"Self-similarity: a new perspective in population genetic models."Hernandez Wences, AlejandroIt is common practice in probabilistic population growth models to assume the branching property (BP). In our results, we propose a shift in focus from the BP to the self-similarity (SS) property, allowing for new dependencies to arise between the reproduction dynamics of the individuals, mainly through the total size of the population. This novel perspective has allowed us to improve important results in the literature while uncovering surprising connections with well-established objects in the field. We employed specialized SS techniques, including a generalization of the Lamperti transformation, to characterize the genealogy of populations whose total size behaves as any positive SS Markov process. A general Lambda-coalescent process may appear describing the underlying genealogy. Our results constitute a "self-similar" generalization of the main result in Birkner et al. 2005 for branching processes in which, however, only the sub-family of the beta coalescents appears. According to their results, such a generalization could only be attained after removing the BP, which also motivates our shift in focus to the SSP. |
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