%0 Journal Article %1 foucart2013impact %A Foucart, Clément %D 2013 %I Institute of Mathematical Statistics %J Electronic Communications in Probability %K coalescent_theory genetic_drift lambda_coalescent selection %N 0 %R 10.1214/ecp.v18-2838 %T The impact of selection in the Lambda-Wright-Fisher model %U http://dx.doi.org/10.1214/ECP.v18-2838 %V 18 %X The purpose of this article is to study some asymptotic properties of the Λ -Wright- Fisher process with selection. This process represents the frequency of a disad- vantaged allele. The resampling mechanism is governed by a finite measure Λ on R 1 0, 1 and selection by a parameter α . When the measure Λ obeys 0 − log(1 − −2 x)x Λ(dx) < ∞ , some particular behaviour in the frequency of the allele can oc- cur. The selection coefficient α may be large enough to override the random genetic drift. In other words, for certain selection pressure, the disadvantaged allele will vanish asymptotically with probability one. This phenomenon cannot occur in the classical Wright-Fisher diffusion. We study the dual process of the Λ -Wright-Fisher process with selection and prove this result through martingale arguments.

@article{foucart2013impact, abstract = {The purpose of this article is to study some asymptotic properties of the Λ -Wright- Fisher process with selection. This process represents the frequency of a disad- vantaged allele. The resampling mechanism is governed by a finite measure Λ on R 1 [0, 1] and selection by a parameter α . When the measure Λ obeys 0 − log(1 − −2 x)x Λ(dx) < ∞ , some particular behaviour in the frequency of the allele can oc- cur. The selection coefficient α may be large enough to override the random genetic drift. In other words, for certain selection pressure, the disadvantaged allele will vanish asymptotically with probability one. This phenomenon cannot occur in the classical Wright-Fisher diffusion. We study the dual process of the Λ -Wright-Fisher process with selection and prove this result through martingale arguments.}, added-at = {2016-07-01T19:12:27.000+0200}, author = {Foucart, Cl{\'{e}}ment}, biburl = {https://www.bibsonomy.org/bibtex/28828487f3a4a41242f4870dcf2574735/peter.ralph}, doi = {10.1214/ecp.v18-2838}, interhash = {ecc1391447b546c17706e2011e4b6db8}, intrahash = {8828487f3a4a41242f4870dcf2574735}, journal = {Electronic Communications in Probability}, keywords = {coalescent_theory genetic_drift lambda_coalescent selection}, number = 0, publisher = {Institute of Mathematical Statistics}, timestamp = {2016-07-01T19:12:27.000+0200}, title = {The impact of selection in the Lambda-Wright-Fisher model}, url = {http://dx.doi.org/10.1214/ECP.v18-2838}, volume = 18, year = 2013 }