Predator-prey interactions: egg-eating predators

Thompson, Robert W.; DiBiasio, David; Mendes, C.

doi:10.1016/0025-5564(82)90034-7

Cited by 21 publications

(4 citation statements)

References 9 publications

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“…Frauenthal ignores this difficulty and ends up with an unconvincing specification, where, in order to avoid negative rates of recruitment, he has to add an extra ad hoe rule. Gurtin and Levine [7] also neglect this problem, while Thompson, DiBiasio, and Mendes [13] suggest a modification that, although negative rates of recruitment are no longer possible, still does not solve the basic problem.…”

Section: Introductionmentioning

confidence: 99%

Simple mathematical models for cannibalism: A critique and a new approach

Diekmann

Nisbet

Gurney

et al. 1986

Mathematical Biosciences

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We show how to incorporate a functional response in recent models of Gurtin, Levine, and others for egg cannibalism. Starting from a relatively complicated model with vulnerability spread over an age interval of finite duration(, we arrive at a much simpler model by passing to the limit £ t 0. It turns out that survivorship through the vulnerable stage is implicitly determined by the solution of a scalar equation. Subsequently we study the existence and stability of steady states, and we find (analytically in a simple case, numerically in more general situations) curves in a two-dimensional parameter space where a nontrivial steady state loses its stability and a periodic solution arises through a Hopf bifurcation.

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Section: Introductionmentioning

confidence: 99%

Simple mathematical models for cannibalism: A critique and a new approach

Diekmann

Nisbet

Gurney

et al. 1986

Mathematical Biosciences

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“…So, concentration of the predator on very young prey can be considered as a stabilizing mechanism. With model formulations that are disputable (see Section 1) Gurtin & Levine (1979) concluded that egg eating is destabilizing while Thompson et al (1982) concluded that it is stabilizing.…”

Section: Discussionmentioning

confidence: 99%

“…This type of interaction is now commonly referred to as an 'egg-eating predator-prey relation'. In continuations of this study many authors have given different forms to the factor with which the birth-rate is reduced to the actual recruitment rate (Gurtin & Levine, 1979;Thompson et al, 1982;Coleman & Frauenthal, 1983). Diekmann et al (1985) criticize all of these.…”

Section: Introductionmentioning

confidence: 96%

Interactions between Egg-eating Predator and Prey: The Effect of the Functional Response and of Age Structure

Bosch

Diekmann²

1986

Math Med Biol

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In this paper we analyse an age-structured predator-prey model in which predators eat only very young prey. The model can be formulated'as a system of three Volterra integral equations with an implicitly defined non-linearity. An interpretation of the implicit relation is given. The linearized stability of the steady states is investigated. It turns out that concentration of the predator on very young individuals is a stabilizing mechanism. Furthermore, it is seen that a compound parameter which is a measure for the efficiency of the predator has a major influence on the stability of the steady states. If the efficiency of the predator decreases the steady state can become unstable and oscillations will arise. Furthermore it is seen from the model that the destabilizing effect of a juvenile period is stronger when it concerns the predator than when it concerns the prey species. In an appendix it is shown that an egg-eating predator and an indiscriminately eating predator can coexist in a stable steady state while feeding on only one prey species.

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“…A key, early paper in this progression is the work by Auslander et al (1974) who derive a general physiological model and apply it to a host-parasite system. Age-dependent predation, where the predator is either indiscriminate or is egg-eating has also been discussed (Gurtin and Levine, 1979;Levine, 1981;Thompson et al, 1982;Coleman and Frauenthal, 1983;Saleem, 1983, 1984, andothers). Many authors make simplifying assumptions to make the equations tractable, for example, assuming only one of the trophic populations is structured, or the predator only consumes the eggs of the prey.…”

Section: Introductionmentioning

confidence: 99%

Phenologically-Structured Predator-Prey Dynamics with Temperature Dependence

Logan¹

2007

Bull. Math. Biol.

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Studies document the fact that temperature changes strongly affect interactions in many consumer-resource systems through altered, or shifted, phenologies. The mistiming of events, such as migration or emergence times, or the contraction or expansion of development times can upset the normal synchronization and lead to increased or decreased predation events. In this paper, we formulate a continuous time, phenologically-structured model of predator-prey interactions that is driven by temperature variations. It is particularly applicable to arthropod interactions because their development rates are so strongly temperature related. The model takes the form of a system of partial differential-integral equations for the species' population densities in development-time variables. In special cases, the model is analytically tractable and we find a closed-form solution. By calculating density variations under different temperature regimes, the model gives a quantitative method for assessing the effects of global temperature change on consumer-resource interactions.

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Predator-prey interactions: egg-eating predators

Cited by 21 publications

References 9 publications

Simple mathematical models for cannibalism: A critique and a new approach

Simple mathematical models for cannibalism: A critique and a new approach

Interactions between Egg-eating Predator and Prey: The Effect of the Functional Response and of Age Structure

Phenologically-Structured Predator-Prey Dynamics with Temperature Dependence

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