314 Margaret Morrison
P 0 =^1 / 2 (σ 0 /σ 1 P 1 )+^1 / 4 (σ 0 /σ 2 P 2 ) + 1/8 (σ 0 /σ 3 P 3 )...P 0 is the predicted deviation of an offspring from the generation mean, P 1 is
a linear function of the deviation of the mid-parent from that generation mean,
P 2 similarly for the mid-grandparent andσ 0 ,σ 1... the standard deviation of the
appropriate generations of the offspring. From this formula Pearson derived theo-
retical values for various regression and correlation coefficients between relatives.^5
Basically, Galton’s shortcomings were traceable to a lack of knowledge of the
correct formula for multiple regression.^6 Had he been able to get beyond regression
in two variates the contradiction between his law of ancestral heredity and his
interpretation of regression would have been clear; that is, the connection between
his mid-parental heredity and his law of ancestral heredity requires a knowledge
of multiple correlation. And, it was this interpretation of regression that was
responsible for his supporting discontinuous evolution. With these corrections
in place Pearson [1898] was able to reconcile Galton’s work with his own views
about variation, claiming that the ancestral law formed the fundamental principle
of heredity from which all the numerical data of inheritance could be deduced, at
least to a first approximation. The extent to which Pearson distanced the law from
specific biological hypotheses is evident from his remark that the confidence he put
in the truth of the law was “not measured” by any of Galton’s empirical research
however strong that evidence may be; instead his support for it was grounded in
the fact that it gave “a priorithe correlation between parents and offspring and
that this correlation is practically identical with the value [he had] determined
from these and other observations” [1895, 387].^7
There are a number of different issues intertwined here, Mendelism vs. blend-
ing inheritance, Darwinism vs. saltation and biology vs. statistics, each of which
needs to be clarified before proceeding. As we saw above Galton’s work engaged
both Mendelism and Darwinism in that he advocated natural selection as an im-
portant feature of evolutionary change, but his theory of heredity was more in
line with what would later be identified as Mendelism than with the gradualism
that characteristic of Darwinism. The Darwinian account emphasised the action
of selection on small alterations that resulted from a blending of the ancestral
traits while Mendelism advocated discontinuously varying traits. This distinction
between continuity and discontinuity was also at the source of the difference be-
tween Darwinism and saltation where the latter describes the evolutionary process
as involving sudden changes in the equilibrium of a species where there is a leap
(^5) He also generalized the geometric series of partial regression coefficients which raised the
parental correlations.
(^6) See [Pearson, 1930, 77–78].
(^7) Pearson further refined Galton’s law in 1900 where he distinguished a law of reversion from
the true ancestral law. In cases of blended inheritance the law of ancestral heredity predicts the
probable character of the individual produced by a given ancestry while in cases of alternative
inheritance the law tells us the percentages of the total offspring which, on average, revert to
each ancestral type. The first is the true law of ancestral heredity while the second he termed
the law of reversion. Both laws assume a geometrically waning ancestral dilution.