The Development of Population Genetics 323The simplifyingmethodologicalassumptions involving independence and an in-
definitely large number of Mendelian units were based on the analogy with gas
theory that Fisher alluded to in his earlier [1915] work. Essentially he treated
large numbers of genes in a way similar to the treatment of large numbers of
molecules and atoms in statistical mechanics. By making these simplifying and
idealising assumptions Fisher was able to calculate statistical averages that ap-
plied to populations of genes in a wayanalogousto calculating the behaviour of
molecules that constitute a gas. But, it is important to stress that the analogy was
a methodological one. If he could construe populations of genes on analogy with
the way statistical mechanics construes populations of molecules, he could perhaps
arrive at solutions that might be applicable to the kinds of populations studied by
the biometricians — large ones that displayed certain phenotypic characteristics.
Pearson, who acted as a referee for the paper, objected that the hypothesis of
an indefinitely large number of Mendelian characteristics was out of the region
of experiment using Mendelian methods. Although he was entirely comfortable
dealing with large populations (a corner stone of biometric methods), the idea that
the manifestation of a character was the result of anindefinitelylarge number of
Mendelian factors was anathema. And, while he acknowledged that one could
increase the number of factors under consideration, from two to perhaps even
four, the idea that these could increase indefinitely was something he took to be
amenable to neither proper statistical/biometrical analysis nor experimental tests
of the kind favoured by the Mendelians. The other referee, Punnett (a Mendelian),
also focused on this assumption. He pointed out that although there were cases
worked out for three factors, the mathematics proved very laborious, making it
unlikely that Fisher’s assumption could ever be tested by experiment. In fact
he put the point rather strongly in a remark comparing this kind of work with
problems that deal with “weightless elephants on frictionless surfaces, where at
the same time we are largely ignorant of the other properties of the said elephants
and surfaces” [Norton and Pearson, 1976, 155].
But for Fisher this degree of idealisation was essential to guarantee his method,
and hence the legitimacy of its conclusions. In other words, he could escape the
difficulties associated with detailed Mendelian analyses by focussing on general
principles. But in order to do this it was necessary that he assume a large num-
ber of factors in order to establish statistically the generality and validity of the
principles. In the way that one can have knowledge about the properties of gases
without detailed knowledge of the molecules and atoms that make up the gas,
one could have knowledge of how a population would evolve without knowing the
details of the heredity of all individual characteristics. And, an indefinite number
of traits was essential to the process of averaging that yielded such knowledge.
The important issue here concerns the correct way to model populations. The
notion of a population as a way of thinking about groups of organisms had become,
for the biometricians, a cornerstone of Darwinian evolutionary theory. Pearson had
specific views about how populations ought to be characterised if one was to be
able to test the extent to which Mendelism accorded with biometrical findings.