Related papers: A predator-2 prey fast-slow dynamical system for r…
In ecology, prey switching refers to a predator's adaptive change of habitat or diet in response to prey abundance. In this paper, we study piecewise-smooth models of predator-prey interactions with a linear trade-off in a predator's prey…
Due to the conventional distinction between ecological (rapid) and evolutionary (slow)timescales, ecological and population models to date have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has…
Drawing on the understanding of the logistic map, we propose a simple predator-prey model where predators and prey adapt to each other, leading to the co-evolution of the system. The special dynamics observed in periodic windows contribute…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
In this paper we explore the eco-evolutionary dynamics of a predator-prey model, where the prey population is structured according to a certain life history trait. The trait distribution within the prey population is the result of interplay…
In this paper, we develop and analyze a model that studies the interaction between a specialist predator, a generalist predator, and their common prey in a two-trophic ecosystem featuring three timescales. We assume that the prey operates…
A coarse grained description of a two-dimensional prey-predator system is given in terms of a 3-state lattice model containing two control parameters: the spreading rates of preys and predators. The properties of the model are investigated…
We study the adaptive dynamics of predator-prey systems modeled by a dynamical system in which the traits of predators and prey are allowed to evolve by small mutations. When only the prey are allowed to evolve, and the size of the…
In this paper, we study the classical two-predators-one-prey model. The classical model described by a system of 3 ordinary differential equations can be reduced to a one-dimensional bimodal map. We prove that this map has at most two…
Two density-dependent branching processes are considered to model predator-prey populations. For both models, preys are considered to be the main food supply of predators. Moreover, in each generation the number of individuals of each…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
We construct two ordinary-differential-equation models of a predator feeding adaptively on two prey types, and we evaluate the models' ability to fit data on freshwater plankton. We model the predator's switch from one prey to the other in…
Identifying early warning signs of sudden population changes and mechanisms leading to regime shifts are highly desirable in population biology. In this paper, a two-trophic ecosystem comprising of two species of predators, competing for…
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…
A two-type two-sex branching process is introduced with the aim of describing the interaction of predator and prey populations with sexual reproduction and promiscuous mating. In each generation and in each species the total number of…
We consider the properties of a slow-fast prey-predator system in time and space. We first argue that the simplicity of prey-predator system is apparent rather than real and there are still many of its hidden properties that have been…
We perform individual-based Monte Carlo simulations in a community consisting of two predator species competing for a single prey species, with the purpose of studying biodiversity stabilization in this simple model system. Predators are…
Critical transitions or regime shifts are sudden and unexpected changes in the state of an ecosystem, that are usually associated with dangerous levels of environmental change. However, recent studies show that critical transitions can also…
Eco-evolutionary frameworks can explain certain features of communities in which ecological and evolutionary processes occur over comparable timescales. Here, we investigate whether an evolutionary dynamics may interact with the spatial…
We consider an ecological model consisting of two species of predators competing for their common prey with explicit interference competition. With a proper rescaling, the model is portrayed as a singularly perturbed system with one-fast…