## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 28, Number 4 (1957), 882-901.

### Some Problems of Stochastic Processes in Genetics

#### Abstract

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 between selection and random genetic drift). (4) Chance of fixation of mutant genes. (5) Population structure and evolution. Finally it is pointed out that new mathematical techniques will be needed for a satisfactory treatment of Wright's theory of evolution.

#### Article information

**Source**

Ann. Math. Statist. Volume 28, Number 4 (1957), 882-901.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aoms/1177706791

**Digital Object Identifier**

doi:10.1214/aoms/1177706791

**Mathematical Reviews number (MathSciNet)**

MR94267

**Zentralblatt MATH identifier**

0085.14101

**JSTOR**

links.jstor.org

#### Citation

Kimura, Motoo. Some Problems of Stochastic Processes in Genetics. Ann. Math. Statist. 28 (1957), no. 4, 882--901. doi:10.1214/aoms/1177706791. http://projecteuclid.org/euclid.aoms/1177706791.