A. Basset et al., THE EFFECT OF FUNCTIONAL-RESPONSE ON STABILITY OF A GRAZER POPULATIONON A LANDSCAPE, Ecological modelling, 101(2-3), 1997, pp. 153-162
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.