Mathematical population genetics and evolutionary games

该提案的最终目标是解释进化论。考虑到生物种群的惊人多样性及其与环境的复杂相互作用，这并不是一项容易的任务。在小种群中可以更容易地研究长期进化，对于小种群来说，可以合理地假设突变将以随机漂移的方式一次一个地灭绝或固定。那么，选择对注视概率的影响就变得至关重要了。必须确定这一概率的近似值，并推导和解释有利于一种类型取代另一种类型的选择条件。 在时间上追溯随机样本历史的合并方法揭示了繁殖方案、重组过程和种群结构的影响。例如，随机配对个体的重复囚徒困境所模拟的基因重组的优势或合作的传播，在稀有情况下无法在大种群中得到解释，令人惊讶地开明。希尔-罗伯逊效应在第一种情况下得到了更好的理解，诺瓦克和他的同事们在第二种情况下推广了三分之一的进化定律。 通过将两个时间尺度的论点应用于合并过程或扩散近似，正在研究具有个体之间相互作用的群体结构种群的进化规则，不仅是成对的或涉及两个以上的策略。 最后，融合了选择和重组的方法，结合计算机算法和模拟，是研究样本DNA序列中的遗传多样性和推断遗传或群体参数值的有力工具。

The ultimate goal of the proposal is to explain evolution. This is not an easy task considering the stunning diversity in biological populations and their complex interactions with the environment. Long-term evolution can be more easily studied in small populations for which it is reasonable to assume that mutants are going to extinction or fixation by random drift one at a time. Then, the effect of selection on the probability of fixation becomes of prime importance. Approximations for this probability have to be ascertained and conditions for selection to favor one type replacing another deduced and interpreted. The coalescent approach for tracing backwards in time the history of random samples reveals the effects of the reproduction scheme, the recombination process and the population structure. The advantage of genetic recombination or the spread of cooperation as modeled by the repeated prisoner's dilemma for randomly paired individuals, for instance, which could not be explained in large populations when rare, are surprisingly enlightened. The Hill-Robertson effect is better understood in the first case, the one-third law of evolution due to Nowak and co-workers extended in the second. The rules of evolution in group-structured populations with interactions among individuals, not only pairwise or involving more than two strategies, are under study by applying two-timescale arguments to coalescence processes or diffusion approximations. Finally, with the incorporation of selection and recombination, the coalescent approach combined to computer algorithms and simulations is a powerful tool to study the genetic diversity in sampled DNA sequences and to infer values of genetic or population parameters.