Department of Mathematics, City, University of London, 10 Northampton Square, London, EC1V 0HB, UK.
Informatics and Knowledge Management Graduate Program, Universidade Nove de Julho, Rua Vergueiro, 235/249, São Paulo, SP, CEP: 01504-000, Brazil.
J Math Biol. 2024 Oct 6;89(5):49. doi: 10.1007/s00285-024-02148-y.
Evolutionary graph theory has considerably advanced the process of modelling the evolution of structured populations, which models the interactions between individuals as pairwise contests. In recent years, these classical evolution models have been extended to incorporate more realistic features, e.g. multiplayer games. A recent series of papers have developed a new evolutionary framework including structure, multiplayer interactions, evolutionary dynamics, and movement. However, so far, the developed models have mainly considered independent movement without coordinated behaviour. Although the theory underlying the framework has been developed and explored in various directions, several movement mechanisms have been produced which characterise coordinated movement, for example, herding. By embedding these newly constructed movement distributions, within the evolutionary setting of the framework, we demonstrate that certain levels of aggregation and dispersal benefit specific types of individuals. Moreover, by extending existing parameters within the framework, we are not only able to develop a general process of embedding any of the considered movement distributions into the evolutionary setting on complete graphs but also analytically produce the probability of fixation of a mutant on a complete N-sized network, for the multiplayer Public Goods and Hawk-Dove games. Also, by applying weak selection methods, we extended existing previous analyses on the pairwise Hawk-Dove Game to encompass the multiplayer version considered in this paper. By producing neutrality and equilibrium conditions, we show that hawks generally do worse in our models due to the multiplayer nature of the interactions.
进化图论极大地推动了结构化种群进化模型的构建过程，该模型将个体之间的相互作用建模为成对竞争。近年来，这些经典的进化模型已经扩展到纳入更现实的特征，例如多人游戏。最近的一系列论文提出了一个新的进化框架，包括结构、多人交互、进化动态和运动。然而，到目前为止，所开发的模型主要考虑了没有协调行为的独立运动。尽管该框架的基础理论已经在各个方向上得到了发展和探索，但已经产生了几种描述协调运动的运动机制，例如羊群行为。通过在框架的进化环境中嵌入这些新构建的运动分布，我们证明了某些聚集和分散水平有利于特定类型的个体。此外，通过扩展框架内的现有参数，我们不仅能够将任何考虑的运动分布嵌入到完整图的进化环境中，还可以分析性地产生在完整的 N 大小网络上突变体固定的概率，对于多人公共物品和鹰鸽博弈。同样，通过应用弱选择方法，我们扩展了之前关于成对鹰鸽博弈的分析，以包含本文所考虑的多人版本。通过产生中性和平衡条件，我们表明由于相互作用的多人性质，鹰派在我们的模型中通常表现不佳。
