Probability and Statistics Problems Concerning DNA Sequence and Genome Evolution

该基金支持的研究将侧重于基因组重排的数学和统计分析，以及自然选择和空间种群结构在塑造基因组多样性方面的相互作用。将开发统计方法来研究由于大规模过程导致的DNA序列的进化：染色体内的倒位，染色体之间的相互易位，移动基因的易位，染色体分裂和融合以及整个基因组的复制。主要目标是获得与不确定性相关测量的事件数量的统计估计，测试假设，例如，谱系之间的突变率的恒定性，并比较拟南芥，玉米和其他生物体中各种基因组复制场景的可能性。还将开发数学结果和统计技术，以区分观察到的基因组间DNA序列变异水平和模式的原因，集中于有利突变的固定（“选择性扫描”）和空间种群结构的影响。统计工作将包括为来自大基因组区域的数据开发复合似然方法，对于这些区域，完全似然或贝叶斯方法不容易处理。这项资助支持的研究将集中在生物体内和生物体之间基因组变异的定量研究。考虑两个尺度。第一个是基因组的进化，这是由于染色体上基因顺序的重新排列或它们之间遗传物质的交换而产生的大规模过程。了解这些变化的速度和规模对于改进物种之间的比较地图非常重要。这些图谱在医学和农业上都很重要，例如，这些图谱可以识别人类基因在小鼠中的同源物，或者给出牛羊基因的相对顺序。第二个尺度是在物种内观察到的DNA变异水平。数学和统计研究将侧重于区分适应（自然选择）和空间（地理）人口结构对人类和其他生物体DNA序列数据中观察到的模式的影响。这些结果将为生物体如何在遗传上应对新的环境和挑战（包括病原体和环境压力）提供见解，并有助于确定那些在适应中重要的基因。这些方法对于理解在人类和大多数其他生物体中检测到的巨大基因组多样性非常重要。拟议活动的一个重要组成部分是培训生物学和数学之间的研究人员。这项赠款是根据联合DMS/NIGMS倡议，以支持研究赠款在数学生物学领域。这是一项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普通医学科学研究所（NIGMS）赞助的联合竞赛。

Research supported by this grant will focus on mathematical and statistical analyses of genome rearrangements and the interaction of natural selection and spatial population structure in shaping genome diversity. Statistical methods will be developed to study the evolution of DNA sequences due to large scale processes: inversions within chromosomes, reciprocal translocations between chromosomes, transpositions that move genes, chromosome fissions and fusions, and duplication of whole genomes. Major goals are to obtain statistical estimates of the number of events with associated measurements of uncertainty, test hypotheses concerning for example, constancy of mutation rates among lineages, and to compare the likelihood of various genome duplication scenarios in Arabidopsis thaliana, maize, and other organisms. Mathematical results and statistical techniques will also be developed to distinguish the causes of observed levels and patterns of DNA sequence variation across genomes, concentrating on the effects of the fixation of advantageous mutations ("selective sweeps") and of spatial population structure. Statistical work will include the development of composite likelihood methods for data from large genomic regions for which full likelihood or Bayesian methods are not tractable. Research supported by this grant will focus on quantitative studies of variation in genomes within and between organisms. Two scales are considered. The first is the evolution of genomes due to large-scale processes which rearrange gene order on chromosomes or exchange genetic material between them. An understanding of the rates and sizes of these changes will be important for improving comparative maps between species. These maps which, for example, identify the mouse homologues of human genes or give the relative order of genes in cattle and sheep are important in medicine and agriculture. A second scale is the level of DNA variation observed within species. Mathematical and statistical studies will focus on distinguishing the effects of adaptation (natural selection) and spatial (geographical) population structure on shaping patterns observed in DNA sequence data from humans and other organisms. These results will provide insights into how organisms respond genetically to novel environments and challenges (including pathogens and environmental stress), and can help identify those genes important in that adaptation. These approaches will be important for understanding the enormous genome diversity detected in humans and most other organisms. An important component of the proposed activities is the training of researchers at the interface between biology and mathematics. 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.