The Mathematical Basis of Population Genetics?
- 9 July 1973
- journal article
- research article
- Published by Taylor & Francis in International Journal of Mathematical Education in Science and Technology
- Vol. 4 (3) , 329-333
- https://doi.org/10.1080/0020739730040312
Abstract
In this paper the topic known to biologists as population genetics is presented in terms of the Cartesian product. The gene, being a set of an ordered pair of elements (alleles), provides an example of a lattice in which the axes represent the composition of the gene in respective parents, and shows as co‐ordinates the possible genetic composition of individuals of the next generation with respect to that gene. When the axes are made to represent, respectively, the set of male and female parents of a population as a whole then it is the next generation as a whole that is represented by the co‐ordinates. Population genetics is also shown to provide an example of the binomial expansion (p+q)n in which n is 2, while on those occasions when the gene can be composed of any two of a number of elements (alleles) it expands to (p+q + r+ ... + w)2 with p,q,r.....w, each representing the frequencies of an allele of the gene in the population. It is upon these mathematical models that the study of population genetics depends and the incidence of alleles in any population is established.Keywords
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