Phenotypic plasticity in fluctuating environments: consequences of the lack of individual optimization

I consider the problem of characterizing the optimal plasticresponse when there are large-scale fluctuations in the environmentaffecting all population members. Individuals differ in theirstate, and each makes a reproductive decision before the environmentalconditions are known. An individual's state, its decision, andenvironmental conditions together determine the number of descendantsleft at the next decision epoch. I restrict attention to thesimple problem in which the state of the descendants left atthis epoch does not depend on these three factors. Because theenvironment is fluctuating, there is no individual optimization;instead the best action in one state implicitly depends on thebest action in other states. I characterize an optimal state-dependentstrategy, give a method of computation, and show how behaviorof each individual following the optimal strategy may be reinterpretedas a form of "individual optimization." Concepts are illustratedwith an example of optimal dutch size as a function of territoryquality.