Department of Mathematics and Statistics, University of Guelph, 50 Stone Road East, Room 437 MacNaughton Building, Guelph, Ontario N1G 2W1, Canada; Department of Physics, University of Notre Dame, Nieuwland Science Hall, Notre Dame, IN 46556, USA; Department of Biology, University of Pennsylvania, Carolyn Lynch Laboratory, Philadelphia, PA 19104, USA.
Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada.
J Theor Biol. 2019 Apr 7;466:64-83. doi: 10.1016/j.jtbi.2019.01.023. Epub 2019 Jan 24.
Natural Selection is frequently modelled via proportional selection where survival is proportional to the average payoff differential. There has been little attention devoted to modelling truncation selection where replicators below a threshold are culled and survivors reproduce. Here, we systematically explore truncation selection for two strategy games in a spatial setting. We employ two variations of truncation selection: independent, where the threshold is fixed; and dependent, where the proportion culled is fixed. Further, we explore the effects of diffusion with the algorithms: contest-diffusion-offspring (CDO), and diffusion-contest-offspring (DCO). CDO and DCO frequently facilitate and diminish cooperation, respectively. For independent truncation, there are three qualitative regimes determined by the payoff threshold: cooperation decreases as the threshold rises; polymorphisms are stable; and extinction is frequent. Further, an intermediate payoff to cooperators playing defectors can maximize cooperation for the DCO algorithm with a high payoff threshold. Dependent truncation affects games differently; lower levels reduce cooperation for the Hawk Dove game and increase it for the Stag Hunt, and higher levels produce the opposite effects. Comparing these truncation methods to proportional selection, we show how they impact the prevalence of cooperation.
自然选择经常通过比例选择来建模，其中生存概率与平均收益差异成正比。很少有人关注截断选择的建模，在这种选择中，低于阈值的复制者被淘汰，幸存者进行繁殖。在这里，我们系统地探索了两种策略游戏在空间环境下的截断选择。我们采用了两种截断选择的变体：独立的，其中阈值是固定的；和依赖的，其中被淘汰的比例是固定的。此外，我们还探索了算法中的扩散效应：竞争-扩散-后代（CDO）和扩散-竞争-后代（DCO）。CDO 和 DCO 通常分别促进和减少合作。对于独立的截断，有三个由收益阈值决定的定性状态：随着阈值的升高，合作减少；多态性稳定；灭绝频繁。此外，对于具有高收益阈值的 DCO 算法，对采用背叛策略的合作者给予中等收益可以最大化合作。依赖的截断对游戏的影响不同；对于鹰鸽博弈，较低的水平会降低合作，而对于猎鹿博弈，较高的水平会增加合作，反之亦然。将这些截断方法与比例选择进行比较，我们展示了它们如何影响合作的普遍性。
