Mathematical population genetics and evolutionary games

该提案的最终目的是解释进化论。 考虑到生物种群惊人的多样性及其与环境的复杂相互作用，这不是一项容易的任务。 在小种群中研究长期进化更容易，因为可以合理地假设突变体会通过随机漂移一次一个地灭绝或固定。 然后，选择对注视概率的影响就变得至关重要。必须确定这种概率的近似值，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。 追溯随机样本历史的结合方法揭示了繁殖方案、重组过程和种群结构的影响。例如，基因重组的优势或合作的传播（如随机配对个体的重复囚徒困境所模拟的）是令人惊讶的启发，当稀有时，这在大种群中无法解释。希尔-罗伯逊效应在第一种情况下得到了更好的理解，诺瓦克及其同事提出的三分之一进化定律在第二种情况下得到了扩展。 群体结构种群的演化规则与个人之间的相互作用，不仅成对或涉及两个以上的战略，正在研究中的应用两个时标参数的合并过程或扩散近似。 最后，结合选择和重组，结合计算机算法和模拟的聚结方法是一个强大的工具来研究采样DNA序列中的遗传多样性，并推断遗传或种群参数的值。

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.