Learning Dynamics and the Co-Evolution of Competing Sexual Species
Learning Dynamics and the Co-Evolution of Competing Sexual Species
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学习动态和有性竞争物种的共同进化
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
L. Schulman
中科院分区：
文献类型：
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作者：
G. Piliouras;L. Schulman
我们分析了任何两个纯粹相互竞争的物种(例如，宿主和寄生虫)之间的共同进化的风格化模型，两者都进行了有性繁殖。与最近Livnat等人的模型相似，个体的适合度取决于通过重组产生的$n$变量上的真值分配是否满足特定的布尔函数。在原始模型中，令人满意的分配总是会带来微小的进化优势，而在我们的模型中，两个物种处于进化竞赛中，如果寄生虫的布尔函数值与其宿主匹配，则寄生虫享受优势，而宿主希望与其寄生虫不匹配。令人惊讶的是，这个模型做出了一个简单而稳健的行为预测。典型的系统行为是EXIT{PERIONAL}。这些周期远离边界，因此，有性物种之间的学习动力竞争可以为遗传多样性提供解释。这种解释完全是由于自然选择过程。不需要调用任何突变、环境变化等。
在基因水平上进行的博弈可能有许多纳什均衡，其适应度水平差异很大。然而，有性进化导致基因协调，从而在物种水平上实施最佳策略，即最佳种群混合。也就是说，许多“自私基因”的作用实现了一种时间平均相关均衡，其中每个物种的平均适应度恰好等于两个物种零和竞争中的值。
我们的分析结合了博弈论、动力系统和布尔函数的工具，建立了一类新的保守动力系统。
We analyze a stylized model of co-evolution between any two purely competing species (e.g., host and parasite), both sexually reproducing. Similarly to a recent model of Livnat etal~cite{evolfocs14} the fitness of an individual depends on whether the truth assignments on $n$ variables that reproduce through recombination satisfy a particular Boolean function. Whereas in the original model a satisfying assignment always confers a small evolutionary advantage, in our model the two species are in an evolutionary race with the parasite enjoying the advantage if the value of its Boolean function matches its host, and the host wishing to mismatch its parasite. Surprisingly, this model makes a simple and robust behavioral prediction. The typical system behavior is extit{periodic}. These cycles stay bounded away from the boundary and thus, extit{learning-dynamics competition between sexual species can provide an explanation for genetic diversity.} This explanation is due solely to the natural selection process. No mutations, environmental changes, etc., need be invoked.
The game played at the gene level may have many Nash equilibria with widely diverse fitness levels. Nevertheless, sexual evolution leads to gene coordination that implements an optimal strategy, i.e., an optimal population mixture, at the species level. Namely, the play of the many "selfish genes" implements a time-averaged correlated equilibrium where the average fitness of each species is exactly equal to its value in the two species zero-sum competition.
Our analysis combines tools from game theory, dynamical systems and Boolean functions to establish a novel class of conservative dynamical systems.