Expansion of error thresholds for the Moran model

Maxime Berger

Theoretical Population Biology, 2022, vol. 143, issue C, 92-104

Abstract: We study a finite population of individuals evolving through mutation and selection. We generalize the Eigen quasispecies model to a finite population with the Moran model. This model also presents an asymptotic phase transition, and a proper definition of the critical parameter is discussed. We retrieve the same expression for the error threshold appearing in the Eigen model along with a correction term due to the finiteness of the population. To achieve this, we estimate the average lifetime of master sequences and find it grows like an exponential in the size of the population. Our technique consists in bounding from above and below the number of master sequences in the Moran model by two simpler birth and death chains. The expectation of this lifetime is then computed with the help of explicit formulas which are in turn expanded with Laplace method.

Keywords: Markov chain; Phase transition; Genetics (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0040580921000861
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:143:y:2022:i:c:p:92-104

DOI: 10.1016/j.tpb.2021.12.002

Access Statistics for this article

Theoretical Population Biology is currently edited by Jeremy Van Cleve

More articles in Theoretical Population Biology from Elsevier
Bibliographic data for series maintained by Catherine Liu ().