| Abstract: | This paper analyses the response of the distribution of diapause switching times in an arthropod population with respect to variation in a catastrophe, which kills nondiapause individuals. For concreteness, the catastrophe will be taken to the onset of winter. The relationship between an individual's switching time and the decision whether to diapause is defined as follows: If she passes through the end of the sensitive period, during which the diapause decision is made, before her switching time, she will complete development and reproduce rather than diapause. If she passes through the sensitive period on or after her switching time, she will diapause. The model follows the evolution of the distribution of switching times for a population over a sequence of years. Random variation in the end of the season is created by sampling from a normal distribution of times at the end of the growing season. The model is for a haploid population in which the distribution of switching times that a female passes to her offspring is normally distributed having her switching time as its mean. This approximates a sexual population with strong positive assortative mating and heritability near 1. This mode of inheritance permits a rapid response to yearly changes in the end of the season as a contrast to earlier models, which incorporated a slow response. Patterns of temporal change in the median switching time are analyzed. The influences of three parameters are considered: the mean and standard deviation of the end of the season, and standard deviation of the offspring distribution. The main conclusion differs from the results of earlier models in that the end of the season must be extremely variable before the median of the distribution of switching times displays conservative behavior, i. e., before it becomes significantly earlier than the median expected when the end of the season is constant and equal to the mean of the normal distribution for the end of the season used in the simulation. Previous models predicted a conservative response even in moderately variable environments. |
