Mathematical population dynamics

14 Jun 2013, Friday

*Kirzhner V.M., (1973). On behaviour of trajectories for a certain class of genetic systems,

Soviet Doklady209, 2,  287-290. (English translation: Soviet Mathematical Doklady, 209

(1973), 2, 378-382).

*Kirzhner V.M., Lyubich Ju.I., (1974). An evolutionary equation and a  limit theorem for

       general   genetic systems without selection, Soviet Doklady215, 4,776‐779.

(English translation: Soviet Mathematical Doklady 215 (1974), 2, 582-586).

*Kirzhner V.M., Korol A.B., Ronin Y.I., Nevo E. (1994). Cyclical  behavior of genotype 

       frequencies in a two-locus population under fluctuating haploid selection, Proceedings

      National Academy of Sciences USA 91, 11432-36.

*Kirzhner V.,  Korol A.B.,  Ronin Y.I., Nevo E. (1995). Genetic super-cycles caused by 

       cyclical selection, Proceedings National Acad. Sci. USA , 92 , 7130-7133.

*Kirzhner V., Korol A.B., Ronin Y.I. (1995). Cyclical environmental changes as factor 

       maintaining genetic polymorphism. I. Two-locus haploid selection, Journal of Evolutionary

Biology8, 93-120.

*Kirzhner V., Korol A.B., Ronin Y. (1995). The dynamics of linkage disequilibrium under

       temporal environmental fluctuation.  Two-locus selection, Theoretical Population Biology,

47, 257-276.

*Korol A., Kirzhner V., Ronin Y.I. (1996). Cyclical environmental changes as factor

      maintaining genetic polymorphism. II. Two-locus diploid selection, Evolution,   50, 1432-


*Kirzhner V., Korol A.B., Nevo E. (1996). Complex non-stationary trajectories in 

       multilocus genetic systems caused by cyclical selection with moving optimum,

Proceedings National Acad. Sci. USA, 93, 6532-6535.

*Nevo E., Kirzhner V., Beiles A., Korol A. (1997). Selection versus random drift: long-term 

       polymorphism persistence in small   populations (evidence and modelling), Phil. Trans.

Roy. Soc.  B.,  352, 381-389.

*Kirzhner V., Lyubich Yu. (1997). Multilocus dynamics under haploid selection, J. Math.

       Biol., 35, 391-408.

*Kirzhner V., Lembrikov B., Korol A.,  Nevo E. (1998). Supercycles, strange attractors and  

      chaos in a standard model of population genetics, Physica A, 249, 565-570.

*Kirzhner V., Korol A., Nevo E. (1998). Complex limiting behavior of multilocus genetic

      systems in cyclical environmentJ. Theoretical Biol. 190 3, 215-225.

*Korol A.. Kirzhner V., and Nevo E. (1998).Dynamics of recombination modifiers 

      caused by cyclical selection: interaction of forced-and auto-oscillations, Genetical

      Research69, 135-147.

 *Kirzhner V., Korol A., Nevo E. (1999). Abudant multilocus polymorphisms caused

        by genomic interaction between species on trait-for-trait basisJournal Theoretical

        Biology , 198,361-70

*Yuri Lyubich, Valery Kirzhner, Anna Ryndin (2001) Mathematical Theory of 

        Phenotypical  Selection, Advances in Applied Mathematics, 26, 4,330-352.


 *Yuri Lyubich, Valery Kirzhner (2003)  Mathematical frameworks for phenotypical

       selection and epistasis, J. Theoretical Biol., 221, 625-638.

*Yuri Lyubich, Valery Kirzhner. (2003) Finiteness of equilibria set for a nonepistatic  

      selection  under multilocus Mendel dominance, Appl. Math. Letters, 16, 421-424.

*Valery Kirzhner and Yuri Lyubich.(2003) The multilocus multiplicative selection

      Equilibria,  Appl. Math. Letters, 16, 6, 853-856.


Chapter in Book:

V.Kirzhner, V.Frencel, A.Korol. (2004) Complex dynamics of multilocus genetics systems. In: Evolutionary Theory and Processes: Modern Horizons (ed.S.Wasser), 65-109.