A U-statistic approach to population genetics

多倍体是指具有两套以上完整染色体的生物体，在植物界普遍存在，在农业中占主导地位，是进化的重要驱动力。许多植物物种都表现出祖先的多倍体，因此，今天了解多倍体的进化行为使研究人员对进化的一般机制有了更深入的了解。然而，多倍体表现出更大的复杂性，这使得建模它们的基因组变得更加困难。该项目将通过开发多倍体基因组群体遗传学的新方法来解决这些增加的统计和计算复杂性。这些方法将使研究人员能够更好地确定多倍体种群内部和之间的结构关系，从而更好地揭示这些物种内部潜在进化过程的各个方面。所有方法都将在开源软件中实现，这将使应用研究人员能够使用这些方法。该项目将为本科生和研究生研究人员提供统计学和计算生物学方面的高级培训，为他们职业生涯的下一步做准备。该项目还将为使用R统计语言的高级统计计算提供公开可用的教育材料，使这些主题更容易被更大的学术界所接受。该项目从群体遗传学的角度重新制定了u统计最小化的关键任务，这是一种用于估计和测试的统计技术。这种方法将使其具有更大的通用性和复杂性，例如多倍体种群。这些方法也将解释经典孟德尔分离的偏差，例如，由双重还原引起的，姐妹染色单体在减数分裂期间共同迁移到同一配子中，这是某些类型多倍体的常见事件。第一个目标是开发多倍体和混合倍体群体平衡的新测试策略。第二个目标是开发新的方法来估计人口结构，同时考虑多倍体数据导致的常见问题。第三个目的是探索u统计方法的其他可能应用，例如近交估计或连锁不平衡估计。该项目强调为研究社区开发可用的软件，并在所有结果中具有极高的可重复性。该项目将为每项创新提供可用的R包，这将被更大的生物界所访问。学生研究人员将接受使用R进行软件开发的基础培训，因此将成为构建该项目R包的重要组成部分。该项目的结果可以在https://github.com/dcgerard/NSF-U-Statistics.This上找到，该奖项反映了美国国家科学基金会的法定使命，并通过基金会的智力价值和更广泛的影响审查标准进行评估，认为值得支持。

Polyploids, organisms with more than two complete sets of chromosomes, are ubiquitous in the plant kingdom, predominant in agriculture, and important drivers of evolution. Many plant species exhibit ancestral polyploidy, and so understanding the evolutionary behavior of polyploids today gives researchers a greater understanding of the mechanisms of evolution in general. However, polyploids manifest greater complexities that make modeling their genomes much more difficult. This project will address these added statistical and computational complexities by developing novel methods for the population genetics of polyploid genomes. These methods will allow researchers to better determine the structural relationships within and between polyploid populations, which could better reveal aspects of the underlying evolutionary processes within these species. All methods will be implemented in open-source software, which will make these approaches accessible to applied researchers. This project will provide advanced training in Statistics and Computational Biology to undergraduate and graduate researchers in preparation for the next steps in their careers. This project will also result in publicly available educational materials for advanced statisticalcomputation using the R statistical language, making such topics more accessible to the greater academic community.This project reformulates key tasks from population genetics in terms of U-statistic minimization, a statistical technique for estimation and testing. This approach will lend itself to greater generality and complexity, such as for polyploid populations. These methods will also account for deviations from classical Mendelian segregation caused, for example, by double reduction, the co-migration of sister chromatids into the same gamete during meiosis, a common event in some types of polyploids. The first aim is to develop novel testing strategies for equilibrium in polyploid and mixed-ploidy populations. The second aim is to develop new approaches to estimate population structure while accounting for common issues that result from polyploid data. The third aim is to explore other possible applications of the U-statistic approach, such as for inbreeding estimation or linkage disequilibrium estimation. This project emphasizes developing usable software for the research community, and extreme reproducibility in all results. This project will deliver usable R packages for each innovation, which will be accessible to the greater biological community. Student researchers will be trained in the fundamentals of software development using R, and so will be an integralpart in building the R packages of this project. The results of the project can be found at https://github.com/dcgerard/NSF-U-Statistics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.