Evolutionary Paths in Strategy Space: An Improvement Algorithm for Life-history Strategies

Abstract

Life-history strategies are analysed using a matrix population model. Within this framework an organism can be characterized at a particular time by a suitable state variable such as age or size, or both. A life-history strategy specifies the action an organism takes in each state. Given a life-history strategy one can find the reproductive value of the various states under this strategy. One can then ask whether an organism following the strategy chooses actions to maximize the reproductive value of itself and its offspring in one year's time. It is shown that if it does not, then a simple procedure identifies a life-history strategy with higher fitness. This strategy-improvement result leads to a necessary and sufficient condition by which (globally) optimal life-history strategies in natural populations can be recognized.We can define two life-history strategies to be one step away from each other if they specify the same actions at all states but one. Using this concept one can then define a topology on the phenotypic space of all life-history strategies. The topology taken together with a fitness measure defines the landscape of "strategy space". Results on strategy improvement are used to show that, in contrast to the landscapes usually envisaged for genotype space, strategy space is unimodal: there are no local optima other than global optima, and from every strategy one can reach a global optimum by a non-descending path.