Mathematical genetics and evolution

这项研究是针对各种各样的群体遗传模型和伴随的进化动力学和统计推断。长期目标是：a)描述和解释生物种群（包括人类种群）的变异水平；B)发展数学、统计和计算方法来分析遗传多态性并对有关参数或假设作出推论；C)推断出由选择、突变和漂变产生的一般进化原理；d)将复杂结构和个体相互作用的影响纳入模型。在接下来的五年里，我们的工作将更精确地指向：(1)推导出在结构种群中选择和漂变的共同作用下，一个等位基因被另一个等位基因取代的确切条件，并将这些条件应用于个体行为或遗传参数的进化；(2)表明在存在选择的情况下，非随机交配在个体之间创造了隐藏的相互作用，但描述其影响所需的亲缘系数通常比通常认为的要复杂；(3)将时间尺度分离理论扩展到元种群遗传多样性和连锁不平衡的研究中；(4)寻找DNA序列样本结构的精确近似公式，改进祖先推断和精细基因定位的复合似然方法。将结合使用数学、统计和计算工具：局部稳定性分析，线性或二次，用于确定性选择模型；有限种群的扩散近似或聚结法；抽样公式的组合学；结构化种群的时间尺度分离；遗传参数估计的模拟和算法。我期望这项研究将有助于更好地理解自然种群中潜在进化过程的遗传机制的影响，以及导致遗传多态性和最终导致人类疾病的多种因素。

This research is directed towards a wide variety of population genetic models and the concomitant evolutionary dynamics and statistical inferences. The long-term objectives are: a) to describe and explain the level of variability in biological populations including human populations; b) to develop mathematical, statistical and computational methods to analyse genetic polymorphisms and make inferences about related parameters or assumptions; c) to deduce general evolutionary principles that result from selection, mutation and drift; and d) to incorporate the effects of complex structures and individual interactions into the models. In the next five years, the efforts will be directed more precisely towards: (1) deducing exact conditions for the replacement of one allele by another under the combined effects of selection and drift in structured populations and applying these conditions to the evolution of individual behaviours or genetic parameters; (2) showing that non random mating creates hidden interactions between individuals in the presence of selection but the coefficients of relatedness necessary to describe their effects are generally more complicated than usually thought; (3) extending separation-of-timescales arguments to the study of genetic diversity and linkage disequilibrium in metapopulations; (4) finding exact and approximate formulas for the sample configurations of DNA sequences and improving composite-likelihood methods for ancestral inference and fine gene mapping. A combination of mathematical, statistical and computational tools will be used: local stability analyses, linear or quadratic, for deterministic selection models; diffusion approximations or coalescent approaches for finite populations; combinatorics for sampling formulas; separation of timescales for structured populations; simulations and algorithms for the estimation of genetic parameters. I expect that this research will contribute to a better understanding of the effects of genetic mechanisms underlying evolutionary processes in natural populations and the multiple factors responsible for genetic polymorphisms and, eventually, human diseases.