Related papers: Understanding the invader-driven replicator dynami…
We consider a continuous time stochastic individual based model for a population structured only by an inherited vector trait and with logistic interactions. We consider its limit in a context from adaptive dynamics: the population is…
We investigate the long-time dynamics of a SIR epidemic model in the case of a population of pathogens infecting a homogeneous host population. The pathogen population is structured by a genotypic variable. When the initial mass of the…
We consider a spatial (line) model for invasion of a population by a single mutant with a stochastically selectively neutral fitness landscape, independent from the fitness landscape for non-mutants. This model is similar to those…
Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the…
Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and…
We analyse the asymptotic behaviour of integro-differential equations modelling $N$ populations in interaction, all structured by different traits. Interactions are modelled by non-local terms involving linear combinations of the total…
We adapt a fitness function from evolutionary game theory as a mechanism for aggregation and dispersal in a partial differential equation (PDE) model of two interacting populations, described by density functions $u$ and $v$. We consider a…
A non-periodic version of the one-predator two-prey system model presented in [L.T.H. Nguyen, Q.H. Ta, T.V. T\d{a}, Existence and stability of periodic solutions of a Lotka-Volterra system, SICE International Symposium on Control Systems,…
What does it mean to fully understand the behavior of a network of adaptive agents? The golden standard typically is the behavior of learning dynamics in potential games, where many evolutionary dynamics, e.g., replicator, are known to…
Cyclic dominance between species may yield spiral waves that are known to provide a mechanism enabling persistent species coexistence. This observation holds true even in presence of spatial heterogeneity in the form of quenched disorder.…
We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…
The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be…
We analyze from basic physical considerations the Darwinian competition for reproduction (evolutionary dynamics) of strategists in a Public Goods Game, the archetype for $n$-agent (group) economical and biological interactions. In the…
We analyze a stylized model of co-evolution between any two purely competing species (e.g., host and parasite), both sexually reproducing. Similarly to a recent model of Livnat \etal~\cite{evolfocs14} the fitness of an individual depends on…
Species sharing a prey or a predator species may go extinct due to exploitative or apparent competition. We examine whether evolution of the shared species acts as a coexistence mechanism and to what extent the answer depends on the genetic…
In the companion paper of this set (Capitan and Cuesta, 2010) we have developed a full analytical treatment of the model of species assembly introduced in Capitan et al. (2009). This model is based on the construction of an assembly graph…
We study evolutionary games with a continuous trait space in which replicator dynamics are restricted to the manifold of multidimensional Gaussian distributions. We demonstrate that the replicator equations are natural gradient flow for…
We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The…
Species-rich ecosystems often exhibit multiple stable states with distinct species compositions. Yet, the factors determining the likelihood of each state's occurrence remain poorly understood. Here, we characterize and explain the…
The present paper deals with a prey-predator model with prey refuge proportion to both species and independent harvesting of each species. Our study shows that using refuge as control, it can break the limit circle of the system and reach…