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.

生物学的一个核心问题是详细了解自然选择如何影响人群的演变。当人口中的一个人获得有益的突变时，该突变最终可能会扩散到大部分人口，甚至整个人群中。当人群一次可能存在许多不同的有益突变时，在数学上对这一现象的建模变得特别具有挑战性。该研究项目研究了反复获得有益突变的不断发展的人群的数学模型。因为在这些模型中，假定种群以随机的方式发展，所以概率理论在分析中起着核心作用。该研究旨在提供对重要生物学问题的数学见解。感兴趣的问题包括确定由于有益突变而增加人口适应性的速度，了解给定时间的个人适应性水平的分布，并了解如何描述人群中样本的家谱。为了模拟接受选择的人群，研究人员将考虑一个随机过程，称为分支布朗运动。每个粒子以给定的速率死亡，每个粒子根据一维的布朗运动独立移动，颗粒偶尔分为两个。在这里，粒子代表一个人群中的个体，沿实际线的粒子位置对应于个人的适应性。可以假定分支速率取决于粒子的位置，因此，适应性较高的个体具有更多的后代。据推测，在长期内，颗粒位置的经验分布大致是高斯。这一结果的证明将为生物学文献中建立良好的思想提供数学上严格的表述，即对于某些接受选择的人群，人口中个人的适应性水平的分布如高斯行动浪潮。由于分支布朗尼运动可用于模拟经历有益或有害突变的种群，因此这项工作还可以阐明一种称为Muller的棘轮的现象，这是指由于有害突变的积累而导致的人群适合度的降低。研究者还将考虑一些人口模型，这些模型纳入了重组的影响，以及一个嵌套的聚集模型，描述了从多种物种采样的个体集合的家谱。