Evolution in Mendelian Populations
Genetics, 16 (2):
97-159 (March 1931)Abstract
One of the major incentives in the pioneer studies of heredity and varia-
tion which led to modern genetics was the hope of obtaining a deeper insight
into the evolutionary process . Following the rediscovery of the Men-
delian mechanism. there came a feeling that the solution of problems of
evolution and of the control of the process. in animal. and plant breeding
and in the human species, was at last well within reach. There has been
no halt in the expansion of knowledge of heredity but the advances in
the field of evolution have, perhaps, seemed disappointingly small. One
finds the subject still frequently presented in essentially the same form as
before 1900, with merely what seems a rather irrelevant addendum on
Mendelian heredity.
The difficulty seems to be the tendency to overlook the fact that the
evolutionary process is concerned, not with individuals, but with the
species, an intricate network of living matter, physically continuous in
space-time, and with modes of response to external conditions which i t
appears can be related to the genetics of individuals only as statistical
consequences of the latter. From a still broader viewpoint (compare LOTKA
1925) the species itself is merely an element in a much more extensive
evolving pattern but this is a phase of the matter which need not concern
us here.
LATER: The population number
It will be well to discuss more fully, before going on, what is to be under-
stood by the symbol N used here for population number. The conception
is that of two random samples of gametes, N sperms and N eggs, drawn
from the total gametes produced by the generation in question (N/2 males
and N/2 females each with a double representation from each series of al-
lelomorphs). Obviously N applies only to the breeding population and
not to the total number of individuaIs of all ages. If the population fluctuates greatly, the effective N is much closer to the minimum number than
to the maximum number. If there is a great difference between the number
of mature males and females, i t is closer to the smaller number than to the
larger. I n fact, as just shown, a population of N, males and an indefinitely
large number of females is approximately equivalent to a population of
4N, individuals equally divided between males and females.
The conditions of random sampling of gametes will seldom be closely ap-
proached. The number of surviving off spring left by different parents may
vary tremendously either through selection or merely accidental causes,
a condition which tends to reduce the effective N far below the actual
number of parents or even of grandparents. How small the effective N of
a population may be is indicated by recent studies of SMITH and CALDER
(1927) on the Clydesdale breed of horses in Scotland, in which they find
a steady increase in the degree of inbreeding (Coefficient F) equivalent to
that in population headed by only about a dozen stallions. Even more
striking is the rapid increase in the coefficient of inbreeding in the early
history of the Shorthorn breed of cattle (MCPHEE and WRIGHT 1925).