The effect of the Holling type II functional response on apparent competition

Křivan, Vlastimil; Eisner, Jan

doi:10.1016/j.tpb.2006.07.004

Cited by 50 publications

(34 citation statements)

References 27 publications

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“…Most studies that have compared accurate and inaccurate switching have found that the latter tends to be more stabilizing (Fryxell and Lundberg 1998;van Baalen et al 2001;Holt 2004, 2005). However, this result is likely to depend on the nature of the lags involved in switching (Abrams 1999;Abrams and Matsuda 2004;Krivan and Eisner 2006), and on the basis for potential instability. When there are endogenously generated cycles, more inaccurate switching appears to reduce the amplitude of population fluctuations (Fryxell and Lundberg 1998;van Baalen et al 2001).…”

Section: Choice Of Resources In Systems Having Nonsubstitutable Resoumentioning

confidence: 99%

Quantitative descriptions of resource choice in ecological models

Abrams

2009

Population Ecology

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This article reviews the subject of resource choice by consumers. It is concerned with how such choice has been and should be represented in quantitative ecological models. This requires consideration of the dynamics of behavioral change and the fitness consequences of different resource intake rates. The topic is important because of the impact of choice on the functional response of the consumer to each of the resources it consumes. A variety of open questions related to choice are addressed. These include: the relationship between optimal diet choice and switching; the relationship between adaptive choice of two or resources and type-3 functional responses to a single resource; whether switching behavior requires choice and whether choice always results in switching behavior; why partial preferences are observed; whether choice between habitats is fundamentally different from choice within habitats; how between-individual variation in parameters related to resource use alters functional responses measured at the population level. The impacts of choice on stability are discussed briefly. The costs of increased resource use and the type of nutritional interactions between resources are particularly important determinants of adaptive resource choice, and are considered in some detail.

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Section: Choice Of Resources In Systems Having Nonsubstitutable Resoumentioning

confidence: 99%

Quantitative descriptions of resource choice in ecological models

Abrams

2009

Population Ecology

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“…This relation takes into account that predators, in order to consume prey, need to search for it, chase, kill, eat, and digest. This is why predators attack not all prey but a limited number of them, which saturates to a constant when the prey density increases [36]. Such predator-prey relations, clearly, do not characterize symbiosis.…”

Section: Introductionmentioning

confidence: 99%

Modeling symbiosis by interactions through species carrying capacities

Yukalov

Yukalova

Sornette

2012

Physica D: Nonlinear Phenomena

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We introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies or to social, economic and financial societies. Our model includes three basic types: symbiosis with direct mutual interactions, symbiosis with asymmetric interactions, and symbiosis without direct interactions. In all cases, we provide a complete classification of all admissible dynamical regimes. The proposed model of symbiosis turned out to be very rich, as it exhibits four qualitatively different regimes: convergence to stationary states, unbounded exponential growth, finite-time singularity, and finite-time death or extinction of species.

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“…In unstable systems, a predator's ability to adapt its attack rate can be either beneficial or harmful to a prey species when it is at low density [5]. For a predator having fixed fractional population abundances in two different patches, switching food sources can destabilize dynamics and, in some cases, cause chaotic dynamics to occur at sufficiently high prey carrying capacities [33]. Oscillation can also occur due to a Hopf bifurcation when predators switch because of group defense in prey [31,40].…”

Section: Introductionmentioning

confidence: 99%

Effect of resource subsidies on predator–prey population dynamics: a mathematical model

Nevai

Gorder

2012

Journal of Biological Dynamics

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The influence of a resource subsidy on predator-prey interactions is examined using a mathematical model. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). In one version of the model, the predator, prey and subsidy all occur in the same location; in a second version, the predator moves between two patches, one containing only the prey and the other containing only the subsidy. Criteria for feasibility and stability of the different equilibrium states are studied both analytically and numerically. At small subsidy input rates, there is a minimum prey carrying capacity needed to support both predator and prey. At intermediate subsidy input rates, the predator and prey can always coexist. At high subsidy input rates, the prey cannot persist even at high carrying capacities. As predator movement increases, the dynamic stability of the predator-prey-subsidy interactions also increases.

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The effect of the Holling type II functional response on apparent competition

Cited by 50 publications

References 27 publications

Quantitative descriptions of resource choice in ecological models

Quantitative descriptions of resource choice in ecological models

Modeling symbiosis by interactions through species carrying capacities

Effect of resource subsidies on predator–prey population dynamics: a mathematical model

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