A Theory of Grasshopper Life Cycles

Abstract

A measure of the fitness of seasonal life cycles of the grasshopper type (one generation per year, overwintering as eggs) is developed and used to investigate a demonstrated trade-off between egg size and juvenile development time. It is suggested that individuals have the option of producing a few large hatchlings which are able to breed early in the following summer, or more smaller hatchlings, which will breed relatively later. A fitness ahalysis is applied to a particular study of the life cycles of two species of grasshopper at three sites differing substantially in the length of the egg-laying period. The optimality analysis shows one species adopts optimal strategies at all three sites, but the other species would do better to lay smaller eggs at all three sites. However a sensitivity analysis shows that these results must be regarded as provisional because the critical parameters have large confidence intervals. The analysis is extended to consider three other possible trade-offs between egg size and date of hatch, egg mortality rate, and juvenile mortality rate.