COMPLEX DYNAMICS OF MULTILOCUS GENETIC SYSTEMS CAUSED BY CYCLICAL SELECTION

We demonstrate that simple cyclical selection, in particular, selection for a trait controlled by multiple additive, dominant, or semidominant loci can result in extremely complex limiting behavior (CLB) of population trajectories including supercycles and chaotic-like phenomena. These CLB may arise in a rather broad and natural class of multilocus systems, both haploid and diploid, with panmixia or more complex breeding systems (such as partial selfing or random mating mixed with asexual reproduction). The observed complex dynamics appear to manifest certain stability with respect to disturbances of parameters specifying the selection, recombination, and breeding system (fixed in population or genotype-dependent). This discovered diversity of multilocus dynamics by far exceeds the range of dynamic patterns described earlier for these ordinary selection models. It may represent a novel evolutionary mechanism increasing genetic diversity over long-term time periods. This novel mechanism could contribute to the observation that biological diversity has increased over geological time regardless of the well known massive extinctions

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  • Numerical iterations have shown that periodic haploid two-locus selection with nonoverlapping generations can produce large-scale cyclical behavior with a period differing significantly from the environmental period. Among other types, we observed slowly damping oscillations with very long periods, stable T-cycles with a length containing several environmental periods, and chaotic-like dynamics. Possible biological implications are discussed.

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. Proc Natl Acad Sci USA 91, 11432-36.(http://www.pnas.org/cgi/reprint/91/24/11432)


  • Typical behavior of a two-locus genetic system experiencing cyclical selection, includes fixation (in one or both loci) or a stable polymorphic cycle with a period equal to that of environmental changes. By considering the time scale in terms of environmental periods, the last case could be trivially classified as a polymorphic stable point. Here we report on some results showing the complex limiting behavior of diploid population trajectories resulting from selection in a cyclically changing environment. We found that simple cyclical selection could produce genetic supercycles composed of many hundreds of environmental periods.

Kirzhner V., Korol A.B., Ronin Y.I., Nevo E. (1995). Genetic super-cycles caused by cyclical selection. Proc Natl Acad Sci USA , 92 , 7130-7133. (http://www.pnas.org/cgi/reprint/92/15/7130)


  • Here we demonstrate that a multilocus system subjected to stabilizing selection with cyclically moving optimum can generate ubiquitous complex limiting behavior including supercycles, T-cycles, and chaotic-like phenomena. This mode of multilocus dynamics far exceeds the potential attainable under ordinary selection models resulting in simple behavior. It may represent a novel evolutionary mechanism increasing genetic diversity over long-term time periods.

Kirzhner V., Korol A.B., Nevo E. (1996). Complex dynamics of multilocus systems subjected to cyclical selection. Proc Natl Acad Sci USA, 93, 6532-6535.(http://www.pnas.org/cgi/reprint/93/13/6532)


  • We carried out a detailed investigation of the standard multilocus genetic system. We evaluated the characteristics of the dynamics of several types of such a system allowing to classify the complex trajectories: the Lyapunov exponent, the information entropy, the information dimension and the capacity. It is shown that such dynamic systems manifest auto-oscillations, strange attractors, and chaos

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. (Article.atract)


  • Here we demonstrate that complex limiting behaviour (supercycles and chaotic-like phenomena) may arise in a rather broad and natural class of multilocus systems, both haploid and diploid, experiencing stabilizing selection with cyclically varying optima over a short period. These include loci with purely additive, dominant, or semidominant effects, with different types of their chromosome distribution. The observed complex dynamics appeared to manifest a certain stability with respect to disturbances of parameters specifying the structure of the selected system and environmental characteristics. This mode of multilocus dynamics by far exceeds the potential attainable under ordinary selection models resulting in simple behaviour. It may represent a novel evolutionary mechanism increasing genetic diversity over long time periods. This novel mechanism could contribute to the observation that biological diversity has increased over geological time regardless of the well-known massive extinctions.

Kirzhner V., Korol A., Nevo E. (1998). Complex limiting behavior of multilocus genetic systems in cyclical environment. J. Theoretical Biol. 190 3, 215-225.(Article.complex)


  • Temporally varying selection is considered to be one of the potential mechanisms of recombination evolution. We found earlier that simple cyclical selection for a trait controlled by multiple additive, dominant or semi-dominant loci can result in extremely complex limiting behaviour (CLB) of population trajectories, including supercycles and more complex attractors. Recombination rate proved to be a key factor affecting the mode of CLB and the very existence of CLB. Therefore, we considered here a generalized model: the fixed recombination rate was replaced by a polymorphic recombination modifier. The modifier-dependent changes included: (a) supercyclical dynamics due to the recombination modifier in a system that does not manifest CLB when recombination rate is a fixed parameter; (b) appearance of a new level of superoscillations (super-supercycles) in a system that manifests supercycles with a fixed modifier; (c) chaotization of the regular supercyclical dynamics. The domain of attraction of these movements appeared to be quite large. It is noteworthy that the modifier locus is an active participant in the observed non-monotonic limiting movements. Interactions between short-period forced oscillations and the revealed long-period auto-oscillations appeared to result in new regimes of recombination evolution (for some range of linkage between the modifier locus and the selected system), as compared with those caused by the forced oscillations alone.

Korol A.. Kirzhner V., and Nevo E. (1998). Dynamics of recombination modifiers caused by cyclical selection: interaction of forced-and auto-oscillations. Genetical Research, 69, 135-147.(Article.modif)


  • This paper deals with the problem of polymorphism maintenance in species coevolution mediated by selection for quantitative traits controlled by Mendelian genes. We showed here that the conditions for polymorphism maintenance in interacting species can be deduced from the behavior of the isolated partners in stable and changing environments. This allows also to address such difficult questions as evolution of sex and recombination, that can not be considered properly in non-Mendelian models. An abundance of polymorphic regimes was revealed in the proposed genetic model. The obtained results demonstrate a remarkable property of trait-dependent coevolution concerning the conditions for maintenance of genetic polymorphism: what seems to be more realistic, that is, non-equal gene effects and deviation from purely additive within-locus gene action, promotes polymorphism.

Kirzhner V., Korol A., Nevo E. (1999). Abudant multilocus polymorphisms caused by genomic interaction between species on trait-for-trait basis. Journal Theoretical Biology, 198,361-70.(Article.abudant)


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