37 Genetics
Genetics is a branch of biology, so why is it in a mathematics book? The answer is that
these two subjects cross-fertilize and enrich each other. The problems of genetics
require mathematics but genetics has also suggested new branches of algebra. Gregor
Mendel is central to the whole theme of genetics, the study of human inheritance.
Hereditary characteristics such as eye colour, hair colour, colourblindness, left/right-
handedness and blood group types are all determined by factors (alleles) of a gene.
Mendel said that these factors pass independently into the next generation.
So how could eye-colour factor be transmitted to the next generation? In the
basic model there are two factors, b and B:
b is the blue eyes factor
B is the brown eyes factor
Population representing the proportions 1:1:3 of genotypes bb, bB and BB
In individuals, the factors appear in pairs giving rise to possible genotypes bb,
bB and BB (because bB is the same as Bb). A person carries one of these three
genotypes, which determines their eye colour. For example, a population could
consist of a fifth of people with the genotype bb, another fifth with the genotype
bB and the remaining three-fifths with the genotype BB. In terms of percentages,
these genotypes would make up 20%, 20% and 60% of the population. This can
be represented by a diagram showing these proportions of genotypes.
The factor B, which denotes brown eye colour, is the dominant factor and b,
the blue eye colour is the recessive factor. A person with a pure genes genotype
BB will have brown eyes, but so too will a person with mixed factors, that is,
those with a hybrid genotype bB because B is dominant. A person with the pure
genes genotype bb will be the only genotype to show blue eyes.