Mathematics of genetic diversity

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Figures and Tables. Citations Publications citing this paper. Purchase Instant Access. View Preview. Learn more Check out. Abstract Throughout the history of population genetics, mathematical models have played an important role in elucidating the effects of mutation and selection on the genetic diversity of organisms.

Mathematics of Genetic Diversity

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Berkeley Symposium on Mathematical Statistics and Probability

Returning user. Many of the statistics used in population genetics are functions of the allele frequencies at a locus, a discrete set of nonnegative numbers that sum to one. This feature of allele frequencies contributes to surprising phenomena affecting some of the most popular population-genetic statistics, such as homozygosity and heterozygosity, the F ST measure of genetic differentiation, and the r 2 statistic for linkage disequilibrium. To facilitate sensible biological interpretations of observations of these statistics, we have been exploring their mathematical properties.

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This mathematical work provides explanations for a number of peculiar patterns seen in past applications of the statistics to population-genetic data. Genetics Molecular Ecology Journal of Mathematical Biology Theoretical Population Biology See Jakobsson, Edge, and Rosenberg for details. Theoretical population genetics of admixture. When mating occurs between members of two or more groups that have long been separated, new populations can form that are admixed.

Admixture is widespread in human populations, as a result of complex histories of migration, conquest, enslavement, and ongoing cultural interactions. A popular population-genetic model treats allele frequencies in an admixed population as linear combinations of the allele frequencies in its source populations, weighting each frequency by an admixture coefficient for its corresponding source population.

Population genetics - Wikipedia

We have examined a number of features of this admixture model in relation to the F st measure of genetic differentiation, statistics for measuring ancestry information content, and neighbor-joining inference of population trees. Further, we have extended beyond the statistical model of admixture to develop a mechanistic model that acocunts for varying contributions of different source populations over time.

This model enables assessments of the impact of different admixture histories on the pattern of admixture across individuals, and we are using it for analysis of the history and structure of admixture in a variety of admixed human populations. Bulletin of Mathematical Biology Pacific Symposium on Biocomputing See Kopelman, Stone, Gascuel, and Rosenberg for details.

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Human migration and spatial expansion. The genomes of living humans carry information about past human migrations.

Patterns of genetic diversity and similarity among individuals and populations reflect a complex history of such phenomena as migration, natural selection, and changes in population size. As population-genetic models of migration and spatial expansion make predictions about extant genetic variation given assumptions about active evolutionary phenomena, they can help to understand the connection between extant genetic variation and past evolutionary processes. We have been developing and studying models of population migration with the aim of understanding the processes that have been active during human evolution, particularly since the advent of anatomically modern humans.

Recent interests include assessments of global models of human migration, evaluations of spatial patterns of genetic variation, and approaches for making use of genome-scale data.