Population genetics models for the statistics of DNA samples under different demographic scenarios - Maximum likelihood versus approximate methods

• Autorzy: Andrzej Polański , Marek Kimmel
• Języki publikacji: EN

Abstrakty

EN

The paper reviews the basic mathematical methodology of modeling neutral genetic evolution, including the statistics of the Fisher-Wright process, models of mutation and the coalescence method under various demographic scenarios. The basic approach is the use of maximum likelihood techniques. However, due to computational problems, intuitive or approximate methods are also of great importance.

Słowa kluczowe

EN

coalescence; DNA samples; demography

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: 13
• Numer: 3
• Strony: 347-355

Daty

wydano

2003

otrzymano

2003-03-01

poprawiono

2003-06-01

Twórcy

autor

Andrzej Polański

• Institute of Automatic Control, Silesian University of Technology, ul. Akademicka 16, 44-101 Gliwice, Poland

autor

Marek Kimmel

• Institute of Automatic Control, Silesian University of Technology, ul. Akademicka 16, 44-101 Gliwice, Poland

Bibliografia

• Bahlo M. and Griffiths R.C. (2000): Inference from gene trees in a subdivided population. — Theor. Popul. Biol., Vol. 57, No. 2, pp. 79–95.
• Beerli P. and Felsenstein J. (2001): Maximum likelihood estimation of a migration matrix and effective population sizes in n subpopulations using a coalescent approach. — Proc. Natl. Acad. Sci. USA, Vol. 98, No. 8, pp. 4563–4568.
• Bellman R., Kalaba R.E. and Lockett J.A. (1966): Numerical Inversion of the Laplace Transform. — New York: Elsevier.
• Cann R.L., Stoneking M. and Wilson A.C. (1987): Mitochondrial DNA and human evolution. — Nature, Vol. 325, No. 6099, pp. 31–36.
• Cox D.R. and Oakes D. (1984): Analysis of Survival Data. — London: Chapman and Hall.
• Ewens W.J. (1972): The sampling theory for selectively neutral alleles. — Theor. Popul. Biol., Vol. 3, No. 2, pp. 87–112.
• Felsenstein J. (1981): Evolutionary trees from DNA sequences: A maximum likelihood approach. — J. Mol. Evol., Vol. 17., No. 6, pp. 368–376.
• Felsenstein J. (1992): Estimating effective population size from samples of sequences, inefficiency of pairwise and segregating sites as compared to phylogenetic estimates. — Genet. Res., Vol. 59, No. 2, pp. 139–147.
• Fu Y.X. and Li W.H. (1993a): Maximum likelihood estimation of population parameters. — Genetics, Vol. 134, No. 4, pp. 1261–1270.
• Fu Y.X. and Li W.H. (1993b): Statistical test of neutrality of mutations. — Genetics, Vol. 133, No. 3, pp. 693–709.
• Griffiths R.C. (1989): Genealogical tree probabilities in the infinitely many sites model. — J. Math. Biol., Vol. 27, No. 6, pp. 667–680.
• Griffiths R.C. and Tavare S. (1994): Sampling theory for neutral alleles in a varying environment. — Proc. Roy. Stat. Soc. B., Vol. 344, No. 1310, pp. 403–410.
• Griffiths R.C. and Tavare S. (1995): Unrooted genealogical tree probabilities in the infinitely many sites model. — Math. Biosci., Vol. 127, No. 1, pp. 77–98.
• Hastings W.K. (1970): Monte Carlo sampling method using Markov chains and their applications. — Biometrica, Vol. 57, pp. 1317–1340.
• Hudson R.R. (1990): Gene genealogies and the coalescent process, In: Oxford Surveys in Evolutionary Biology (D. Futuyama and J. Antonovics, Eds.). — New York: Oxford University Press, Vol. 7, pp. 1–44.
• Kaplan N.L., Hill W.G. and Weir B.S. (1995): Likelihood methods for locating disease genes in nonequilibrium populations. — Am. J. Hum. Genet., Vol. 56, No. 1, 18–32.
