Allocation under multiple resource constraints

Models of reproductive ecology and life history usually resort to arguments of optimal or ESS allocation of a single limiting resource. Yet real organisms may be limited by multiple resources. We present a verbal-graphical method for analysing allocation problems under multiple resource constraints, focusing on an example of allocation to two structures or functions, subject to two resource constraints. The logic behind this intuitive model is justified by an analytical model, which is applied to a sex allocation example. The evolutionarily stable strategy (ESS) or optimal allocation will usually depend on which constraints are limiting at the ESS. For example, if the carbon:nitrogen ratio required to produce seeds differs from that required to produce pollen, the ESS numbers of seeds and pollen grains will differ depending on which resource is limiting (and take on yet another value if both resources are limiting at the ESS). We show how to determine whether one, the other or both constraints are limiting at the ESS. The degree of difference in the ESS allocation under different constraints is determined by the degree of difference in the 'resource recipes' of the structures or functions in question. ESS allocations to structures or functions are predicted to be more sensitive to changes in resource availability when both constraints are limiting than when only one is limiting. In contrast, ESSs are predicted to be more sensitive to changes in fitness equation parameters when one resource is limiting than when both are limiting. Nutrient manipulation experiments are suggested that can test the importance of these ideas. Plastic developmental responses in resource acquisition may result in multiple resource constraints frequently being binding at ESSs. To the degree that resources are substitutable, rather than being required in specific ratios, multiple resource allocation problems can be rephrased as single resource problems.