Mathematical genetics and evolution

数学遗传学和进化论

• 批准号: 8833-2006
• 负责人: Lessard, Sabin
• 金额: $ 2.11万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=389844
• 关键词: Mathematical; genetics; evolution

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.

这项研究针对各种群体遗传模型以及随之而来的进化动力学和统计推论。长期目标是： a) 描述和解释包括人类在内的生物种群的变异水平； b) 开发数学、统计和计算方法来分析遗传多态性并对相关参数或假设做出推断； c) 推导出由选择、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中。未来五年，我们将更加精准地致力于：（1）在结构群体中选择和漂移的综合作用下，推导一个等位基因被另一种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）表明非随机交配在存在选择的情况下在个体之间产生了隐藏的相互作用，但描述其影响所需的相关性系数通常比通常想象的更复杂； (3) 将时间尺度分离论证扩展到集合群体遗传多样性和连锁不平衡的研究中； (4) 寻​​找DNA序列样本配置的精确和近似公式，并改进用于祖先推断和精细基因定位的复合似然方法。将使用数学、统计和计算工具的组合：用于确定性选择模型的线性或二次局部稳定性分析；有限总体的扩散近似或合并方法；抽样公式的组合学；结构化人群的时间尺度分离；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进化过程中遗传机制的影响，以及导致遗传多态性和最终人类疾病的多种因素。