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Probabilistic Models of Evolving Populations

人口演变的概率模型

基本信息

批准号：
1707953
负责人：
Jason Schweinsberg
金额：
$ 24.13万
依托单位：
University of California-San Diego
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-07-01 至 2021-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1707953&HistoricalAwards=false
关键词：
Probabilistic Models Evolving Populations

项目摘要

A central question in biology is to understand in detail how natural selection affects the evolution of a population. When one individual in a population acquires a beneficial mutation, that mutation may eventually spread to a large fraction of the population, or even the entire population. Modeling this phenomenon mathematically becomes particularly challenging when there can be many different beneficial mutations in the population at a time. This research project studies mathematical models of evolving populations that repeatedly acquire beneficial mutations. Because, in these models, populations are assumed to evolve in a random way, the theory of probability plays a central role in the analysis. The research aims to provide mathematical insight into important biological problems. Questions of interest include determining the rate at which the fitness of the population increases as a result of beneficial mutations, understanding the distribution of the fitness levels of individuals in the population at a given time, and understanding how to describe the genealogy of a sample from the population. To model populations undergoing selection, the investigator will consider a stochastic process called branching Brownian motion. Each particle dies at a given rate, each particle moves independently according to one-dimensional Brownian motion, and particles occasionally split into two. Here particles represent individuals in a population, and the position of the particle along the real line corresponds to the individual's fitness. It will be assumed that the branching rate depends on the position of the particle, so that individuals with higher fitness have more offspring. It is conjectured that in the long-run, the empirical distribution of the positions of the particles is approximately Gaussian. A proof of this result would provide a mathematically rigorous formulation of the idea, well-established in the biology literature, that for certain populations undergoing selection, the distribution of the fitness levels of individuals in the population evolves like a Gaussian traveling wave. Because branching Brownian motion can be used to model populations experiencing either beneficial or deleterious mutations, this work could also shed light on a phenomenon known as Muller's ratchet, which refers to the decrease in the fitness of a population resulting from the accumulation of deleterious mutations. The investigator will also consider some population models that incorporate the effects of recombination, as well as a nested coalescent model that describes the genealogy of a collection of individuals sampled from multiple species.

生物学中的一个中心问题是详细了解自然选择如何影响种群的进化。当一个种群中的一个个体获得了有益的突变时，该突变最终可能会扩散到该种群的一大部分，甚至整个种群。当人群中同时存在许多不同的有益突变时，对这种现象进行数学建模就变得特别具有挑战性。这项研究项目研究不断进化的种群的数学模型，这些种群反复获得有益的突变。因为在这些模型中，假设种群以随机方式进化，所以概率理论在分析中起着核心作用。这项研究旨在为重要的生物学问题提供数学见解。感兴趣的问题包括确定由于有益的突变而导致群体的适应度增加的速度，了解在给定时间群体中个体的适应度水平的分布，以及了解如何描述来自群体的样本的谱系。为了对正在进行选择的种群建模，研究人员将考虑一种称为分枝布朗运动的随机过程。每个粒子以给定的速度死亡，每个粒子按照一维布朗运动独立运动，粒子偶尔分裂成两个。在这里，粒子表示群体中的个体，粒子沿实线的位置对应于个体的适应度。它将假设分枝率取决于粒子的位置，因此适应度较高的个体有更多的后代。推测从长期来看，粒子位置的经验分布近似为正态分布。这一结果的证明将为这一观点提供一个数学上的严谨表述，这一观点在生物学文献中得到了很好的确立，即对于正在进行选择的某些种群，种群中个体的适应度水平的分布就像高斯行波一样演变。由于分枝布朗运动可以用来为经历有益或有害突变的种群建模，这项工作也可以解释一种被称为穆勒棘轮的现象，它指的是有害突变的积累导致种群适应度的下降。研究人员还将考虑一些包含重组影响的种群模型，以及描述从多个物种采样的一组个体的系谱的嵌套合并模型。