68 Sahotra Sarkar
a general account of evolution: (i) discontinuous changes (for instance through
hybridization); and (ii) the mutations to generate the necessary variation. As
Haldane put it:
if we come to the conclusion that natural selection is probably the
main cause of change in a population, we certainly need not go back
completely to Darwin’s point of view [though without cause (b)]. In
the first place we do have reason to believe that new species may arise
quite suddenly, sometimes through hybridisation, sometimes perhaps
by other means. Such species do not arise, as Darwin thought, by nat-
ural selection. When they have arisen they must justify their existence
before the tribunal of natural selection, but that is a very different
matter....
Secondly, natural selection can only act on the variations available, and
these are not, as Darwin thought, in every direction. In the first place,
most mutations lead to a loss of complexity.... This is probably the
reason for the at first sight paradoxical fact that... most evolutionary
change has been degenerative. But further,... mutations only seem
to occur along certain lines, which are very similar in closely related
species, but differ in more distant species. (pp. 138–140)
For the next generation of population geneticists, the Appendix ofThe Causes
of Evolutionwas at least as important as the text. In the Appendix, Haldane sum-
marized the mathematical results obtained by Fisher, Wright and himself. Given
that Fisher had uncharitably altogether ignored both Haldane’s and Wright’s work
in theGenetical Theory, and Wright did not write a general review or book during
this period, this Appendix becane the only compendium of mathematical genetics.
Besides the summary, Haldane presented a new analysis of altruism. Explaining
altruism within families, or in insect societies where many individuals were genetic
clones of each other, was relatively straightforward. But Haldane went further:
consider a group ofNdiploid individuals, mating at random with respect to the
altruism trait in a one locus-twoalleles (A,a) model with complete recessivity.
Then the relative proportions of the three possible genotypes areu^2 nAA:2unAa:
1 aa. Let the recessives,aa, leave (1 -k) times as many progeny as theAAorAa
(0<k<1). Thus the altruism trait decreases individual fitness. However, let
the presence of a proportionxof altruistic (aa) individuals result in an increase
in the probably progeny of all individuals by a factor (1 +Kx). If it is assumed
that a group consisting entirely of altruistic individuals should grow,K>k.In
the next generation, sincex=(1+^1 un) 2 , the size of the group will have increased to
N
[
1+(1+Kun) 2]. The recessive allele number will thus have changed from1+Nun
toN
[
1+(1+Kun) 2]
un+1−k
(1+un)^2. NeglectingkK, the change in the number ofaalleles,
∆xis then given by:
∆x=N((1+Kun)−k)
(1 +un)^2
.