62 Sahotra Sarkar
Haldane had begun to appreciate how stochastic factors could influence the
course of evolution. In Part VIII, perhaps the most interesting of the entire series
of papers, he analyzed a two locus-two allele model with complete dominance and
extended this discussion to a rudimentary analysis ofnloci [Haldane, 1931b]. If
there are two alleles at each locus, the genotypic space is ann-dimensional hy-
percube, with the genotypes at the vertices and edges connecting those genotypes
that differ exactly at one locus. If fitnesses are assigned at random to these geno-
types, there are at most 2n−^1 stable points, that is, genotypes which were fitter
than their nearest mutational neighbors. Haldane called populations in which such
stable genotypes were fixed “metastable”. The paper concluded with an intriguing
remark: “It is suggested that in many cases related species represent stable types
such as I have described, and that the process of species formation may be a rup-
ture of the metastable equilibrium. Clearly such a rupture will be specially likely
where small communities are isolated” [1931b, 141–142]. He had fully realized
the power of stochastic factors, and this remark was an anticipation of Wright’s
“shifting balance theory” of evolution (see below). But it was no more than that
— Haldane did not pursue the idea any further. In fact, Wright [1931] had just
published the first version of that theory but that paper was unknown to Haldane
when Part VIII was written.
Meanwhile, in Part VII, another intriguing paper, Haldane [1931a] analyzed the
relation between competition and selection. Competition was modeled by what
has come to be known as “truncation selection”, acting on a normally distributed
character: all individuals with a value higher than a specified value were eliminated
from the population. Haldane showed that the intensity of selection may, under
certain circumstances, decrease with an increase with the intensity of competition.
This paper drove home the power of quantitative analysis on which Haldane had
insisted right from Part I. As he put it, quantitative analysis showed that the
assumption “often made that when competition is extremely intense at any stage
in a life cycle, natural selection is bound to be intense also” [1931a, 131], was
false. In fact, and even more surprising, “the intensity of selection may diminish
and become negative at high rates of elimination” [1931a, 131]. Quantitative
analysis thus exposed the limitations of qualitative argument.
In Part IX, Haldane [1932a] took up a one-locus model of rapid selection acting
on a diploid model with full dominance. The model was the same as the one he
had analyzed in Part I except, now, he set out to find an approximate solution of
equation (4.1) without assuming that|k|<<1.^23 The analysis permitted a quan-
titative evaluation of the ecologist, Charles Elton’s [1927] intriguing suggestion
that episodic intense selection, such as that due to plagues or famines, was more
effective in changing the composition of a population than less intense selection
acting every generation. Haldane found that this was true if selection favored the
dominants, but not if it favored the recessives. Once again, quantitative analysis
revealed intricacies that no amount of qualitative argument could have shown.
(^23) The mathematical difficulty of finding such a solution was formidable, and Haldane [1932c]
published the formal analysis separately.