Effects of Spatial Grouping on the Functional Response of Predators

Cosner, Chris; Jiang, Jiang; Ault, Jerald S.; Olson, Donald B.

doi:10.1006/tpbi.1999.1414

Cited by 458 publications

(313 citation statements)

References 38 publications

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“…(Beddington(1975), DeAngelis et al(1975), Hassell and Varley(1969)). This view is also plausible biologically (Cosner et al(1999)). When p(x) = αx/(m + x) and g(x/K) = r(1 − x/K), model (1.2) becomes the following well studied Michaelis-Menten type predator-prey system (see the references cited in Kuang and Freedman(1988)).…”

Section: Introductionmentioning

confidence: 77%

Rich dynamics of a ratio-dependent one-prey two-predators model

Hsu

Hwang

Kuang

2001

Journal of Mathematical Biology

112

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Abstract. The objective of this paper is to systematically study the qualitative properties of a ratio-dependent one-prey two-predator model. We show that the dynamics outcome of the interactions are very sensitive to parameter values and initial data. Specifically, we show the interactions can lead to all the following possible outcomes: 1) competitive exclusion; 2) total extinction, i.e., collapse of the whole system; 3) coexistence in the form of positive steady state; 4) coexistence in the form of oscillatory solutions; and 5) introducing a friendly and better competitor can save a otherwise doomed prey species. These results reveal far richer dynamics compared to similar prey dependent models. Biological implications of these results are discussed.

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Section: Introductionmentioning

confidence: 77%

Rich dynamics of a ratio-dependent one-prey two-predators model

Hsu

Hwang

Kuang

2001

Journal of Mathematical Biology

112

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“…The public believes this resulted from the fragmentation of habitats and the ever shrinking sizes of these patches which may diminish or deprive of prey refugees (Fischer (2000)). The consensus view is that ratio dependent formulation breaks down when the patch size is large and both the prey and predator densities are low (Arditi and Ginzburg (1989), Cosner et al (1999), Abrams and Ginzburg (2000)), since in such case, predators will spend most effort in searching rather than interfering each other. Hence, the functional response is likely to be much more sensible to prey density than predator density.…”

Section: Discussionmentioning

confidence: 99%

“…In short, deterministic mutual extinction is an extreme outcome calls for extreme measures. Ratio dependence, while a special case of the general predator dependence ones, such as the Beddington-DeAngelis or Hassel-Varley type (Cosner et al (1999)), is currently the only one that provides a simple and plausible explanation of such extinction dynamics.…”

Section: Discussionmentioning

confidence: 99%

“…Recently there is a growing evidences , Akcakaya et al (1995), Cosner et al (1999)) that in some situations, especially when predator have to search for food (and therefore have to share or compete for food), a more suitable general predator-prey theory should be based on the so called ratio-dependent theory, which can be roughly stated as that the per capita predator growth rate should be a function of the ratio of prey to predator abundance. This is supported by numerous field and laboratory experiments and observations (Arditi and Ginzburg (1989), ).…”

Section: Introductionmentioning

confidence: 99%

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Global analysis of the Michaelis-Menten-type ratio-dependent predator-prey system

Hsu

Hwang

Kuang³

2001

Journal of Mathematical Biology

330

171

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Abstract. The recent broad interest on ratio-dependent based predator functional response calls for detailed qualitative study on ratio-dependent predator-prey differential systems. A first such attempt is documented in the recent work of Kuang and Beretta(1998), where Michaelis-Menten-type ratio-dependent model is studied systematically. Their paper, while contains many new and significant results, is far from complete in answering the many subtle mathematical questions on the global qualitative behavior of solutions of the model. Indeed, many of such important open questions are mentioned in the discussion section of their paper.Through a simple change of variable, we transform the Michaelis-Menten-type ratiodependent model to a better studied Gause-type predator-prey system. As a result, we can obtain a complete classification of the asymptotic behavior of the solutions of the MichaelisMenten-type ratio-dependent model. In some cases we can determine how the outcomes depend on the initial conditions. In particular, open questions on the global stability of all equilibria in various cases and the uniqueness of limit cycles are resolved. Biological implications of our results are also presented.

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“…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

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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.

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Effects of Spatial Grouping on the Functional Response of Predators

Cited by 458 publications

References 38 publications

Rich dynamics of a ratio-dependent one-prey two-predators model

Rich dynamics of a ratio-dependent one-prey two-predators model

Global analysis of the Michaelis-Menten-type ratio-dependent predator-prey system

Biodiversity, Habitat Area, Resource Growth Rate and Interference Competition

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