Applications of the Galton–Watson process to human DNA evolution and demography

Armando G.M. Neves and Carlos H.C. Moreira

Physica A: Statistical Mechanics and its Applications, 2006, vol. 368, issue 1, 132-146

Abstract: We show that the problem of existence of a mitochondrial Eve can be understood as an application of the Galton–Watson process and presents interesting analogies with critical phenomena in Statistical Mechanics. In the approximation of small survival probability, and assuming limited progeny, we are able to find for a genealogic tree the maximum and minimum survival probabilities over all probability distributions for the number of children per woman constrained to a given mean. As a consequence, we can relate existence of a mitochondrial Eve to quantitative demographic data of early mankind. In particular, we show that a mitochondrial Eve may exist even in an exponentially growing population, provided that the mean number of children per woman N¯ is constrained to a small range depending on the probability p that a child is a female. Assuming that the value p≈0.488 valid nowadays has remained fixed for thousands of generations, the range where a mitochondrial Eve occurs with sizeable probability is 2.0492Keywords: Branching processes; Mitochondrial Eve; Mitochondrial DNA; Y Chromosome; Evolutionary genetics (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437106001099
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

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:phsmap:v:368:y:2006:i:1:p:132-146

DOI: 10.1016/j.physa.2005.11.055

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().