Problems of regular behaviour and deterministic chaos in mathematical models of Mendelian limited populations

We investigate the fitness differences model with Mendelian one-locus di-allele limited population in cases of linear and exponential rules of selection. We present an analytical and numerical investigation of the model. The possibility of population number fluctuations with stable genetic structure was shown. Also found were joint fluctuations of genetic structure and population number. This result contradicts the well-known hypothesis of "genetic control" . The stable chaotic attractors with non-integer dimensions were found. It was made the generalization of model for polyallele population with some admissions and its analytical investigation was carried out.