# Asympotic behavior of the total length of external branches for Beta-coalescents

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* Corresponding author 1 LAGA - Laboratoire Analyse, Géométrie et Applications

Abstract : We consider a ${\Lambda}$-coalescent and we study the asymptotic behavior of the total length $L^{n} {ext}$ of the external branches of the associated $n$-coalescent. For Kingman coalescent, i.e. ${\Lambda}={\delta} 0$, the result is well known and is useful, together with the total length $L^{n}$, for Fu and Li-s test of neutrality of mutations% under the infinite sites model asumption . For a large family of measures ${\Lambda}$, including Beta$2-{\alpha},{\alpha}$ with \$0

Author: Jean-Stephane Dhersin - Linglong Yuan -

Source: https://hal.archives-ouvertes.fr/