The minimal observable clade size of exchangeable coalescents

2019/06/27 by Freund, Fabian, Siri-Jégousse, Arno
#60F15 #60G09 #FOS: Biological sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE) #Primary 60C05 #Probability (math.PR) #Secondary 92D20

paper · doi:10.48550/arxiv.1906.11709

Abstract

For Λ-n-coalescents with mutation, we analyse the size O_n of the partition block of i∈\1,…,n\ at the time where the first mutation appears on the tree that affects i and is shared with any other j∈\1,…,n\. We provide asymptotics of O_n for n→∞ and a recursion for all moments of O_n for finite n. This variable gives an upper bound for the minimal clade size [2], which is not observable in real data. In applications to genetics, it has been shown to be useful to lower classification errors in genealogical model selection [10].

Related

• Asymptotic results on the length of coalescent trees
• Genealogies of regular exchangeable coalescents with applications to sampling
• Asymptotic sampling formulae for Lambda-coalescents
• Minimal clade size in the Bolthausen-Sznitman coalescent
• The allelic partition for coalescent point processes