UDC 519.24
1 Institute of Telecommunication and Global Information Space of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
 dimitri.koroliouk@ukr.net
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2 Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
vskorol@yahoo.com
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EQUILIBRIUM IN WRIGHT–FISHER MODELS
OF POPULATION GENETICS
Abstract. For multivariant Wright–Fisher models in population genetics, we introduce equilibrium states, expressed by fluctuations of probability ratio, in distinction of the traditionally used fluctuations, expressed by the difference between the current value of the random process and its equilibrium value. Then the drift component of the gene frequencies dynamic process, primarily expressed as a ratio of two quadratic forms, is transformed into a cubic parabola with a certain normalization factor.
Keywords: Wright–Fisher model, population genetics, evolutionary process, equilibrium state, fluctuations of probability ratio.
FULL TEXT
REFERENCES
- Ethier S.N., Kurtz T.G. Markov processes: Characterization and convergence. New York: Willey, 1986. 534 p.
- Koroliouk D., Koroliuk V.S., and Rosato N. Equilibrium process in biomedical data analysis: The Wright–Fisher model. Cybernetics and System Analysis. 2014. Vol. 50, N 6. P. 890–897.
- Koroliouk D. Two component binary statistical experiments with persistent linear regression. Theor. Probability and Math. Statist. 2014. Vol. 90. P. 103–114.
- Korolyuk V.S., Koroliouk D. Diffusion approximation of stochastic Markov models with persistent regression. Ukrainian Mathematical Journal. 1995. Vol. 47, N 7. P. 1065–1073.
- Skorokhod A.V., Hoppensteadt F.C., Salehi H. Random perturbation methods with applications in science and engineering. New York: Springer-Verlag, 2002. 488 p.
- Koroliouk D. Multivariant statistical experiments with persistent linear regression and equilibrium. Theor. Probability and Math. Statist. 2015. Vol. 92. P. 71–78.
