Dynamics of Strategy Distribution in a One-Dimensional Continuous Trait Space with a Bi-linear and Quadratic Payoff Functions

Unfair and Anomalous Evolutionary Dynamics from Fluctuating Payoffs

Evolution occurs in populations of reproducing individuals. Reproduction depends on the payoff a strategy receives. The payoff depends on the environment that may change over time, on intrinsic uncertainties, and on other sources of randomness. These temporal variations in the payoffs can affect which traits evolve. Understanding evolutionary game dynamics that are affected by varying payoffs remains difficult. Here we study the impact of arbitrary amplitudes and covariances of temporally varying payoffs on the dynamics. The evolutionary dynamics may be "unfair", meaning that, on average, two …

二次适应度景观下连续时间与空间复制-突变方程的数学描述

Mathematical description of continuous time and space replicator-mutator equations for quadratic fitness landscapes

该研究推导了二次适应度景观下连续时间与空间复制-突变方程的解析解，无需数值模拟即可解释并量化多种进化现象，为种群进化动力学研究提供了理论工具。

Evolutionary Dynamics of Group Formation

We introduce a model, based on the Evolutionary Game Theory, for studying the dynamics of group formation. The latter constitutes a relevant phenomenon observed in different animal species, whose individuals tend to cluster together forming groups of different size. Results of previous investigations suggest that this phenomenon might have similar reasons across different species, such as improving the individual safety (e.g. from predators), and increasing the probability to get food resources. Remarkably, the group size might strongly vary from species to species, and sometimes even within t…

Single Equalizer Strategy with no Information Transfer for Conflict Escalation

In an iterated two-person game, for instance prisoner's dilemma or the snowdrift game, there exist strategies that force the payoffs of the opponents to be equal. These equalizer strategies form a subset of the more general zero-determinant strategies that unilaterally set the payoff of an opponent. A challenge in the attempts to understand the role of these strategies in the evolution of animal behavior is the lack of iterations in the fights for mating opportunities or territory control. We show that an arbitrary two-parameter strategy may possess a corresponding equalizer strategy which pro…

Imitate or innovate: competition of strategy updating attitudes in spatial social dilemma games

Evolution is based on the assumption that competing players update their strategies to increase their individual payoffs. However, while the applied updating method can be different, most of previous works proposed uniform models where players use identical way to revise their strategies. In this work we explore how imitation-based or learning attitude and innovation-based or myopic best response attitude compete for space in a complex model where both attitudes are available. In the absence of additional cost the best response trait practically dominates the whole snow-drift game parameter sp…

The σlaw of evolutionary dynamics in community-structured populations

Evolutionary game dynamics in finite populations provides a new framework to understand the selection of traits with frequency-dependent fitness. Recently, a simple but fundamental law of evolutionary dynamics, which we call σ law, describes how to determine the selection between two competing strategies: in most evolutionary processes with two strategies, A and B, strategy A is favored over B in weak selection if and only if σR + S > T + σP. This relationship holds for a wide variety of structured populations with mutation rate and weak selection under certain assumptions. In this paper, we p…