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The objective of this paper is to give a rigorous analysis of a stochastic spatial model of producer-consumer systems that has been recently introduced by Kang and the author to understand the role of space in ecological communities in…
Rock-paper-scissors (RPS) game is a nice model to study the biodiversity in ecosystem. However, the previous studies only consider the nearest- neighbor- interaction among the species. In this paper, taking the long range migration into…
Dynamic environments shape diverse dynamics in evolutionary game systems. We introduce spatial heterogeneity of resources into the prisoner's dilemma game model to explore coevolutionary game dynamics with environmental feedback. The…
We establish a theoretical framework to address evolutionary dynamics of spatial games under strong selection. As the selection intensity tends to infinity, strategy competition unfolds in the deterministic way of winners taking all. We…
Computer simulations of minimal population-dynamics models have long been used to explore questions in ecosystems coexistence and species biodiversity, via simple agent-based models of three interacting species, referred to as $R$, $P$, and…
In this communication, a simple mechanism in the optional public goods game is experimentally investigated using two experimental settings; and first time, the cyclic strategy pattern in full state space is demonstrated by means of…
Spatial evolutionary games provide a valuable framework for elucidating the emergence and maintenance of cooperative behavior. However, most previous studies assume that individuals are profiteers and neglect to consider the effects of…
The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local…
We consider the lifetimes of metastable states in bistable evolutionary games (coordination games), and examine how they are affected by spatial structure. A semiclassical approximation based on a path integral method is applied to…
A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption…
We consider a broad class of stochastic lattice predator-prey models, whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the…
Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of…
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator…
In this monograph, we introduce a new model in population dynamics that describes two species sharing the same environmental resources in a situation of open hostility. The interactions among these populations are described not in terms of…
We study a dynamical system defined by a repeated game on a 1D lattice, in which the players keep track of their gross payoffs over time in a bank. Strategy updates are governed by a Boltzmann distribution which depends on the neighborhood…
What determines species diversity is dramatic concern in science. Here we report the effect of doping on diversity in spatiotemporal rock-paper-scissors (RPS) games, which can be observed directly in ecological, biological and social…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in…
We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition there are one or several possibilities to opt out from the game by…
An organism that is newly introduced into an existing population has a survival probability that is dependent on both the population density of its environment and the competition it experiences with the members of that population.…