The largest strongly connected component in the cyclical pedigree model of Wakeley et al.

Jochen Blath, Stephan Kadow, Marcel Ortgiese

Research output: Contribution to journalArticle

Abstract

We establish a link between Wakeley et al.’s (2012) cyclical pedigree model from population genetics and a randomized directed configuration model (DCM) considered by Cooper and Frieze (2004). We then exploit this link in combination with asymptotic results for the in-degree distribution of the corresponding DCM to compute the asymptotic size of the largest strongly connected component SNSN (where NN is the population size) of the DCM resp. the pedigree. The size of the giant component can be characterized explicitly (amounting to approximately 80%80% of the total populations size) and thus contributes to a reduced ‘pedigree effective population size’. In addition, the second largest strongly connected component is only of size O(logN)O(logN). Moreover, we describe the size and structure of the ‘domain of attraction’ of SNSN. In particular, we show that with high probability for any individual the shortest ancestral line reaches SNSN after O(loglogN)O(loglogN) generations, while almost all other ancestral lines take at most O(logN)O(logN) generations.
Original languageEnglish
Pages (from-to)28-37
Number of pages10
JournalTheoretical Population Biology
Volume98
DOIs
Publication statusPublished - Dec 2014

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pedigree
population size
effective population size
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The largest strongly connected component in the cyclical pedigree model of Wakeley et al. / Blath, Jochen; Kadow, Stephan; Ortgiese, Marcel.

In: Theoretical Population Biology, Vol. 98, 12.2014, p. 28-37.

Research output: Contribution to journalArticle

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