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Diffusion and the Predator-Prey Interaction
SIAM Journal on Applied Mathematics, 1977We consider the system of partial differential equations which describe the predator-prey interaction, where diffusion and spatial dependence are taken into account. The equations reduce to the Kolmogorov equations, when spatial dependence is neglected.
Conway, Edward D., Smoller, Joel A.
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Predator-Prey Interactions with Hunger Structure
SIAM Journal on Applied Mathematics, 2020We present, analyze, and simulate a model for predator-prey interaction structured by hunger. The model consists of a nonlocal transport equation for the predator, coupled to an ordinary differential equation for the prey. We deduce a system of 3 ODEs for some integral quantities of the transport equation, which generalizes some classical Lotka ...
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2007
Predation is a widespread population process that has evolved many times within the metazoa. It can affect the distribution, abundance, and dynamics of species in ecosystems. For instance, the distribution of western tussock moth is known to be affected by a parasitic wasp (Maron and Harrison, 1997; Hastings et al., 1998), the abundance of different ...
Michael B. Bonsall, Michael P. Hassell
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Predation is a widespread population process that has evolved many times within the metazoa. It can affect the distribution, abundance, and dynamics of species in ecosystems. For instance, the distribution of western tussock moth is known to be affected by a parasitic wasp (Maron and Harrison, 1997; Hastings et al., 1998), the abundance of different ...
Michael B. Bonsall, Michael P. Hassell
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1991
Predator-prey interactions have been among the most intensively studied areas of aquatic biology during the past several decades. Investigations have focused particularly on theories of “optimal foraging,” which seeks to describe predator behavior [e.g., Charnov (1976), Werner and Hall (1974), and Pyke (1984)], and “predator mediated community ...
Robert G. Wetzel, Gene E. Likens
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Predator-prey interactions have been among the most intensively studied areas of aquatic biology during the past several decades. Investigations have focused particularly on theories of “optimal foraging,” which seeks to describe predator behavior [e.g., Charnov (1976), Werner and Hall (1974), and Pyke (1984)], and “predator mediated community ...
Robert G. Wetzel, Gene E. Likens
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A multigroup model for predator‐prey interactions
Biotechnology and Bioengineering, 1975AbstractThe predator‐prey interactions between the protozoan Tetrahymena pyriformis and the bacterium Aerobacter aerogenes have been studied experimentally and mathematically. A mathematical model for the ciliates defines the mass distribution of cells within the population.
E, Villarreal, R P, Canale, Z, Akcasu
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Predator-prey interactions in natural communities
Journal of Theoretical Biology, 1975Abstract The familiar concepts of harvest and yield are developed for the purpose of describing predator-prey interactions in a community context. In this regard the functional response (appropriate for one predator-one prey systems) is replaced by a community harvest function.
David J. Rapport, James E. Turner
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COEVOLUTIONARY DYNAMICS OF PREDATOR-PREY INTERACTIONS
International Journal of Biomathematics, 2012In this paper, with the method of adaptive dynamics, we investigate the coevolution of phenotypic traits of predator and prey species. The evolutionary model is constructed from a deterministic approximation of the underlying stochastic ecological processes. Firstly, we investigate the ecological and evolutionary conditions that allow for continuously
Zu, Jian +2 more
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Modelling the fear effect in predator–prey interactions
Journal of Mathematical Biology, 2016A recent field manipulation on a terrestrial vertebrate showed that the fear of predators alone altered anti-predator defences to such an extent that it greatly reduced the reproduction of prey. Because fear can evidently affect the populations of terrestrial vertebrates, we proposed a predator-prey model incorporating the cost of fear into prey ...
Wang, Xiaoying +2 more
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2001
Predation has been given many different definitions. For the purposes of this chapter, it is an interaction in which one free-living individual kills and derives resources from another organism. This definition includes finches that consume seeds but does not include fish that eat the siphons of clams that are unable to retract them quickly enough ...
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Predation has been given many different definitions. For the purposes of this chapter, it is an interaction in which one free-living individual kills and derives resources from another organism. This definition includes finches that consume seeds but does not include fish that eat the siphons of clams that are unable to retract them quickly enough ...
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A Semi-Markovian Model for Predator-Prey Interactions
Biometrics, 1978In the study of population dynamics, the predator-prey system is recognized as a vitally important aspect in natural population control. On aspect of predator-prey interactions is studied in this paper. The attack cycle of a predator is assumed to consist of four different activities, namely, search, pursuit, handle and eat, and digestion.
Rao, Chennupati R., Kshirsagar, A. M.
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