Probability and Statistics Problems Concerning DNA Sequence and Genome Evolution

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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.