• Kimmel M., Chakraborty R., King J.P., Bamshad M., Wattkins W.S. and Jorde L.B. (1998): Signatures of population expansion in microsatellite repeat data. — Genetics, Vol. 148, No. 4, pp. 1921–1930.
• King J.P., Kimmel M. and Chakraborty R. (2000): A power analysis of microsatlelite-based statistics for inferring past population growth. — Molec. Biol. Evol., Vol. 17, No. 12, pp. 1859–1868.
• Kingman J.F.C. (1982): The coalescent. — Stoch. Proc. Appl., Vol. 13, pp. 235–248.
• Klein J. and Takahata N. (2002): Where Do We Come from? The Molecular Evidence for Human Descent. — Berlin: Springer.
• Kuhner M.K., Yamato J. and Felsenstein J. (1995): Estimating effective population size and mutation rate from sequence data using Metropolis-Hastings sampling. — Genetics, Vol. 140, No. 4, pp. 1421–1430.
• Kuhner M.K., Yamato J. and Felsenstein J. (1998): Maximum likelihood estimation of population growth rates based on coalescent. — Genetics, Vol. 149, No. 1, pp. 429–434.
• Li W.H. (1997): Molecular Evolution. — Sunderland: Sinauer Associates.
• Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H. and Teller E. (1953): Equations of state calculations by fast computing machines. — J. Chem. Phys., Vol. 21, pp. 1087–1092.
• Nordborg M. (2001): Coalescence theory, In: Handbook of Statistical Genetics (D.J. Balding, M.J. Bishop and C. Cannings, Eds.). — New York: Wiley, pp. 153–177.
• Pankratz V.S. (1998): Stochastic models and linkage disequilibrium: Estimating the recombination coefficient. — Ph.D. thesis, Rice University, USA.
• Polanski A., Kimmel M. and Chakraborty R. (1998): Application of a time-dependent coalescent process for inferring the history of population changes from DNA sequence data. — Proc. Natl. Acad. Sci. USA, Vol. 95, No. 10, pp. 5456–5461.
• Pybus O.G., Rambaut A. and Harvey P.H. (2000): An integrated framework for the inference of viral population history from reconstructed genealogies. — Genetics, Vol. 155, No. 3, pp. 1429–1437.
• Relethford J. (2001): Genetics and the Search for Modern Human Origins. — New York: Wiley.
• Rogers A.R. and Harpending H. (1992): Population growth makes waves in the distribution of pairwise genetic differences. — Molec. Biol. Evol., Vol. 9., No. 3, pp. 552–569.
• Sabeti P.C., Reich D.E., Higgins J.M., Levine H.Z.P., Richter D.J., Schaffner S.F., Gabriel S.B., Platko J.V., Patterson N.J., McDonald G.J., Ackerman H.C., Campbell S.J., Altshuler D., Cooper R., Kwiatkowski D., Ward R. and Lander E.S. (2002): Detecting recent positive selection in the human genome from haplotype structure. — Nature, Vol. 419, No. 6909, pp. 832–837.
• Serre J.R., Simon-Bouy B., Monet E., Jaume-Roig B., Balassopoulou A., Schwartz M., Taillandier A., Boue J. and Boue A. (1990): Studies of RFLP closely linked to the cystic fibrosis locus throughout Europe lead to new considerations in populations genetics. — Hum. Genet., Vol. 84, No. 5, pp. 449–54.
• Swofford D.L. and Olsen G.J. (1990): Phylogeny reconstruction, In: Molecular Systematics (D.M. Hillis and C. Moritz, Eds.). — Sunderland: Sinauer Associates, pp. 411–501.
• Tajima F. (1989): Statistical method for testing the neutral mutation hypothesis by DNA polymorphism. — Genetics, Vol. 123, No. 5, pp. 585–595.
• Tavare S. (1997): Ancestral inference from DNA sequence data, In: Case Studies in Mathematical Modeling in Modeling: Ecology, Physiology, and Cell Biology (H.G. Othmer, F.R. Adler, M.A. Lewis, J. Dallon, Eds.). — New York: Prentice Hall, pp. 81–96.
• Watterson G.A. (1975): On the number of segregating sites in genetical models without recombination. — Theor. Popul. Biol., Vol. 7, No. 2, pp. 387–407.