Generalized aphid population growth models with immigration and cumulative-size dependent dynamics

Mechanistic models in which the per-capita death rate of a population is proportional to cumulative past size have been shown to describe adequately the population size curves for a number of aphid species. Such previous cumulative-sized based models have not included immigration. The inclusion of immigration is suggested biologically as local aphid populations are initiated by migration of winged aphids and as reproduction is temperature-dependent. This paper investigates two models with constant immigration, one with continuous immigration and the other with restricted immigration. Cases of the latter are relatively simple to fit to data. The results from these two immigration models are compared for data sets on the mustard aphid in India.