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May 2021 The minimal observable clade size of exchangeable coalescents
Fabian Freund, Arno Siri-Jégousse
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Braz. J. Probab. Stat. 35(2): 281-292 (May 2021). DOI: 10.1214/20-BJPS480


For Λ-n-coalescents with mutation, we analyse the minimal observable clade size On. For a given individual i{1,,n}, the minimal observable clade size On(i) is 1 plus the number of other individuals j such that every non-singleton mutation inherited by i is also inherited by j. We provide asymptotics of On as n and a recursion for all moments of On for finite n. This statistic gives an upper bound for the minimal clade size (Advances in Applied Probability 37 (2005) 647–662) which is not observable in real data (in contrast to On). In applications to genetics, it has been shown to be useful to lower classification errors in genealogical model selection (Freund and Siri-Jégousse, 2020).


The authors would like to thank Henry Pantí and the UADY for their warm welcome. FF was funded by DFG grant FR 3633/2-1 through Priority Program 1590: Probabilistic Structures in Evolution.


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Fabian Freund. Arno Siri-Jégousse. "The minimal observable clade size of exchangeable coalescents." Braz. J. Probab. Stat. 35 (2) 281 - 292, May 2021.


Received: 1 December 2019; Accepted: 1 July 2020; Published: May 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.1214/20-BJPS480

Keywords: Clade size , recursion , Λ-coalescent

Rights: Copyright © 2021 Brazilian Statistical Association


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Vol.35 • No. 2 • May 2021
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