318 Margaret Morrison
stable equilibrium should be established from the second generation. In other
words, no dominant character would have influence over a population. The law
states that the Mendelian 1:2:1 ratio will be stable from one generation to the next
under conditions of random breeding, provided that there are no outside influences
like mutation or selection (except for balanced rates) and the population is large
enough to rule out sampling errors. This can be expressed as the expansion of the
algebraic binomial p^2 +2pq+q^2 = 1.0 where p is the frequency of A and q the
frequency of a in the population as a whole.
The Hardy-Weinberg law was also formulated independently in 1908 by Wilhelm
Weinberg (1862-1937) a German obstetrician. The law can be understood as
a direct consequence of Mendel’s law of segregation. Mendel’s studies indicated
that an immediate consequence of segregation in self-fertilizing organisms like peas
was an orderly and predictable decrease in the proportion of heterozygotes in
successive generations produced from a cross between two initial homozygotes.
Hence, inbreeding should result in a gradual reversion of offspring populations to
the original homozygotic parental types. So, when non-random mating is the rule
the frequency of heterozygotes will be expected to decline; in other words, the
splitting of Aa hybrids into A+2Aa+a offspring leads to a progressive reduction
in the proportion of Aa hybrids. After n generations the population will have the
following structure: (2n-1)A:2Aa(2n-1)a.
What is significant about the Hardy-Weinberg law is not so much the bino-
mial form of the genotype frequency and the prediction of genotypes based on
the stability of the population, but rather what the stability actually shows or
presupposes. Despite the idealizing assumptions the stability allows us to under-
stand something about Mendelian populations that is significant for understanding
heredity and variation. What it says is that if no external forces act then there
is no intrinsic tendency for the variation caused by the three different genotypes
that exist in a population to disappear. It also shows that because the distribu-
tion of genotype frequencies is independent of dominance, dominance alone cannot
change genotype frequencies. In other words, there is no evidence that a dominant
character will show a tendency to spread or a recessive one die out. Instead the
genotypes frequencies are maintained in constant proportions. The probabilistic
genetic structure is conserved indefinitely; but should it be influenced by an out-
side force, e.g. mutation, the effect would be preserved in a new stable distribution
in the succeeding generation. In other words, it expresses the variation preserving
character of the hereditary mechanism and gives a specification of the number of
generations required to alter gene frequencies.
This was crucial for understanding the debate between the Darwinians who
advocated blending inheritance and the Mendelians. Under blending inheritance
variation was thought to decrease rapidly with each successive generation, but
Hardy-Weinberg shows that under a Mendelian scheme it is maintained. This
pointed to yet another fundamental aspect of Mendelism, namely the discontinu-
ous nature of the gene, and why it was important for the preservation of variation
required for selection. How was it possible for the genetic structure to be main-