JOINT MATHEMATICS COLLOQUIUM

UNIVERSITY OF IDAHO

WASHINGTON STATE UNIVERSITY


Department of Mathematics

University of Idaho


Spring 2016

Thursday,  February 18, 3:30-4:20 pm, room TLC 249

Refreshments in Brink 305 at 3:00 pm


Mathematical genetics, Hardy way,  a Hardy-Weinberg law for
admixture fractions


 

Erkan Buzbas




 
Department of Statistical Science

University of Idaho



I present fundamental mathematical results on the distribution of admixture fractions in an admixed population undergoing continuous admixture events,  founded by two source populations. I show that the admixture fractions at one locus follow a Hardy-Weinberg law. This is surprising due to gene flow between the hybrid population and the two source populations, since Hardy-Weinberg laws assume a closed population. For more than one locus, I show that a stationary distribution of the admixture fractions exists: I solve for this distribution  analytically for two loci, and calculate it by deterministic simulations when the number of loci is greater than two. I provide a Bayesian method to estimate the introgression (admixture) parameters and discuss the implications of reaching stationarity on
estimability of parameters when there are more than one admixture processes.



G.H. Hardy was an influential mathematician of the 20th century. He discovered the Hardy-Weinberg law,
a fundamental mathematical rule stating that gene and genotype frequencies in a population will remain constant in the absence of external forces. Hardy has written a book ``A Mathematician's Apology" which has inspired me enormously.