DYAR RULE AND THE INVESTMENT PRINCIPLE - OPTIMAL MOLTING STRATEGIES IF FEEDING RATE IS SIZE-DEPENDENT AND GROWTH IS DISCONTINUOUS

We consider animals whose feeding rate depends on the size of structur es that grow only by moulting (e.g. spiders' leg). Our Investment Prin ciple predicts optimum size increases at each moult; under simplifying assumptions these are a function of the scaling of feeding rate with size, the efficiency of moulting and the optimum size increase at the preceeding moult. We show how to test this quantitatively, and make th e qualitative prediction that size increases and instar durations chan ge monotonically through development. Thus, this version of the model does not predict that proportional size increases necessarily remain c onstant, which is the pattern described by Dyar's Rule. A literature s urvey shows that in nature size increases to tend to decline and insta r durations to increase, but exceptions to monotonicity occur frequent ly - we consider how relaxing certain assumptions of the model could e xplain this. Having specified various functions relating fitness to ad ult size and time of emergence, we calculate (using dynamic programmin g) the effect of manipulating food availability, time of hatching and size of the initial (or some intermediate) instar. The associated norm s of reaction depend on the fitness function and differ from those whe n growth follows Dyar's Rule or is continuous. We go on to consider op timization of the number of instars. The Investment Principle then pre dicts upper and lower limits to observed size increases and explains w hy increases usually change little or decline through development. Thi s is thus a new adaptive explanation for Dyar's Rule and for the most common deviation from the Rule.