Mathematical population genetics and evolutionary games

该提案的最终目标是解释进化论。 考虑到生物种群惊人的多样性及其与环境的复杂相互作用，这并不是一件容易的事。 在小种群中可以更容易地研究长期进化，因此可以合理地假设突变体将通过随机漂移一次灭绝或固定。 那么，选择对固定概率的影响就变得至关重要。必须确定该概率的近似值，并推断和解释选择一种类型替代另一种类型的条件。 用于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，以随机配对个体的重复囚徒困境为模型的基因重组或合作传播的优势，在稀有情况下无法在大群体中得到解释，但却令人惊讶地受到启发。在第一种情况下，希尔-罗伯逊效应得到了更好的理解，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。 通过将两个时间尺度的参数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种以上的策略。 最后，通过结合选择和重组，与计算机算法和模拟相结合的合并方法成为研究采样 DNA 序列中的遗传多样性并推断遗传或群体参数值的强大工具。

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.