324 Margaret Morrison
There were a variety of assumptions required for the specification of each of the
individual Mendelian factors:
- which allelomorph was dominant
- to what extent did dominance occur
- what were the relative magnitudes of the effects produced by different factors
- in what proportion did the allelomorphs occur in the general population
- were the factors dimorphic or polymorphic, to what extent were they coupled
etc.
If one assumed, as Fisher did, an indefinite number of Mendelian factors then
the nature of the population could not be specified in any complete sense; thereby
undermining any statistical result that might follow. In addition to these assump-
tions there were the more general considerations that needed to be taken into
account regarding homogomy (preferential mating) as opposed to random mating,
selection and environmental effects, all of which needed to be treated separately
if one was to determine the genetic basis of the inheritance of particular char-
acteristics. So, not only did Fisher differ from Pearson with respect to specific
assumptions about thenatureof Mendelian factors (that all were equally impor-
tant, etc.) but the way in which one characterised or ‘modelled’ a Mendelian
population was also much more general.
On the view advocated by the biometricians one needs to have variability at the
level of individuals as a basis for blending inheritance; but in order to predict how
populations will evolve one begins by averaging over this variability to arrive at
a statistical characterization of the population. By contrast, Fisher’s model of a
Mendelian population was based on the molecular models of statistical mechanics.
The idealised nature of the assumptions from that domain served as a methodolog-
ical model or analogy on which he based his own views about how to characterise a
Mendelian population. Knowledge of individuals simply wasn’t important; hence
the idea that each was a source of variation had no role to play in the general
conception of the population; variation came at the level of Mendelian characters.
But this kind of idealisation or abstraction over the domain of individuals could
not be accommodated in Pearson’s model world. His objections were not simply
to the presence of idealising assumptions since his own statistical methods and the
process of averaging obviously involved idealisations as well. Instead, what Pear-
son objected to was thekindsof idealisations Fisher used. Detailed knowledge of
the Mendelian factors that characterized the individuals in the population was not
considered. Instead one could simplyassumean indefinite number of such factors
and then average over these. But, as we saw above, Pearson thought that many
different specifications were required for each factor, and because these factors
were understood as the defining characteristics of the individual it was anathema
to Pearson that they not be explicitly specified.