Probability and Statistics Problems Concerning DNA Sequence and Genome Evolution

这笔赠款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。统计方法将被用来研究大规模过程引起的DNA序列的进化：染色体内的倒置、染色体之间的相互易位、移动基因的转位、染色体的分裂和融合以及整个基因组的复制。主要目标是获得事件数量的统计估计以及相关的不确定性测量，测试例如关于谱系之间突变率恒定的假设，并比较拟南芥、玉米和其他生物体中各种基因组复制情景的可能性。还将开发数学结果和统计技术，以区分观察到的基因组DNA序列差异水平和模式的原因，重点放在优势突变的固定(“选择性扫描”)和空间种群结构的影响上。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，完全似然方法或贝叶斯方法是不容易处理的。这笔赠款支持的研究将侧重于对生物内部和生物之间基因组变异的定量研究。考虑了两种尺度。第一个是由于大规模的过程而导致的基因组的进化，这些过程重新安排了染色体上的基因顺序，或者在染色体之间交换遗传物质。了解这些变化的速度和大小对于改善物种之间的比较图谱将是重要的。例如，这些图谱可以识别人类基因的老鼠同源物，或者给出牛和羊基因的相对顺序，在医学和农业中都很重要。第二个尺度是观察到的物种内DNA变异的水平。数学和统计研究将侧重于区分适应(自然选择)和空间(地理)种群结构对从人类和其他生物的DNA序列数据中观察到的塑造模式的影响。这些结果将为生物体如何在遗传上对新的环境和挑战(包括病原体和环境压力)做出反应提供洞察力，并有助于识别在这种适应中重要的基因。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将是重要的。拟议活动的一个重要组成部分是对生物学和数学之间的研究人员进行培训。这笔赠款是在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。这是一项由国家科学基金会数学科学部(DMS)和国立卫生研究院(NIGMS)国家普通医学研究所(NIGMS)主办的联合竞赛。

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.