510 Paul Thompson
a confirmation of the phenomenon of segregation and recombination in the new
field of cytology.
Building on this early work, a sophisticated mathematical model of the complex
dynamics of heredity emerged during the 1920s and 1930s, principally through
the work of John Haldane [1924; 1931; 1932], Ronald Fisher [1930] and Sewall
Wright [1931; 1932]. What has become modern population genetics began during
this period. From that period, the dynamics of heredity in populations has been
studied from within a mathematical framework.^38
As previously indicated, one of the fundamental principles of the theory of
population genetics, in the form of a mathematical model, is the Hardy-Weinberg
Equilibrium. Like Newton’s First Law, this principle of equilibrium states that
after the first generation if nothing changes then allelic (gene) frequencies will
remain constant. The presence of a principle(s) of equilibrium in the dynamics
of a system is of fundamental importance. It defines the conditions under which
nothing will change. All changes, therefore, require the identification of cause(s)
of the change. Newton’s dynamics of motion include an equilibrium principle that
states that in absence of unbalanced forces an object will continue in uniform
motion or at rest. Hence acceleration, deceleration, change of direction all require
the presence of an unbalanced force. In population genetics, in the absence of some
perturbing factor, allelic frequencies at a locus will not change. Factors such as
selection, mutation, meiotic drive, and migration are all perturbing factors. Like
many complex systems, population genetics also has a stochastic perturbing force,
commonly call random genetic drift.
In what follows, the central features of the mathematical model of contemporary
population genetic theory are set out. Quite naturally, the exposition begins with
the Hardy-Weinberg Equilibrium. It is useful to begin with the exploration of
a one locus, two-allele system. In anticipation, however, of multi allelic loci, we
switch fromAandato ‘A 1 ’ and ‘A 2 ’. Hence, according to the Hardy-Weinberg
Equilibrium, if there are two different alleles ‘A 1 ’ and ‘A 2 ’ at a locus and the ratio
in generation 1 isA 1 :A 2 =p:q, and if there are no perturbing factors, then in
generation 2, and in all subsequent generations, the alleles will be distributed:
(p^2 )A 1 A 1 :(2pq)A 1 A 2 :(q^2 )A 2 A 2.The ratio ofp:qis normalised by requiring thatp+q= 1. Hence,q=1−p
and 1−pcan be substituted forqat all occurrences. The proof of this equilibrium
is remarkably simply.
The boxes contain zygote frequencies. In the upper left box, the frequency of
the zygote arising from the combination of anA 1 sperm andA 1 egg isp×p,or
p^2 , since the initial frequency ofA 1 isp. In the upper right box, the frequency of
the zygote arising from the combination of anA 2 sperm andA 1 egg isp×q,or
pq, since the initial frequency of anA 2 isqand the initial frequency ofA 1 isp.
his name is not often used in connection with the principle, probably because his results were
not in an abstract generalized form.
(^38) For an excellent history of the development of population genetics, see Provine [1971].