Aydogmus Ozgur, Zhou Wen, Kang Yun
Department of Economics, Social Sciences University of Ankara, Ankara, Turkey.
Department of Statistics, Colorado State University, Fort Collins, CO 80523, USA.
Math Biosci. 2017 Mar;285:25-42. doi: 10.1016/j.mbs.2016.12.001. Epub 2016 Dec 13.
Nonlocal interactions such as spatial interaction are ubiquitous in nature and may alter the equilibrium in evolutionary dynamics. Models including nonlocal spatial interactions can provide a further understanding on the preservation and emergence of cooperation in evolutionary dynamics. In this paper, we consider a variety of two-strategy evolutionary spatial games with nonlocal interactions based on an integro-differential replicator equation. By defining the invasion speed and minimal traveling wave speed for the derived model, we study the effects of the payoffs, the selection pressure and the spatial parameter on the preservation of cooperation. One of our most interesting findings is that, for the Prisoners Dilemma games in which the defection is the only evolutionary stable strategy for unstructured populations, analyses on its asymptotic speed of propagation suggest that, in contrast with spatially homogeneous games, the cooperators can invade the habitat under proper conditions. Other two-strategy evolutionary spatial games are also explored. Both our theoretical and numerical studies show that the nonlocal spatial interaction favors diversity in strategies in a population and is able to preserve cooperation in a competing environment. A real data application in a virus mutation study echoes our theoretical observations. In addition, we compare the results of our model to the partial differential equation approach to demonstrate the importance of including non-local interaction component in evolutionary game models.
诸如空间相互作用之类的非局部相互作用在自然界中无处不在，并且可能改变进化动力学中的平衡。包含非局部空间相互作用的模型能够进一步加深我们对进化动力学中合作的维持与出现的理解。在本文中，我们基于积分 - 微分复制方程考虑了各种具有非局部相互作用的双策略进化空间博弈。通过为所推导的模型定义入侵速度和最小行波速度，我们研究了收益、选择压力和空间参数对合作维持的影响。我们最有趣的发现之一是，对于囚徒困境博弈，在无结构种群中背叛是唯一的进化稳定策略，但对其渐近传播速度的分析表明，与空间均匀博弈不同，在适当条件下合作者能够侵入栖息地。我们还探索了其他双策略进化空间博弈。我们的理论和数值研究均表明，非局部空间相互作用有利于种群中策略的多样性，并且能够在竞争环境中维持合作。病毒突变研究中的一个实际数据应用印证了我们的理论观察结果。此外，我们将模型结果与偏微分方程方法进行比较，以证明在进化博弈模型中纳入非局部相互作用成分的重要性。
