A U-statistic approach to population genetics

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 statistical

computation 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 integral

part 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.