Overcompensation and population cycles in an ungulate

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Abstract
ALTHOUGH theoretical studies show that overcompensatory density-dependent mechanisms can potentially generate regular or chaotic fluctuations in animal numbers, the majority of realistic single-species models of invertebrate populations are not overcompensatory enough to cause sustained population cycles1–3. The possibility that Overcompensation may generate cycles or chaos in vertebrate populations has seldom been considered. Here we show that highly overcompensating density-dependent mortality can generate recurrent population crashes consistent with those observed in a naturally limited population of Soay sheep. The observed interval of three or more years between crashes points to sharp 'focusing' of mortality over a narrow range of population density.