Haldane and the Emergence of Modern Evolutionary Theory 59The slowness of the response to selection bothered Haldane. He worried whether
the theory would satisfy the critical requirement: that selection must be able to
“cause [a species] to change at a rate which will account for present and past
transmutations” (p. 19). Change was most rapid if amphimixis (gametic fu-
sion during sexual reproduction) could be avoided but this was not an option for
most populations. Moreover, he observed, selection was particularly ineffective on
most recessive traits. He suggested four ways of escaping from this conclusion:
(i) self-fertilization or intense inbreeding; (ii) assortative mating; (iii) incomplete
dominance; and (iv) heterozygote advantage. He also raised the possibility that
isolation preferentially benefits the spread of recessives over dominants.
The first two of these factors — (i) self-fertilization and inbreeding and (ii) as-
sortative mating — were taken up in Part II of this series of papers, incomplete
dominance in Part III, and Haldane provided a general discussion of isolation in
Part VI. If recessives were rare, self-fertilization and inbreeding greatly helped
their spread. However, assortative mating had very little effect [Haldane, 1924b].
Incomplete dominance of an autosomal trait could help the spread of recessives;
with sex-linked traits, it was of little help [Haldane, 1926]. Part III also included
pioneering discussions of models of selection with multiple alleles at one locus;
selection with tetraploidy; as well as a two locus model with linkage but no selec-
tion, where Haldane [1926] apparently independently rederived (with less elegance)
some of the results of Robbins [1918b]. In Part IV, Haldane [1927a] turned to a
demographic model with overlapping generations.^19 The mathematical tools re-
quired for the analysis of this model proved to be far more sophisticated than
anything that had been necessary in the earlier papers: difference equations had
to be replaced by integral equations. Most of Haldane’s results had been previ-
ously obtained by Norton in 1910, and proved with much more rigor though they
(^19) In passing, he provided a new — and simple — proof of Lotka’s [1922] theorem of the stability
of the normal age distribution.