Access the full text.
Sign up today, get DeepDyve free for 14 days.
R.M. Nesse (1995)
Technology Review
R. Kanzafarova, A. Kazantseva, E. Khusnutdinova (2015)
Genetic and environmental aspects of mathematical disabilitiesRussian Journal of Genetics, 51
R. Buerger (2000)
The Mathematical Theory of Selection, Recombination, and Mutation
A. Jacquard (1974)
The Genetic Structure of Populations
G. Terrell (1969)
Applied ProbabilityJournal of the American Statistical Association, 99
D. Hartl, A. Clark (1981)
Principles of population genetics
Cedric Smith (1980)
The Geometry of Population Genetics, 143
K. Schneider (2006)
A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competitionJournal of Mathematical Biology, 52
M. Turelli, N. Barton (1990)
Dynamics of polygenic characters under selection.Theoretical Population Biology, 38
A. Markel (2015)
Evolutionary and genetic roots of hypertensive diseaseRussian Journal of Genetics, 51
R. Bürger (2005)
A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative traitJournal of Mathematical Biology, 50
S. Thurer (1984)
Review of When bad things happen to good people.Psychosocial rehabilitation journal, 7
E. Ignatieva, E. Ignatieva, O. Podkolodnaya, Y. Orlov, Y. Orlov, G. Vasiliev, N. Kolchanov, N. Kolchanov (2015)
Regulatory genomics: Combined experimental and computational approachesRussian Journal of Genetics, 51
R. Elandt-Johnson (1972)
Probability models and statistical methods in genetics
J. Bennett (1954)
On the theory of random mating.Annals of eugenics, 18 4
E. Akin (1982)
Cycling in simple genetic systemsJournal of Mathematical Biology, 13
Reinhard Bürger (1991)
Moments, cumulants, and polygenic dynamics.Journal of mathematical biology, 30 2
Ching Li (1976)
First Course in Population Genetics
K. Lange (1993)
A stochastic model for genetic linkage equilibrium.Theoretical population biology, 44 2
T. Nagylaki (1992)
Introduction to Theoretical Population Genetics
L. Cavalli-Sforza, Walter Bodmer (1972)
The genetics of human populations.Scientific American, 231 3
H. Geiringer (1945)
Further Remarks on Linkage Theory in Mendelian HeredityAnnals of Mathematical Statistics, 16
K. Schneider (2007)
Long-term evolution of polygenic traits under frequency-dependent intraspecific competition.Theoretical population biology, 71 3
S. Karlin (1972)
Some Mathematical Models of Population GeneticsAmerican Mathematical Monthly, 79
N.H. Barton, P.D. Keightley (2002)
Understanding quantitative genetic variationNat. Rev. Genet., 3
R. Bürger (2011)
Some Mathematical Models in Evolutionary Genetics
N. Barton, M. Turelli (1987)
Adaptive landscapes, genetic distance and the evolution of quantitative characters.Genetical research, 49 2
N.H. Barton, M. Turelli (1987)
Adaptive landscapesgenetic distance and the evolution of quantitative characters, Genet. Res., 49
V. Efremov (2005)
Equilibrium between Genetic Drift and Migration at Various Mutation Rates: Simulation AnalysisRussian Journal of Genetics, 41
Yu.M. Svirezhev (1972)
Optimality principles in population genetics, in Studies in Theoretical Genetics
J. Crow, M. Kimura (1971)
An introduction to population genetics theory
Charles Darwin (1930)
The Genetical Theory of Natural SelectionNature, 126
N. Barton, P. Keightley (2002)
Multifactorial genetics: Understanding quantitative genetic variationNature Reviews Genetics, 3
N. Barton, M. Turelli (1991)
Natural and sexual selection on many loci.Genetics, 127 1
O. Zhdanova, E. Frisman (2014)
Modelling of selection acting upon the pleioptropic locus in a population with two age classesRussian Journal of Genetics, 50
S. Shahshahani (1979)
A New Mathematical Framework for the Study of Linkage and Selection
T. Mackay (2001)
Quantitative trait loci in DrosophilaNature Reviews Genetics, 2
E. Trifonova, M. Spiridonova, V. Stepanov (2008)
Genetic diversity and the structure of linkage disequilibrium in the methylenetetrahydrofolate reductase locusRussian Journal of Genetics, 44
J. Hofbauer, G. Iooss (1984)
A Hopf bifurcation theorem for difference equations approximating a differential equationMonatshefte für Mathematik, 98
R. Lande (1979)
QUANTITATIVE GENETIC ANALYSIS OF MULTIVARIATE EVOLUTION, APPLIED TO BRAIN:BODY SIZE ALLOMETRYEvolution, 33
T. Nagylaki (1991)
Error bounds for the fundamental and secondary theorems of natural selection.Proceedings of the National Academy of Sciences of the United States of America, 88
A. Hastings (1981)
Stable cycling in discrete-time genetic models.Proceedings of the National Academy of Sciences of the United States of America, 78 11
R. Bürger (1991)
Momentscumulants, and polygenic dynamics, J. Math. Biol., 30
In this study, we present some of the basic ideas of population genetics. The founders of population genetics are R.A. Fisher, S. Wright, and J. B.S. Haldane. They, not only developed almost all the basic theory associated with genetics, but they also initiated multiple experiments in support of their theories. One of the first significant insights, which are a result of the Hardy–Weinberg law, is Mendelian inheritance preserves genetic variation on which the natural selection acts. We will limit to simple models formulated in terms of differential equations. Some of those differential equations are nonlinear and thus emphasize issues such as the stability of the fixed points and time scales on which those equations operate. First, we consider the classic case when selection acts on diploid locus at which wу can get arbitrary number of alleles. Then, we consider summaries that include recombination and selection at multiple loci. Also, we discuss the evolution of quantitative traits. In this case, the theory is formulated in respect of directly measurable quantities. Special cases of this theory have been successfully used for many decades in plants and animals breeding.
Russian Journal of Genetics – Springer Journals
Published: Sep 28, 2016
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.