Interrelation of the genetic structure evolution and the modes of population dynamics

Frisman E.Ya., Zhdanova O.L.1, Neverova G.P.

Institute for complex analysis of regional problems, FEB RAS, Russia,Birobidzhan

The population number dynamics and change in the genetic structure of a population are in complex multiple cause-effect relations. The quantitative analysis of this interrelation is still an important fundamental problem. We have developed some mathematical evolutionary models for the dynamics of populations uniting both genetic and ecological approaches to investigate this problem.

These models analysis shows us that the evolutionary change of adaptive alleles frequencies accompanied by the population average fitness increase has resulted to cyclic and chaotic modes of population dynamics. The progressive increase in average fitness of ecologically limited populations proves to be dissonant with the population increase stability. This result obviously contradicts the intuitive concepts of population stability increase with its average fitness augmentation.

After that we investigated the more complex nonlinear dynamics models of age-structured populations. It was found that the average individual fitness increase leads to chaotic attractors occurrence, their structure and dimension varying with change in model parameters. In particular, the birth rate increase and the age groups death rate reduction result in complication of the attractor’s structure and the fractal dimension augmentation.

We have shown that all of the listed population dynamics modes could consistently occur in the limited population evolution affected by the density-independent natural selection increasing average fitness in populations according to the Fisher’s fundamental theorem of natural selection.

The effect of cumulative simultaneous interaction between the density-independent selection and the density-dependent non-selective ecological limiting factors is called F-selection by us. The paradox of F-selection is that being independent from density it leads to fluctuations and chaotic modes of population dynamics, creating conditions for the density-dependent selection, the type of r- and K-selection.

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