The Development of Population Genetics 319tained over successive generations? The reason for the stability could be traced
directly to the absence of fusion which was indicative of a type of genetic structure
that could conserve modification. The constancy of the Mendelian ratios can be
seen as a property of genetic structure. In that sense then one can see the Hardy-
Weinberg law as the beginnings of a new understanding of the role of mutation
and selection and how they affect our understanding of evolution.
In 1903 the American geneticist William Castle (1867-1962) was the first to at-
tempt an account of selection using Mendelism. His work went largely unnoticed
but a more sophisticated version was given by the biologist Punnett in 1915 in
a book entitledMimicry in Butterflies. However, it was not until 1918 and the
publication of R.A. Fisher’s paper “On the Correlation between Relatives on the
Supposition of Mendelian Inheritance” that a truly quantative account of the op-
eration of selection as a process of gene replacement in Mendelian populations was
given. But, establishing the relation between Mendelism and Darwinism was not
an easy task; efforts to do so suffered strong opposition from Pearson’s biometric
school, despite the fact that Fisher himself used biometric methods in arriving at
his conclusions. The way the story unfolds is important not only from the point of
view of mathematising genetics but also because of the nature of the idealisations
introduced by Fisher. We saw above that the Hardy-Weinberg law introduced
certain idealizing assumptions about the size of populations and the fact that they
were not acted upon by outside influences. What Fisher’s work does is introduce
other kinds of idealizing assumptions that characterise populations; assumptions
that Pearson and some Mendelians felt were unacceptable for representing biolog-
ical individuals and populations.
3 FROM STATISTICAL BIOLOGY TO MATHEMATICAL POPULATIONSWhile Fisher is usually credited with showing that natural selection operates
in Mendelian populations, thereby reconciling Darwinain and Mendelian views
on heredity and evolution, it is important to emphasise that he also reconciled
Mendelian and biometricapproachesto the problem of heredity. In other words,
not only did his synthesis involve a substantial claim about the mechanisms of
inheritance but also a methodological solution to a problem that for Pearson was
irreconcilable. The idea that Mendelism and Darwinism might be compatible was
pursued and developed by Pearson in [1904]. There he showed that if a trait like
stature depended linearly and additively onnindependent Mendelian loci, each
with complete dominance, the expectation of the distribution of stature for large
nwould be very close to the normal (due to the normal approximation for the
binomial distribution). Although these same suppositions led to an expectation of
linear regression between relatives, the regression coefficients took values that dif-
fered from Pearson’s own investigations — 1/3 as opposed to 0.45-0.5. Moreover,
the size ofnwas found not to affect the predicted value, whereas his observations
led to regression coefficients that varied from organ to organ and species to species.
Instead of interpreting the results as evidence for a possible confirmation of