Some Problems of Stochastic Processes in Genetics
@article{Kimura1957SomePO, title={Some Problems of Stochastic Processes in Genetics}, author={Motoo Kimura}, journal={Annals of Mathematical Statistics}, year={1957}, volume={28}, pages={882-901} }
In genetics, stochastic processes arise at all levels of organization ranging from subunits of the gene to natural populations. Types of stochastic processes involved are also diverse. In the present paper, the following five topics have been selected for mathematical discussion and new results are presented: (1) Random assortment of subunits of a gene. (2) Senescence in paramecium due to random assortment of chromosomes. (3) Process of natural selection in a finite population (interaction…
431 Citations
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References
SHOWING 1-6 OF 6 REFERENCES
A Mathematical Theory of Natural and Artificial Selection, Part V: Selection and Mutation
- Biology
- 1927
This work shall first consider initial conditions, when only a few of the new type exist as the result of a single mutation; and then the course of events in a population where the new factor is present in such numbers as to be in no danger of extinction by mere bad luck.
Statistical genetics and evolution
- Biology
- 1942
The deductive approach, to which the author shall confine himself here, involves many questions that can only be settled by observation and experimental work on natural populations and that a remarkable resurgence of interest in such work is in progress.
Evolution in mendelian populations
- Geology
- 1931
Page 108, last line of text, for "P/P″" read "P′/P″."
Page 120, last line, for "δ v " read "δ y ."
Page 123, line 10, for "4Nn" read "4Nu."
Page 125, line 1, for "q" read "q."
Page 126, line 12,…
Stochastic processes and distribution of gene frequencies under natural selection.
- Biology, MedicineCold Spring Harbor symposia on quantitative biology
- 1955