Functional Responses with Predator Interference: Viable Alternatives to the Holling Type II Model

Skalski, Garrick T.; Gilliam, James F.

doi:10.2307/2679836

Cited by 209 publications

(304 citation statements)

References 0 publications

Supporting

Mentioning

292

Contrasting

Unclassified

Order By: Relevance

“…It matters little whether or not the per-capita y-nullcline is vertical or monotonically increasing in x. Consequently, the exponential model works as well as the logistic model. The same results apply to models based on various Holling Type II expanded functional forms ( [9,19]) for which predator's interspecific interference is considered in the context of spacial interference of predation. All these forms will generate a nonvertical prey-supported capacity nullcline for the predator whether or not the death rate coefficient, s, of the predator is zero.…”

Section: Box 1 Textmentioning

confidence: 64%

Biological control does not imply paradox

Deng

Jessie

Ledder

et al. 2007

Mathematical Biosciences

View full text Add to dashboard Cite

Section: Box 1 Textmentioning

confidence: 64%

Biological control does not imply paradox

Deng

Jessie

Ledder

et al. 2007

Mathematical Biosciences

View full text Add to dashboard Cite

“…Another important factor is intraspecific interference within a population of competitors, which includes aggressive displays, posturing, fighting, infanticide, and cannibalism [30]. When the principal effect of the intraspecific interference is a reduced rate of feeding or resource intake, the effects can be modeled via an altered functional response for the consumer [8,10,40]. Recently, Cantrell et al [6] extended system (1.2) to incorporate conspecific feeding interference for one of the competitors.…”

Section: Introductionmentioning

confidence: 99%

Coexistence in competition models with density-dependent mortality

Ruan

Ardito

Ricciardi

et al. 2007

Comptes Rendus. Biologies

View full text Add to dashboard Cite

We consider a two-competitor/one-prey model in which both competitors exhibit a general functional response and one of the competitors exhibits a density-dependent mortality rate. It is shown that the two competitors can coexist upon the single prey.As an example, we consider a two-competitor/one-prey model with a Holling II functional response. Our results demonstrate that density-dependent mortality in one of the competitors can prevent competitive exclusion. Moreover, by constructing a Liapunov function, the system has a globally stable positive equilibrium.

show abstract

“…Ranked in order of increasing intensity, these can include aggressive displays and posturing, fighting, and intraspecific killing (e.g., infanticide) and cannibalism (Fox, 1975;Krebs and Davies, 1981). When the principal effect of the intraspecific interference is a reduced rate of feeding or resource intake, the effects are probably best modeled via an altered functional response for the consumer (DeAngelis et al, 1975;Cosner et al, 1999;Skalski and Gilliam, 2001). However, even adaptive foraging can lead to intraspecific interference (Abrams, 1984b).…”

Section: Introductionmentioning

confidence: 99%

Biodiversity, Habitat Area, Resource Growth Rate and Interference Competition

Kuang

Fagan

Loladze

2003

Bulletin of Mathematical Biology

View full text Add to dashboard Cite

For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simple Lotka-Volterra forms in which consumer species lack intraspecific competition terms. Here we show that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment. In addition, our work suggests a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity. In the special case of a modified Lotka-Volterra model describing multiple predators competing for a single resource, we present an ordering procedure that determines the deterministic fate of each specific consumer. Moreover, we find that the growth rate of a resource species is proportional to the maximum number of consumer species that resource can support. In the limiting case, when the resource growth rate is infinite, a model with intraspecific interference reduces to the conventional Lotka-Volterra competition model where there can be an unlimited number of coexisting consumers.

show abstract

Functional Responses with Predator Interference: Viable Alternatives to the Holling Type II Model

Cited by 209 publications

References 0 publications

Biological control does not imply paradox

Biological control does not imply paradox

Coexistence in competition models with density-dependent mortality

Biodiversity, Habitat Area, Resource Growth Rate and Interference Competition

Contact Info

Product

Resources

About