382
CHARLES J. KREBS AND JUDITH H. MYERS
there would be a lag between the gene frequency change and the density
change as occurs in the age-specific selection model of King and Anderson
(1971). This does not seem to be the case (Fig. 42). However, if there are
genotypes which grow faster and reproduce earlier during the phase of
population increase as suggested by the work of Gaines and Krebs
(1971), the population increase will result in a higher proportion of this
genotype unless mortality compensates for the greater reproductive
potential .
Charlesworth and Giesel (1972) propose a model which considers the
influence of demographic structures, particularly the age structure,
on changes in gene frequency of polymorphic systems. The basis of the
model is that if a genotype produces early in its life, there will be little
advantage if the population is primarily composed of older individuals
which are already reproducing. However, if the age structure favors
growing animals, those individuals which are able t o reproduce early
will have a greater advantage. Therefore, if there is a change in the age
structure of the population, a fluctuation in gene frequency follows.
While these authors claim that their model produces a population cycle
and gene-frequency change which resembles the observations of
Tamarin and Krebs (1969), we see some differences. First, the genefrequency changes produced by the model were only in the order of
6-9% while observed changes in Microha populations are more often
in the vicinity of 20% (Fig. 42).
Furthermore, if it is assumed that a cycle of the model is equal to
the period of time for an individual to reproduce (about three weeks for
microtines), the rate of the gene-frequency change is very slow as
compared with those of field studies. With the model a 9% genefrequency change required 40 cycles. This would be the equivalent of
over two years on a microtine time scale which clearly doesn’t apply
to field observations.
One of the observations arising from the field data is that gene
frequencies in males and females are often quite different and it is not
clear that the model would allow this result. The Charlesworth-Giesel
model showed changing death rates to have little influence on gene
frequencies. We have found that differential survival particularly
during the decline is a major factor in gene-frequency changes.
Finally we find it impossible to interpret the correspondence between
simulated population declines caused by decreasing m(x) functions and
declines of field populations which arise both from decreased natality
and from increased mortality. We feel that the responsibility lies with
the authors of theoretical models to interpret the biological consequences
of assumptions made in their models, for without them statements
such as “The resultant population cycle resembles vaguely the pattern
CHARLES J. KREBS AND JUDITH H. MYERS
there would be a lag between the gene frequency change and the density
change as occurs in the age-specific selection model of King and Anderson
(1971). This does not seem to be the case (Fig. 42). However, if there are
genotypes which grow faster and reproduce earlier during the phase of
population increase as suggested by the work of Gaines and Krebs
(1971), the population increase will result in a higher proportion of this
genotype unless mortality compensates for the greater reproductive
potential .
Charlesworth and Giesel (1972) propose a model which considers the
influence of demographic structures, particularly the age structure,
on changes in gene frequency of polymorphic systems. The basis of the
model is that if a genotype produces early in its life, there will be little
advantage if the population is primarily composed of older individuals
which are already reproducing. However, if the age structure favors
growing animals, those individuals which are able t o reproduce early
will have a greater advantage. Therefore, if there is a change in the age
structure of the population, a fluctuation in gene frequency follows.
While these authors claim that their model produces a population cycle
and gene-frequency change which resembles the observations of
Tamarin and Krebs (1969), we see some differences. First, the genefrequency changes produced by the model were only in the order of
6-9% while observed changes in Microha populations are more often
in the vicinity of 20% (Fig. 42).
Furthermore, if it is assumed that a cycle of the model is equal to
the period of time for an individual to reproduce (about three weeks for
microtines), the rate of the gene-frequency change is very slow as
compared with those of field studies. With the model a 9% genefrequency change required 40 cycles. This would be the equivalent of
over two years on a microtine time scale which clearly doesn’t apply
to field observations.
One of the observations arising from the field data is that gene
frequencies in males and females are often quite different and it is not
clear that the model would allow this result. The Charlesworth-Giesel
model showed changing death rates to have little influence on gene
frequencies. We have found that differential survival particularly
during the decline is a major factor in gene-frequency changes.
Finally we find it impossible to interpret the correspondence between
simulated population declines caused by decreasing m(x) functions and
declines of field populations which arise both from decreased natality
and from increased mortality. We feel that the responsibility lies with
the authors of theoretical models to interpret the biological consequences
of assumptions made in their models, for without them statements
such as “The resultant population cycle resembles vaguely the pattern