences in the allocation dependence of efficiencies (and hence the ESS sex allocation) among populations/species create a negative relation of realised efficiency to male allocation among species, like that observed empirically. Diminishing returns arise for various processes that affect siring (e.g. pollen export and local pollen competition to fertilise ovules), which may differ in their relative influence on sex allocation among species.