The Interaction of Selection and Linkage. I. General Considerations; Heterotic Models
Genetics, 49 (1):
49-67 (January 1964)Abstract
WHILE the theory of the genetic changes in a population due to selection is
quite well understood for single loci, our theory for multiple-gene characters
is in a rudimentary stage. Most of the formulations for multiple-gene characters
are simply extensions of single-locusmodels, extensions which ignore the problem
of linkage. There are, however, a few papers in which the role of linkage has been
1956; LEWONTIN
investigated for more or less special cases of selection (KIMURA
1962). The results of these investiga-
and KOJIMA
1960; BODMER PARSONS
and
tions were sufficient to show that even for relatively simple cases (two loci, simple
symmetrical selective values) linkage might have profound effects on the course
of natural selection and, pari passu, natural selection may have major effects on
the distribution of coupling and repulsion linkage in a population.
The results of the investigations of LEWONTIN KOJIMA(1960) of the two-
and
locus model can be summarized as follows: (1) If the fitnesses are additive be-
tween loci (no epistasis), linkage does not effect the final equilibrium state of the
population. (2) If linkage is tighter than the value demanded by the magnitude
of the epistasis (the greater the epistasis the greater the value) there may be
permanent linkage disequilibrium and alteration of equilibrium gene frequencies.
(3) The rate of genetic change with time is affected by the tightness of the link-
age. (4)In some cases stable gene frequency equilibria are possible only if link-
age is tight enough.
Although these conclusions were based only on two-locus model and for selec-
tive values of a fairly restricted sort, they point clearly to the importance of taking
linkage into account in understanding the changes of gene frequencies in popula-
tions. In fact, some experimental results (an example of which will be given
below) can be understood only if the interaction of selection and linkage is taken
into account.
The equations describing the interaction between selection and linkage (see
below) do not usually have general literal solutions. It is for this reason that the
authors cited above have restricted themselves to relatively simple cases. In view
of the interesting findings of those previous papers, however, it is worthwhile to
explore the subject more intensively. To do so requires the numerical rather than
general literal solutions to the equations, but such numerical solutions apply,
obviously, only to the particular parameter values chosen. T o make such a nu
merical approach at all useful, it is necessary to cover a variety of models of
selection and to vary each model so that an empirical “feel” for general results
can be obtained. In this sense, numerical calculations are like experiments: the
generality of the results depends upon the variety of conditions of the experiments.
In this and the succeeding two papers of this series, three main types of selec-
tion are discussed. While these are not completely exhaustive of all possibilities,
they represent the main modes of selection in natural and artificial populations.
I n this paper I will consider heterotic models, in which heterozygotes at each
locus are more fit than homozygotes. In the second paper of the series optimum
selection will be examined; that is, selection operating against individuals whose
phenotypes deviate from some intermediate optimum. The last paper will deal
with unidirectional selection in which an extreme phenotype or genotype is select-
ed against. Since the effect of linkage is rather different in these three cases,
separate discussions of each are required.
Description
The Interaction of Selection and Linkage. I. General Considerations; Heterotic Models