Mathematical genetics and evolution

这项研究是针对各种各样的人口遗传模型和随之而来的进化动力学和统计推断。长期目标是：a）描述和解释生物群体包括人类群体的变异程度; B）发展数学、统计和计算方法，分析遗传多态性，并对相关参数或假设作出推论; c）推断选择、突变和漂移产生的一般进化原则; d）将复杂结构和个体相互作用的影响纳入模型。在今后五年中，将更精确地致力于：（1）推导出在结构化群体中选择和漂变的综合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;（二）表明非随机交配在选择的存在下创造了个体之间隐藏的相互作用，但描述其影响所需的相关系数通常更高。（3）将时间尺度分离的论点扩展到集合种群的遗传多样性和连锁不平衡的研究中;（4）找到DNA序列样本构型的精确和近似公式，改进用于祖先推断和精细基因定位的合成似然方法。将综合使用数学、统计和计算工具：确定性选择模式的线性或二次局部稳定性分析;有限群体的扩散近似或合并方法;抽样公式的组合学;结构化群体的时标分离;遗传参数估计的模拟和算法。我希望这项研究将有助于更好地理解自然群体中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.