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UID:20250717T164759EDT-2705cuSg38@132.216.98.100
DTSTAMP:20250717T204759Z
DESCRIPTION:Lambda-coalescent and lookdown model with selection\n\nWe study
  the lookdown model with selection in the case of a population containing 
 two types of individuals\, where the genealogy backward in time is describ
 ed by the standard Lambda-coalescent with a non-trivial 'Kingman part'. We
  show that the proportion of one of the two types converges\, as the popul
 ation size N tends to infinity\, towards the solution to a stochastic diff
 erential equation driven by a Poisson point process (the same equation\, i
 n case without selection\, already appeared in the work of Bertoin and Le 
 Gall). We show that one of the two types fixates in finite time if and onl
 y if the Lambda-coalescent comes down from infinity. In the case of no fix
 ation\, we prove that for a certain selection pressure\, the disadvantage 
 allele will vanish asymptotically with probability one. This phenomenon ca
 nnot occur in the classical Wright-Fisher diffusion. We give precise asymp
 totic results in the case of the Bolthausen-Sznitman coalescent. In partic
 ular we obtain in that case an explicit formula for the probability that o
 ne of the two alleles fixates\, which is different from the classical one 
 for the Wright-Fisher model.\n
DTSTART:20180129T190000Z
DTEND:20180129T200000Z
LOCATION:Room 1214\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Boubacar Bah\, AIMS-Cameroon
URL:/mathstat/channels/event/boubacar-bah-aims-cameroo
 n-284243
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