A burning question in the field of biology arose at the beginning of the 19th
century. Would brown eyes eventually take over and blue eyes die out? Would
blue eyes become extinct? The answer was a resounding ‘No’.
The Hardy–Weinberg law
This was explained by the Hardy–Weinberg law, an application of basic
mathematics to genetics. It explains how, in the Mendelian theory of inheritance,
a dominant gene does not take over completely and a recessive gene does not
die out.
G.H. Hardy was an English mathematician who prided himself on the non-
applicability of mathematics. He was a great researcher in pure mathematics but
is probably more widely known for this single contribution to genetics – which
started life as a piece of mathematics on the back of an envelope done after a
cricket match. Wilhelm Weinberg came from a very different background. A
general medical practitioner in Germany, he was a geneticist all his life. He
discovered the law at the same time as Hardy, around 1908.
The law relates to a large population in which mating happens at random.
There are no preferred pairings so that, for instance, blue-eyed people do not
prefer to mate with blue-eyed people. After mating, the child receives one factor
from each parent. For example, a hybrid genotype bB mating with a hybrid bB
can produce any one of bb, bB, BB, but a bb mating with a BB can only produce
a hybrid bB. What is the probability of a b-factor being transmitted? Counting the
number of b-factors there are two b-factors for each bb genotype and one b
factor for each bB genotype giving, as a proportion, a total of three b-factors out
of 10 (in our example of a population with 1:1:3 proportions of the three
genotypes). The transmission probability of a b-factor being included in the
genotype of a child is therefore 3/10 or 0.3. The transmission probability of a B-
factor being included is 7/10 or 0.7. The probability of the genotype bb being
included in the next generation, for example, is therefore 0.3 × 0.3 = 0.09. The
complete set of probabilities is summarized in the table.