Correction on ‘Population genetics models with skewed fertilities: a forward and backward analysis’. (English) Zbl 1367.92075

Huillet, Thierry; Möhle, Martin

Stoch. Models 28, No. 3, 527-532 (2012).

Summary: The article [ibid. 27, No. 3, 521–554 (2011; Zbl 1367.92074)] contains at the top of page 536 a formula for the joint factorial moments of the offspring numbers \(\mu_1,\dots, \mu_N\), which is wrong in that generality. The only compound Poisson models for which this formula holds true are skewed generalized Wright-Fisher models and skewed generalized Dirichlet models. In this note we correct the erroneous results in Section 4 of the mentioned article from Proposition 4.2 on. The main conclusion that many symmetric compound Poisson population models are in the domain of attraction of the Kingman coalescent, remains valid. However, the proofs turn out to be more involved and the time-scaling differs from the erroneous time-scaling provided in the original article.

MSC:

92D10	Genetics and epigenetics
92D25	Population dynamics (general)
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
60K35	Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

compound Poisson model; Kingman coalescent

Citations:

Zbl 1367.92074

References:

[1]	DOI: 10.1080/15326349.2011.593411 · Zbl 1367.92074 · doi:10.1080/15326349.2011.593411
[2]	Huillet , T. ; Möhle , M. Asymptotics of symmetric compound Poisson population models. In preparation. · Zbl 1181.92067
[3]	Möhle , M. Coalescent processes derived from some compound Poisson population models. Electron. Comm. Probab.2011,16, 567–582. MR2846651 · Zbl 1367.92105