THE EFFECT OF FUNCTIONAL-RESPONSE ON STABILITY OF A GRAZER POPULATIONON A LANDSCAPE

The dynamics of interacting consumer and resource populations is one o f the most thoroughly studied problems of theoretical population biolo gy. Among the key results from the study of simple mathematical models of interacting populations is that the Holling Type 2 functional resp onse tends to be unstable for a wide range of realistic parameters. Fu nctional responses such as Holling Type 3, which might be thought of a s implicitly incorporating the existence of consumer refuges, are more stable than the Type 2. We studied consumer-resource models with thes e different functional responses on a landscape level by modeling graz ers that can disperse across a space of patchily distributed grass res ources. For certain assumptions concerning the movement of grazers on the landscape, the effect of these functional responses on stability i s reversed; the Holling Type 2 functional response confers greater sta bility. The reason for this apparently paradoxical result is that the Holling Type 2 functional response allows grazers to graze individual grass patches to lower levels than Type 3, as the energy balance remai ns favorable for grazing at lower grass biomasses. However, this local overexploitation leads the grazers to be slower in reaching areas of the landscape where resource densities are higher. It decreases the li kelihood that the resource will be overexploited over the whole landsc ape simultaneously, which results in a stronger tendency towards syste m stability. It appears, then, that consumer overexploitation of resou rces locally may contribute to lower stability. (C) 1997 Elsevier Scie nce B.V.