Aydogmus Ozgur
Department of Economics, Social Sciences University of Ankara, Ulus-Ankara, Turkey.
J Theor Biol. 2018 Apr 7;442:87-97. doi: 10.1016/j.jtbi.2018.01.016.
The classical idea of evolutionarily stable strategy (ESS) modeling animal behavior does not involve any spatial dependence. We considered a spatial Hawk-Dove game played by animals in a patchy environment with wrap around boundaries. We posit that each site contains the same number of individuals. An evolution equation for analyzing the stability of the ESS is found as the mean dynamics of the classical frequency dependent Moran process coupled via migration and nonlocal payoff calculation in 1D and 2D habitats. The linear stability analysis of the model is performed and conditions to observe spatial patterns are investigated. For the nearest neighbor interactions (including von Neumann and Moore neighborhoods in 2D) we concluded that it is possible to destabilize the ESS of the game and observe pattern formation when the dispersal rate is small enough. We numerically investigate the spatial patterns arising from the replicator equations coupled via nearest neighbor payoff calculation and dispersal.
进化稳定策略（ESS）建模动物行为的经典观点不涉及任何空间依赖性。我们考虑了动物在具有环绕边界的斑块环境中进行的空间鹰鸽博弈。我们假定每个位点包含相同数量的个体。通过在一维和二维栖息地中经由迁移和非局部收益计算耦合的经典频率依赖莫兰过程的平均动态，找到一个用于分析ESS稳定性的进化方程。对该模型进行了线性稳定性分析，并研究了观察空间模式的条件。对于最近邻相互作用（包括二维中的冯·诺依曼邻域和摩尔邻域），我们得出结论，当扩散率足够小时，有可能使博弈的ESS不稳定并观察到模式形成。我们通过数值研究了经由最近邻收益计算和扩散耦合的复制方程产生的空间模式。
