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Muller's ratchet

Description of the project:
- no english description available -

The evolution of allele frequencies is determined by random mating, mutation, selection and recombination. While the first three mechanisms are arguably necessary for any theory of evolution, the question arises why recombination, which is only present in sexually reproducing species, evolved. One approach explaining the disadvantage of asexual reproduction is provided by the theory around Muller’s ratchet. Assume deleterious mutations accumulate in an asexually reproducing population. All offspring of an individual carrying n deleterious mutations will at least have n mutations, as well. Thus, the population is divided in classes of individuals carrying the same number of deleterious mutations. The least loaded class contains all 3 individuals carrying no deleterious mutation. If all offspring of the least loaded class have accumulated at least one new mutation the ratchet has clicked. Ignoring random fluctuations in the frequency of classes, it was shown in Haigh (The accumulation of deleterious genes in a population-Muller’s Ratchet. Theor. Popul. Biol, 14(2):251-267, 1978) that a Poisson distribution describes the distribution of deleterious mutations on the popu- lation. Moreover, Etheridge et al. (2009) provide the exact path to this equilibrium for any starting condition. However, the techniques used in these papers do not suffice to give any formal result on the rate of clicks in Muller’s ratchet if random fluctuations are taken into account.

Additional information: http://www.stochastik.uni-freiburg.de
Phone: 0761/203-5667
Email: peter.pfaffelhuber@stochastik.uni-freiburg.de
Runtime:
Start of project: 01.04.2008
End of project: 31.12.2014
Project Management:
Albert-Ludwigs-University Freiburg
Prof. Dr. Peter Pfaffelhuber
Abteilung für Mathematische Stochastik
Prof. Dr. Peter Pfaffelhuber
Ernst-Zermelo-Straße 1
79104 Freiburg
Germany

Phone: 0761/203-5664
Fax: 0761/203-5661
Email: sekretariat@stochastik.uni-freiburg.de
http://www.stochastik.uni-freiburg.de/pfaffelhuber
Actual Research Report
Financing:
  • BMBF (FRISYS)
project-related publications:
  • Etheridge A, Pfaffelhuber P, Wakolbinger A: How often does the ratchet click? Facts, heuristics, asymptotics. In: London Mathematical Society (Hrsg.): Trends in Stochastic Analysis. Papers dedicated to Professor Heinrich von Weizsäcker on the occasion of his 60th birthday. Cambridge: Cambridge University Press, 2009; 365-390 (Lecture Notes Series 353).: http://arxiv.org/abs/0709.2775