Hauert Christoph, Szabó György
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, CanadaV6T 1Z2.
Department of Zoology, University of British Columbia, 6270 University Boulevard, Vancouver, BC, CanadaV6T 1Z4.
PNAS Nexus. 2024 Aug 9;3(9):pgae326. doi: 10.1093/pnasnexus/pgae326. eCollection 2024 Sep.
In mutualistic associations, two species cooperate by exchanging goods or services with members of another species for their mutual benefit. At the same time, competition for reproduction primarily continues with members of their own species. In -species interactions, the prisoner's dilemma is the leading mathematical metaphor to study the evolution of cooperation. Here we consider -species interactions in the spatial prisoner's dilemma, where members of each species reside on one lattice layer. Cooperators provide benefits to neighbouring members of the other species at a cost to themselves. Hence, interactions occur across layers but competition remains within layers. We show that rich and complex dynamics unfold when varying the cost-to-benefit ratio of cooperation, . Four distinct dynamical domains emerge that are separated by critical phase transitions, each characterized by diverging fluctuations in the frequency of cooperation: for large cooperation is too costly and defection dominates; for lower cooperators survive at equal frequencies in both species; lowering further results in an intriguing, spontaneous symmetry breaking of cooperation between species with increasing asymmetry for decreasing ; finally, for small , bursts of mutual defection appear that increase in size with decreasing and eventually drive the populations into absorbing states. Typically, one species is cooperating and the other defecting and hence establish perfect asymmetry. Intriguingly and despite the symmetrical model set-up, natural selection can nevertheless favour the spontaneous emergence of asymmetric evolutionary outcomes where, on average, one species exploits the other in a dynamical equilibrium.
在互利共生关系中，两个物种通过与另一物种的成员交换货物或服务来进行合作，以实现互利共赢。与此同时，繁殖竞争主要仍在其自身物种的成员之间展开。在种内相互作用中，囚徒困境是研究合作进化的主要数学隐喻。在此，我们考虑空间囚徒困境中的种间相互作用，其中每个物种的成员位于一个晶格层上。合作者以自身为代价向另一物种的相邻成员提供益处。因此，相互作用发生在层间，但竞争仍在层内。我们表明，当改变合作的成本效益比c时，会展现出丰富而复杂的动态变化。出现了四个不同的动态区域，它们由临界相变分隔开，每个区域的特征是合作频率的波动发散：对于较大的c，合作成本过高，背叛占主导；对于较低的c，合作者在两个物种中以相等的频率存活；进一步降低c会导致一种有趣的、自发的种间合作对称性破缺，随着c的减小，不对称性增加；最后，对于较小的c，会出现相互背叛的爆发，其规模随着c的减小而增大，最终使种群进入吸收态。通常，一个物种合作而另一个物种背叛，从而建立起完美的不对称性。有趣的是，尽管模型设置是对称的，但自然选择仍可能有利于不对称进化结果的自发出现，即在动态平衡中，平均而言一个物种会利用另一个物种。
