Abstract
The consequences of background-level radiation often provoke debates, and here statistical ideas and their mathematical basis are considered in view of adaptation processes. Statistical modelling presents the data of investigations in the form of frequency function of events occurrence that allows studying the laws and regularities of respective probability processes. It is qualified to investigate the processes induced by the low factors and accompanied by Darwinian selection in different systems. Three themes are discussed: (1) A geometric model of adaptation, (2) Research of the biological communities’ structure, and (3) A statistical view of the cytogenetic investigations of instabilities. The first and second topics present development of statistical ideas on live systems under environmental conditions. The last part is devoted to models of appearance of cells with abnormalities, chromosomal abnormalities in cells, proliferated cells and interrelation between the distributions on the number and frequency of abnormalities. We can assume that a strong factor leads to the same laws of regulated abundance of the communities of species and cell population.
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Notes
- 1.
The full paper is published in (Florko and Korogodina 2007).
- 2.
- 3.
We suggested that the probability of the appearance of late damage in the non-damaged target due to induction by two or more damages is small.
- 4.
A.N. Kolmogorov studied the lognormal distribution of particle sizes under fragmentation. This process has to fulfill the condition that the sum of the fragment sizes does not exceed the whole particle size. This condition is fulfilled for any processes of reproduction in nature, as for cells, and for any live species.
- 5.
It is appropriate here to refer to F.W. Preston, who introduced a lognormal distribution into biology (Preston 1948, 1962). He described a distribution of the species in the natural community on their numbers by the lognormal law. The comparison inevitably comes to mind between the numbers of cells in sprout meristem and the numbers of species in the community. Maximal numbers of plants and species correspond to the fitness conditions for propagation of each of these objects.
- 6.
Earlier, we considered not the binomial, but the Poisson law of the appearance of CCAs (Florko and Korogodina 2007; Korogodina and Florko 2007). The Poisson law corresponds to the case of a great number of PCs, among which a rare number of CCAs (k) appeared. The binomial law describes the case, when the number of PCs (n) is low. Poisson (n is great) and Gauss (n, k are great) laws can be obtained by the limiting process from the binomial law (Feller 1957).
- 7.
- 8.
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Korogodina, V.L., Florko, B.V., Osipova, L.P. (2013). Excursus on Statistical Modelling for Population Biology. Statistical Solution of Some Radiobiological Tasks. In: Radiation-Induced Processes of Adaptation. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6630-3_3
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