Equilibrium in the Population of the Plants

Gennadiy Vladimirovich Zhizhin


On the basis Mendel's experiments, a mathematical model is constructed that describes the results of these experiments in a wide range of parameters. This model is compared with the Hardy -Weinberg logistic model, based only on probabilistic ideas about the presence of dominant and recessive alleles in the chromosomes of living organisms. There is shown that in the mathematical model of Mendel's experiments, based on real patterns of plant development, there are equilibrium positions between the dominant and recessive forms. Its consists in the fact that with an increase in the number of generations of the number all of dominant and recessive phenotypes of organisms, with any number of sings, they quickly equalize and then synchronously (in the absence of death of organisms) increase together, seeking asymptotically to a stable isolated equilibrium position of the type of a multidimensional node. This newly discovered behavior of the dominant and recessive forms in the vicinity of the equilibrium position (true) differs significantly from the logistic equilibrium position in the Hardy -Weinberg principle, built without taking into account the real patterns in the plant population.


Plant, Chromosome, Crossing, Hybrid, Allele

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