Predator-prey relationships are a central component of community dynamics. Classic approaches have tried to understand and predict these relationships in terms of consumptive interactions between predator and prey species, but characterizing the interaction this way is insufficient to predict the complexity and context dependency inherent in predator-prey relationships. Recent approaches have b...

We are interested in the impact of natural selection in a prey-predator community. We introduce an individual-based model of the community that takes into account both prey and predator phenotypes. Our aim is to understand the phenotypic coevolution of prey and predators. The community evolves as a multi-type birth and death process with mutations. We first consider the infinite particle approx...

We study the qualitative properties of population cycles in a predator-prey system where genetic variability allows contemporary rapid evolution of the prey. Previous numerical studies have found that prey evolution in response to changing predation risk can have major quantitative and qualitative effects on predator-prey cycles, including: (1) large increases in cycle period, (2) changes in ph...

1. The behaviour of predators is rarely considered in models of predator–prey interactions, nor is it common to include multiple predators in models of animal behaviour. 2. We introduce a model of optimal diel vertical migration in zooplankton prey facing predation from two functionally different predators, fish and other zooplankton. Zooplankton predators are themselves subject to predation fr...

In this paper, a prey-predator model with a social activity of prey population has been analyzed. In some ecological situations, the prey-predator interaction occurs only at the outer surface of a herd formed by prey population. To model this phenomenon, the square root of prey density has been used in the functional response. The basic model is formulated with this modified functional response...

We examined conspicuous signalling displays in the context of predator-prey interactions. To determine in which context Puerto Rican crested anoles, Anolis cristatellusperform conspicuous signals, we exposed wild lizards to a model of a natural snake predator. The lizards gave six behavioural responses to the model: immobility, predator inspection, flight, lateral face-off, dewlapping and push-...

In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model. Keywords— Predator-prey model, Holling II type functional response, Positive periodic solution, Coincidence degree theorem

We are interested in prey-predator communities where the predator population evolves much faster than the prey’s (e.g. insect-tree communities). We introduce a piecewise deterministic model for these prey-predator communities that arises as a limit of a microscopic model when the number of predators goes to infinity. We prove that the process has a unique invariant probability measure and that ...

A reaction-diffusion model describing the evolutionary dynamics of a food-web was constructed. In this model, predator-prey relationships among organisms were determined by their position in a two-dimensional phenotype space defined by two traits: as prey and as predator. The mutation process is expressed with a diffusion process of biomass in the phenotype space. Numerical simulation of this m...

A discrete predator-prey model with Holling II and Beddington-DeAngelis functional responses is investigated. With the aid of differential equations with piecewise constant arguments, a discrete version of continuous nonautonomous delayed predator-prey model with BeddingtonDeAngelis functional responses is proposed. By using Gaines andMawhin’s continuation theorem of coincidence degree theory, ...