Related papers: Age structure, replicator equation, and the prison…
Exploiting others is beneficial individually but it could also be detrimental globally. The reverse is also true: a higher cooperation level may change the environment in a way that is beneficial for all competitors. To explore the possible…
We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with…
Despite the wealth of empirical and theoretical studies, the origin and maintenance of cooperation is still an evolutionary riddle. In this context, ecological life-history traits which affect the efficiency of selection may play a role,…
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…
We study the long-time behaviour of a population structured by age and a phenotypic trait under a selection-mutation dynamics. By analysing spectral properties of a family of positive operators on measure spaces, we show the existence of…
The properties of competition models where all individuals are identical are relatively well-understood; however, juveniles and adults can experience or generate competition differently. We study here less well-known structured competition…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
The rate of biological evolution depends on the fixation probability and on the fixation time of new mutants. Intensive research has focused on identifying population structures that augment the fixation probability of advantageous mutants.…
We present a novel approach allowing the study of rare events like fixation under fluctuating environments, modeled as extrinsic noise, in evolutionary processes characterized by the dominance of one species. Our treatment consists of…
Microscopic strategy update rules play an important role in the evolutionary dynamics of cooperation among interacting agents on complex networks. Many previous related works only consider one \emph{fixed} rule, while in the real world,…
Most papers about the evolutionary game on graph assume the statistic network structure. However, social interaction could change the relationship of people. And the changing social structure will affect the people's strategy too. We build…
Species-rich communities, such as the microbiota or microbial ecosystems, provide key functions for human health and climatic resilience. Increasing effort is being dedicated to design experimental protocols for selecting community-level…
The spatial structure of an evolving population affects which mutations become fixed. Some structures amplify selection, increasing the likelihood that beneficial mutations become fixed while deleterious mutations do not. Other structures…
We put a probabilistic framework on the Demographic Prisoner's Dilemma. In this model, cooperating and defecting individuals are placed on a torus to move and play prisoner's dilemma game, if they are on the same site. Each individual…
The significance of network structures in promoting group cooperation within social dilemmas has been widely recognized. Prior studies attribute this facilitation to the assortment of strategies driven by spatial interactions. Although…
Cooperation is usually represented as a Prisoner's Dilemma game. Although individual self-interest may not favour cooperation, cooperation can evolve if, for example, players interact multiple times adjusting their behaviour accordingly to…
The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters they might share the benefit of cooperation while being more protected against non-cooperating individuals, which…
In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…
It is well-known that population structure is a catalyst for the evolution of cooperation since individuals can reciprocate with their neighbors through local interactions defined by network structures. Previous research typically relies on…
Understanding how cooperation can evolve in populations despite its cost to individual cooperators is an important challenge. Models of spatially structured populations with one individual per node of a graph have shown that cooperation,…