322 Margaret Morrison
where two independent causes of variability acting together produce a variance
which is the sum of the variances produced by either separately. Hence, each con-
stituent cause is expressed as a fraction or percentage of the total variance that
they jointly produce.
What Fisher wanted to do was determine the extent to which characteristics
such as stature were determined by a large number of Mendelian factors. Studies
had shown that in the case of brothers the correlation coefficient was around .54,
(amount of variance due to ancestry) which leaves 46 percent of the variance to be
accounted for in some other way. Both Galton and Pearson had shown that this
could not be due to environmental effects and moreover, Galton himself determined
that the variance is far less in identical twins. According to the Mendelian hypoth-
esis the large variance among children of the same parents is due to the segregation
of those factors in respect to which the parents are heterozygotes. Yule had earlier
argued that the effects of dominance and the environment in reducing correlations
between relatives were identical, something that Fisher hoped to disprove by sep-
arating how much of the total variance was due to dominance, how much resulted
from other environmental causes and how much from additive genetic effects. If
one could resolve observed variance into these different fractions (i.e. expressing
these fractions as functions of observed correlations) then one could easily deter-
mine the extent to which nature dominated over nurture. The paper succeeded
in showing that the hypothesis of cumulative (multiple) Mendelian factors (genes)
fit the observed data and so provided a plausible hypothesis for the inheritance of
continuous variates like stature. He demonstrated that the effect of dominance in
individual effects expressed itself in a single dominance ratio. And, using frater-
nal correlation Fisher was able to determine the dominance ratio and distinguish
dominance from all non-genetic causes such as environment (which might possibly
lower correlations). Essentially what Fisher succeeded in doing was distinguish-
ing not only between genetic and environmental variance but also between the
different components of genetic variance itself.
But what exactly was it that enabled Fisher to perform this kind of statistical
analysis? Largely it was due to a significant departure from the kind of methodol-
ogy employed by Pearson and the biometricians. Fisher made a number of explicit
assumptions that were clearly at odds with Pearson’s earlier work [1904] and [1909].
His main complaint was that Pearson’s method was too restrictive with respect to
the nature of Mendelian factors. Contra Pearson he did not assume that different
Mendelian factors were of equal importance and allowed that different phases of
each could occur in any proportions consistent with the conditions of mating. The
heterozygote could take any value between dominant or recessive (and even out-
side that range) resulting in the terms loosing their polarity and becoming simply
the means of distinguishing one pure phase from the other. So, all dominant genes
did not have a like effect. In order to simplify his calculations Fisher also assumed
random mating as well as the independence of the different factors. Finally, and
perhaps most importantly, he assumed that the factors were sufficiently numerous
so that some small quantities could be neglected.