508 Paul Thompson
3.2 Formalisation in Population Genetics
The phenomenon of heredity, although widely accepted since at least the Greco-
Roman period, is extremely complex and an adequate theory proved allusive for
several thousand years. Indeed, features of heredity seemed almost magical. Breed-
ers from antiquity had a sophisticated understanding of the effects of selective
breeding but even the most accomplished breeders found many aspects of heredity
to be capricious. Even Darwin in the middle 19thcentury knew well the techniques
of selective breeding (artificial selection) but did not have available a satisfactory
theory of heredity when he published theOrigin of Species[1859]. Although, he
realized that his theory of evolution depended on heredity, he was unable to pro-
vide an account of it. Instead, he relied on the widely known effects of artificial
selection and by analogy postulated the effects of natural selection in which the
culling of breeders was replaced by forces of nature.
The first major advance came from the simple experiments and mathemati-
cal description of the dynamics of heredity by Gregor Mendel [1865]. Although
Mendel’s work went largely unnoticed until the beginning of the 20thcentury,
its great strength lay in its mathematical description — elementary though that
description was. Mendel performed a number of experiments which provided im-
portant data but it was his elementary mathematical description of the underlying
dynamics that has had a lasting impact on genetics. His dynamics were uncompli-
cated. He postulated that a phenotypic characteristic (characteristic of organisms)
is the result of the combination of two “factors” in the hereditary material of the
organism. Different characteristics are caused by different combinations. Focusing
on one characteristic at a time made the problem of heredity tractable. Factors
could be dominant or recessive. If two dominant factors combined, the organism
would manifest the characteristic controlled by that factor. If a dominant and a
recessive factor combined, the organism would manifest the characteristic of the
dominant factor (that is the sense in which it is dominant). If two recessive factors
combine, the organism will manifest the characteristic of the recessive factor.
Mendel postulated two principles (often now referred to as Mendel’slaws): a
principle of segregation and a principal of independent assortment. The principle
of segregation states that the factors in a combination will segregate (separate)
in the production of gametes. That is gametes will contain only one factor from
a combination. The principle of independent assortment states that the factors
do not blend but remain distinct entities and there is no influence of one factor
over the other in segregation. The central principle is the law of segregation. The
law of independent assortment can be folded into the law of segregation as part of
the definition of segregation. When gametes come together in a fertilised ovum (a
zygote), a new combination is made.
AssumeAis a dominant factor andais a recessive factor. Three combinations
are possibleAA,Aa andaa. Mendel’s experimental work involved breedingAA
plants andaaplants. He then crossed the plants which produced onlyAaplants.
He then bred theAa plants. What resulted was .25AA,.5Aa and .25aa.His