Modeling evolution of quantitative traits with finite locus effects in structured populations

数量遗传学的最新进展表明，位点效应对数量性状具有一定的分布规律，其中一些位点（以下称为qtl）对基因型性状变异的解释占很大比例，而另一些位点对表型的影响较小，但可以检测到。为了将QTL结果纳入现有理论，一个关键的任务是建立数量性状变异模型，该模型允许有限数量的位点具有有限的效应。本项目对这些模型进行了开发和分析。我们的理论工作集中在扩散模型上，即时间和等位基因频率都是连续的模型。将开发的模型与先前导出的模型、模拟结果和实验数据进行比较，目的是确定对预测自然和农业种群数量性状进化有用的模型。分析和模拟的结果用于建立种群中选择对数量性状的作用的统计检验。数量特征是生物体最显著的特征之一，是我们一眼就能认出的特征。这样的例子比比皆是，包括人类的身高、一株玉米上的穗数或一窝小猪的重量。数量性状及其遗传基础的研究是我们理解进化生物学以及应用遗传学（如动植物育种）的基础。利用最近开发的技术，现在有可能确定基因组中与数量性状有关的区域。这种“QTL定位”研究揭示了数据与旨在解释个体基因对这些性状的贡献的经典理论之间的差异。本项目旨在扩展我们对数量性状的理论认识，并利用所开发的理论创建实用的统计方法来分析数量性状数据。这项资助是在DMS/NIGMS联合倡议下提供的，以支持数学生物学领域的研究资助。这是一个由美国国家科学基金会数学科学部（DMS）和美国国立卫生研究院国家综合医学科学研究所（NIGMS）联合主办的竞赛。

Recent advances in quantitative genetics show that there is a distribution of locus effects on quantitative traits, with some loci (henceforth called QTLs) explaining a large proportion of the genotypic trait variance and others having minor but detectable effects on phenotype. For QTL results to be incorporated into existing theory, a crucial task is to develop models of quantitative trait variation that allow for a finite number of loci with finite effects. In this project, such models are developed and analyzed. Our theoretical work focuses on diffusion models, i.e. models in which both time and allele frequencies are continuous. The models developed are compared with previously-derived models, with the results of simulations, and with experimental data, with the aim of identifying models useful for predicting quantitative trait evolution in natural and agricultural populations. The results of the analysis and simulations are used to create statistical tests for the action of selection on quantitative traits in populations. Quantitative traits are among the most conspicuous features of organisms, features that we immediately recognize. Examples abound, including the height of humans, the number of ears on a corn plant or the weight of piglets in a litter. The study of quantitative traits and their genetic basis is fundamental to our understanding of evolutionary biology as well as to applied genetics such as animal and plant breeding. Using recently developed technology, it is now possible to identify regions of the genome that contribute to quantitative traits. Such "QTL mapping" studies have revealed discrepancies between the data and classical theories intended to explain the contribution of individual genes to such traits. This project aims to extend our theoretical understanding of quantitative traits, and to use the theory developed to create practical statistical methods for analyzing quantitative trait data. This grant is made under the Joint DMS/NIGMS Initiative to Support Research Grants in the Area of Mathematical Biology. This is a joint competition sponsored by the Division of Mathematical Sciences (DMS) at the National Science Foundation and the National Institute of General Medical Sciences (NIGMS) at the National Institutes of Health.