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

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 |

### Citations:

Zbl 1367.92074
PDFBibTeX
XMLCite

\textit{T. Huillet} and \textit{M. Möhle}, Stoch. Models 28, No. 3, 527--532 (2012; Zbl 1367.92075)

Full Text:
DOI

### 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 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.