The effect of functional response on stability of a grazer population on a landscape

Alberto Basset, Donald L. DeAngelis, James E. Diffendorfer

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

The dynamics of interacting consumer and resource populations is one of the most thoroughly studied problems of theoretical population biology. Among the key results from the study of simple mathematical models of interacting populations is that the Holling Type 2 functional response tends to be unstable for a wide range of realistic parameters. Functional responses such as Holling Type 3, which might be thought of as implicitly incorporating the existence of consumer refuges, are more stable than the Type 2. We studied consumer-resource models with these different functional responses on a landscape level by modeling grazers that can disperse across a space of patchily distributed grass resources. For certain assumptions concerning the movement of grazers on the landscape, the effect of these functional responses on stability is reversed; the Holling Type 2 functional response confers greater stability. 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 remains 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 likelihood that the resource will be overexploited over the whole landscape simultaneously, which results in a stronger tendency towards system stability. It appears, then, that consumer overexploitation of resources locally may contribute to lower stability.

Original languageEnglish
Pages (from-to)153-162
Number of pages10
JournalEcological Modelling
Volume101
Issue number2-3
DOIs
StatePublished - Aug 15 1997

Fingerprint

functional response
functional response models
resource
grasses
grass
energy balance
mathematical models
grazing
Biological Sciences
refuge
effect
biomass
modeling

Keywords

  • Functional response
  • Grazer population
  • Individual-based model
  • Landscape model
  • Spatially-explicit model
  • Stability

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecological Modeling
  • Ecology

Cite this

The effect of functional response on stability of a grazer population on a landscape. / Basset, Alberto; DeAngelis, Donald L.; Diffendorfer, James E.

In: Ecological Modelling, Vol. 101, No. 2-3, 15.08.1997, p. 153-162.

Research output: Contribution to journalArticle

Basset, Alberto ; DeAngelis, Donald L. ; Diffendorfer, James E. / The effect of functional response on stability of a grazer population on a landscape. In: Ecological Modelling. 1997 ; Vol. 101, No. 2-3. pp. 153-162.
@article{c8d1bd395065416381cc45d294b9efb6,
title = "The effect of functional response on stability of a grazer population on a landscape",
abstract = "The dynamics of interacting consumer and resource populations is one of the most thoroughly studied problems of theoretical population biology. Among the key results from the study of simple mathematical models of interacting populations is that the Holling Type 2 functional response tends to be unstable for a wide range of realistic parameters. Functional responses such as Holling Type 3, which might be thought of as implicitly incorporating the existence of consumer refuges, are more stable than the Type 2. We studied consumer-resource models with these different functional responses on a landscape level by modeling grazers that can disperse across a space of patchily distributed grass resources. For certain assumptions concerning the movement of grazers on the landscape, the effect of these functional responses on stability is reversed; the Holling Type 2 functional response confers greater stability. 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 remains 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 likelihood that the resource will be overexploited over the whole landscape simultaneously, which results in a stronger tendency towards system stability. It appears, then, that consumer overexploitation of resources locally may contribute to lower stability.",
keywords = "Functional response, Grazer population, Individual-based model, Landscape model, Spatially-explicit model, Stability",
author = "Alberto Basset and DeAngelis, {Donald L.} and Diffendorfer, {James E.}",
year = "1997",
month = "8",
day = "15",
doi = "10.1016/S0304-3800(97)01975-3",
language = "English",
volume = "101",
pages = "153--162",
journal = "Ecological Modelling",
issn = "0304-3800",
publisher = "Elsevier",
number = "2-3",

}

TY - JOUR

T1 - The effect of functional response on stability of a grazer population on a landscape

AU - Basset, Alberto

AU - DeAngelis, Donald L.

AU - Diffendorfer, James E.

PY - 1997/8/15

Y1 - 1997/8/15

N2 - The dynamics of interacting consumer and resource populations is one of the most thoroughly studied problems of theoretical population biology. Among the key results from the study of simple mathematical models of interacting populations is that the Holling Type 2 functional response tends to be unstable for a wide range of realistic parameters. Functional responses such as Holling Type 3, which might be thought of as implicitly incorporating the existence of consumer refuges, are more stable than the Type 2. We studied consumer-resource models with these different functional responses on a landscape level by modeling grazers that can disperse across a space of patchily distributed grass resources. For certain assumptions concerning the movement of grazers on the landscape, the effect of these functional responses on stability is reversed; the Holling Type 2 functional response confers greater stability. 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 remains 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 likelihood that the resource will be overexploited over the whole landscape simultaneously, which results in a stronger tendency towards system stability. It appears, then, that consumer overexploitation of resources locally may contribute to lower stability.

AB - The dynamics of interacting consumer and resource populations is one of the most thoroughly studied problems of theoretical population biology. Among the key results from the study of simple mathematical models of interacting populations is that the Holling Type 2 functional response tends to be unstable for a wide range of realistic parameters. Functional responses such as Holling Type 3, which might be thought of as implicitly incorporating the existence of consumer refuges, are more stable than the Type 2. We studied consumer-resource models with these different functional responses on a landscape level by modeling grazers that can disperse across a space of patchily distributed grass resources. For certain assumptions concerning the movement of grazers on the landscape, the effect of these functional responses on stability is reversed; the Holling Type 2 functional response confers greater stability. 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 remains 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 likelihood that the resource will be overexploited over the whole landscape simultaneously, which results in a stronger tendency towards system stability. It appears, then, that consumer overexploitation of resources locally may contribute to lower stability.

KW - Functional response

KW - Grazer population

KW - Individual-based model

KW - Landscape model

KW - Spatially-explicit model

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=0030838846&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030838846&partnerID=8YFLogxK

U2 - 10.1016/S0304-3800(97)01975-3

DO - 10.1016/S0304-3800(97)01975-3

M3 - Article

VL - 101

SP - 153

EP - 162

JO - Ecological Modelling

JF - Ecological Modelling

SN - 0304-3800

IS - 2-3

ER -