Oscillations in Housefly Population Sizes Due to Time Lags
1976
Taylor, Charles E. | Sokal, Robert R.
Oscillations of animal population size can be caused by time delays due to development. Mathematical representations of this have been studied by previous workers. We investigated the applicability of their models to laboratory populations of houseflies. Estimates of the necessary parameters–death rate, oviposition rate, development time, and the association of larval survivorship with density–were obtained from various experiments. A stability analysis of the model by the method of Maynard Smith predicted oscillations in adult population size for these parameter values. This was also predicted by numerical solutions to the equations of the model. Four population cages of houseflies maintained for periods up to 2.5 yr showed the predicted pattern. The populations fluctuated markedly and regularly in adult size, generally between 200 and 1,600, with a periodicity of 5—6 wk. The correspondence between prediction and observation was reasonably close and was improved when further complications were considered and the behavior of the populations was simulated on a computer. In another cage maintained under different conditions of husbandry, where oviposition was less but other parameters were the same, the stability and population size differed in a manner predicted by the model. Of several theories that might explain oscillations, only that of time delays is likely to be appropriate for these populations.
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