Evolutionary balancing of fitness-limiting factors.

Debates concerning the roles of different factors that may limit an organism's reproductive success pervade evolutionary ecology. We suggest that a broad class of limiting-factors problems involving essential resources or essential components of reproductive effort can be analyzed with an evolutionary application of Liebig's law of the minimum. We explore life-history evolution using the metaphor of an organism that must harvest two essential resources (resources 1 and 2) from a stochastically varying environment. Our models make three predictions. First, organisms should overinvest, relative to the deterministic case, in harvesting the resource whose per-offspring harvest cost is smaller. Second, at the optimum, organisms balance multiple fitness-limiting factors rather than being consistently limited by one factor. Third, the optimal investment in harvesting a resource is directly linked to the probability that the organism's fitness will be limited by that resource. Under temporal variation, the optimal proportional investment in harvesting resource 1 is equal to the probability that resource 1 will limit fitness. Our results help to explain why the responses of populations to environmental perturbations are hard to predict: as an organism transitions between different limiting factors, its responses to perturbations of those factors will likewise change.