MODELS OF COMPLEX GENETIC SYSTEMS

这项研究计划的总体目标是发展和 数学和统计方法的应用 应用于人类和非人类群体的遗传数据 其意图是了解过去和现在的力量 确定它们的基因组成。数据的类型将是 考虑来自不同个体的DNA序列或 可区分的遗传变异，如微卫星座位上的等位基因， 一类相对较新且极其有用的遗传标记。这 提案将重点关注四类相互关联的问题：(L) 微卫星座位的突变过程，(2)个体的历史 等位基因，包括致病等位基因；(3)变异程度 在单个基因座的致病等位基因中，(4) 紧密连锁等位基因间的非随机关联度 遗传基因。微卫星基因座具有相当大的实用价值。 因为它们在人类体内极其丰富且高度多变 和其他哺乳动物。因此，它们被广泛应用于基因工程 测绘和分析种群结构。然而，它们的使用 出于这些目的，依赖于关于 突变的过程。还需要进一步的理论工作才能 种群水平的变化可以用来检验关于 突变过程。这项提案的几个部分解决了这个问题 紧密关联的非随机关联或链接不平衡 相关基因，包括与疾病密切相关的基因- 造成了基因定位。连锁不平衡的程度取决于 对各种因素的复杂方式，包括突变、自然 选择，种群间的迁徙，以及 人口规模。需要数学模型来预测 不同条件下的连锁不平衡程度。是这样的 由于联动的广泛使用，现在需要模型 定位人类致病基因的不平衡 人口。拟议的研究将使用一种 分析理论的结合，特别是马尔科夫理论 过程和计算机模拟。许多结果将会在 具有期望的数学似然函数的术语 用于估计参数和检验假设的性质。

The overall goal of this research program is the development and application of mathematical and statistical methods that can be applied to genetic data from human and non-human populations with the intention of understanding the past and present forces that determine their genetic composition. The kinds of data that will be considered are DNA sequences from different individuals or distinguishable genetic variants such as alleles at microsatellite loci, a relatively new and extremely useful class of genetic markers. This proposal will focus on four interrelated classes of problems: (l) the mutation process at microsatellite loci, (2) the history of individual alleles, including disease-causing alleles, (3) the extent of variation among disease-causing alleles at a single genetic locus, (4) the degree of non-random association among alleles at closely linked genetic loci. Microsatellite loci are of considerable practical interest because they are extremely abundant and highly variable in humans and other mammals. As a result, they are widely used in genetic mapping and in the analysis of population structure. Yet their use for these purposes depends on untested assumptions about the process of mutation. Further theoretical work is needed before population-level variation can be used to test hypotheses about the mutation process. Several parts of this proposal address the problem of the nonrandom association, or linkage disequilibrium, of closely linked genes, including genes that are closely linked to disease- causing loci. The extent of linkage disequilibrium depends in a complex way on various factors, including mutation, natural selection, migration among populations, and the history of population sizes. Mathematical models are needed that predict the extent of linkage disequilibrium under different conditions. Such models are needed now because of the widespread use of linkage disequilibrium for mapping disease-causing genes in human populations. The proposed research will be carried out using a combination of analytic theory, particularly the theory for Markov processes, and computer simulations. Many of the results will be in terms of mathematical likelihood functions that have desirable properties for estimating parameters and for testing hypotheses.