Discrete and Continuous Insect Populations in Tropical Environments

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Abstract
(1) There are several examples in the literature of insect populations in the tropics showing generation cycles with a period of approximately one generation. We review nine examples where such cycles have been documented or reported from a range of arthropod pest species in the tropics. The cycles either persist, or tend to die away as the outbreaks decline. In all these cases, natural enemies are an important cause of mortality and have been thought responsible for driving the cycles. (2) This paper shows that natural enemies are indeed able to cause generation cycles in their hosts or prey in relatively aseasonal environments. (3) We develop age-structured population models of host-parasitoid interactions based on an idealized interaction between a tropical lepidopteran and its specific parasitoid. The host population is assumed to be made up of pre-parasitism, susceptible, post-parasitism and adult reproductive stages while the parasitoid population comprises immature and adult searching stages. (4) We construct models of two types: first, an extension of the simulation model developed by Godfray and Hassell (1987) and second, a time-delayed differential equation model using the ''lumped'' age-class techniques of R. M. Nisbet and W. S. C. Gurney. The analytical results obtained from this model complement those from the numerical exploration of the simulation model. (%) Both models show clearly that discrete generation cycles are favoured by a parasitoid life cycle 0.5 or 1.5 times that of its host and a relatively short adult reproductive lifespan. Conversely, parasitoids with generation times approximately the same, or twice as long, as those of their hosts, or with relatively long reproductive lifespans, are more likely to promote continuous generations. Sensitivity analysis shows these conclusions to be relatively robust. (6) Since parasitoid generation times of the order of half that of their hosts are widespread in tropical host .sbd. parasitoid systems, we conclude that generation cycles often seen in tropical insect populations can be explained by the internal dynamics of the interaction with their natural enemies.