Coalescent processes and population models

聚结过程和群体模型

• 批准号: 0504882
• 负责人: Jason Schweinsberg
• 金额: $ 9.96万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0504882&HistoricalAwards=false
• 关键词: Coalescent; processes; population; models

The PI studies several problems related to coalescentprocesses and population models. Coalescent processesare stochastic processes that model a system of particleswhich start out separated and merge into clusters as timegoes forward. These processes can be used to describethe genealogy of a population because if one takes asample from a population and follows the ancestral linesbackwards in time, the ancestral lines will coalesce.When a beneficial mutation occurs in a population andspreads rapidly, many ancestral lines will merge atalmost the same time, as they will all be traced back tothe individual that had the beneficial mutation. Onegoal is to use results from the theory of coalescentprocesses with multiple mergers to get further insightinto tests that are used to detect beneficial mutations.A second project is to determine the distribution of thetime that it takes for one individual in a population toexperience k mutations. The PI will also study a modelof coalescence in which the total mass of the systemincreases over time. A coalescent model in which newparticles appear at rate one and clusters merge at a rateproportional to the product of the masses has previouslybeen studied, but a qualitatively different phasetransition is conjectured to arise in an alternativemodel in which clusters merge at a rate proportional tothe sum of the masses.Stochastic models of coalescence have a wide range ofapplications in other fields of science such as biology,physical chemistry, and astronomy. Biologists interestedin understanding evolution are concerned with the mergingof the ancestral lines of a sample from a population. Itshould be possible to use the mathematical theory ofcoalescence to gain further insight into how beneficialmutations impact this process. The project of determiningthe amount of time for one individual in a population toexperience several mutations is motivated by simple modelsof cancer, in which it is assumed that a cell becomescancerous only after several harmful mutations take place.The study of coalescent processes in which the mass of thesystem increases over time is motivated by recent interestin randomly growing networks.

PI研究了与聚结过程和种群模型有关的几个问题。 聚结过程是一种随机过程，它模拟了一个粒子系统，这些粒子开始分离，随着时间的推移合并成簇。 这些过程可以用来描述一个种群的系谱，因为如果从一个种群中提取样本并沿着祖先线追溯过去，那么祖先线就会合并。当一个有益的突变在种群中发生并迅速传播时，许多祖先线几乎会同时合并，因为它们都可以追溯到发生有益突变的那个个体。 一个目标是利用多重合并的合并过程理论的结果，进一步深入了解用于检测有益突变的测试。第二个项目是确定群体中一个个体经历k个突变所需的时间分布。 PI还将研究一种聚结模型，其中系统的总质量随着时间的推移而增加。 一个新粒子以1的速率出现，而团簇以与质量乘积成正比的速率合并的聚结模型以前曾被研究过，但在另一个团簇以与质量之和成正比的速率合并的替代模型中，一个质上不同的相变被证明会出现。聚结的随机模型在其他科学领域，如生物学、物理化学、和天文学。 对理解进化感兴趣的生物学家关注的是从种群中抽取样本的祖先谱系的融合。 它应该有可能使用数学理论的聚结，以获得进一步的洞察力，以了解如何突变影响这一进程。 确定群体中一个个体经历几次突变所需时间的项目是由简单的癌症模型激发的，在该模型中，假设细胞只有在发生几次有害突变后才发生癌变。对细胞质量随时间增加的结合过程的研究是由最近对随机增长网络的兴趣激发的。