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Human social life is shaped by repeated interactions, where past experiences guide future behavior. In evolutionary game theory, a key challenge is to identify strategies that harness such memory to succeed in repeated encounters. Decades…
We study how the community structure of bipartite mutualistic networks changes in a dynamic context. First, we consider a real mutualistic network and introduce extinction events according to several scenarios. We model extinctions as node…
In a previous paper we proposed a model to study the dynamics of opinion formation in human societies by a co-evolution process involving two distinct time scales of fast transaction and slower network evolution dynamics. In the transaction…
Many life-history traits, like the age at maturity or adult longevity, are important determinants of the generation time. For instance, semelparous species whose adults reproduce once and die have shorter generation times than iteroparous…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
In a laboratory experiment, round by round, individual interactions should lead to the social evolutionary rotation in population strategy state space. Successive switching the incentive parameter should lead to successive change of the…
We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly…
A longitudinal social network evolves over time through the creation and/ or deletion of links among a set of actors (e.g. individuals or organizations). Longitudinal social networks are studied by network science and social science…
The processes leading to change in languages are manifold. In order to reduce ambiguity in the transmission of information, agreement on a set of conventions for recurring problems is favored. In addition to that, speakers tend to use…
Convergence of discrete-time Markov chains with two timescales is a powerful tool to study stochastic evolutionary games in subdivided populations. Focusing on linear games within demes, convergence to a diffusion process for the strategy…
We analyze a replicator-mutator model arising in the context of directed evolution [23], where the selection term is modulated over time by the mean-fitness. We combine a Cumulant Generating Function approach [13] and a spatio-temporal…
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the…
Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often…
We propose a simple model of network co-evolution in a game-dynamical system of interacting agents that play repeated games with their neighbors, and adapt their behaviors and network links based on the outcome of those games. The…
Simulation of population dynamics is a central research theme in computational biology, which contributes to understanding the interactions between predators and preys. Conventional mathematical tools of this theme, however, are incapable…
Linguistic norms emerge in human communities because people imitate each other. A shared linguistic system provides people with the benefits of shared knowledge and coordinated planning. Once norms are in place, why would they ever change?…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
Global change is reshaping ecosystems and societies. Strategic choices that were best yesterday may be sub-optimal tomorrow; and environmental conditions that were once taken for granted may soon cease to exist. In this setting, how people…
We investigate the evolutionary dynamics in directed and/or weighted networks. We study the fixation probability of a mutant in finite populations in stochastic voter-type dynamics for several update rules. The fixation probability is…