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Bulletin of Mathematical Biology 62:1109-1136 (2000)Download free pdf

Population cycles caused by selection by density dependent competitive interactions

Lars Witting

Abstract: Several animal species have cyclic population dynamics with phase-related cycles in life history traits such as body mass, reproductive rate, and pre-reproductive period. Although many mechanisms have been proposed there is no agreement on the cause of these cycles, and no population equation that deduces both the abundance and the life history cycles from basic ecological constraints has been formulated. Here I deduce a population dynamic equation from the selection pressure of density dependent competitive interactions in order to explain the cyclic dynamics in abundance and life history traits. The model can explain cycles by evolutionary changes in the genotype or by plastic responses in the phenotype. It treats the population dynamic growth rate as an initial condition, and its density independent fundament is Fisher's (1930, The Genetical Theory of Natural Selection, Oxford: Clarendon) fundamental theorem of natural selection that predicts a hyper-geometrical increase in abundance. The predicted periods coincide with the cyclic dynamics of Lepidoptera, and the Calder hypothesis, which suggests that the period of population cycles is proportional to the 1/4 power of body mass, follows from first principles of the proposed density dependent ecology.

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