This material is published by the Journal of theoretical Biology (2005, vol 234, pp 593-604).

Model of microtine cycles caused by lethal toxins in non-preferred food plants

Adam Kent, Susanne Plesner Jensen and C. Patrick Doncaster

A recent model of microtine cycles has hypothesised that plant chemical defences can drive the precipitous decline phase, through periodic lethal toxin production (PLTP) by non-preferred plant foods. Here we enumerate possible mechanisms using a previously published model of optimal foraging by one consumer (microtine rodent) of two types of food plant (1 preferred and 1 non-preferred). Rate constants for each of the model parameters were sought from the extensive literature on vole cycles. For a range of likely values of input parameters, we evaluated model fit by applying five empirically derived criteria for cyclic behaviour. These were: cycles with a period length of 2-5 yr, peak densities of 100-350 voles per ha and trough densities of 0-25 ha-1, ratio of peak to trough densities of 10-100, and the occurrence of a catastrophic collapse in the vole population followed by a prolonged low phase. In contrast to previous models of food-induced microtine cycles, the optimal foraging model successfully reproduced the first four criteria and the prolonged low phase. The criterion of population collapse was met if the non-preferred food began producing lethal toxins at a threshold grazing intensity, as predicted by PLTP. Fewer criteria could be met in variations on the model, in which the non-preferred food was equally as nutritious as the preferred food or was continuously toxic.

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