22
M. 1. SOLOMON
the influence of weather, etc. Can the method be used to detect densitydependence in such populations? Figure 10 shows three curves, H , J and
K , representing the density of three hypothetical populations increasing
and decreasing in unison as if under the influence of common environmental changes. They differ however in that H increases at the same
geometric rate at all the levels of density involved, whereas J increases
at a slower rate as density becomes greater, and K increases at a faster
rate as density becomes greater. Correspondingly, H declines at a constant proportionate rate as density falls, whereas J declines more slowly
as density falls, and K more rapidly. In H and J the rate of decrease
is greater than the rate of increase (there is of course no reason to expect
rates of increase and decrease to be equal, and sustained increase
followed by a relatively rapid decrease is characteristic of many insect
populations, and others). The graphs of log N,,, against log N , again
show a slope of 1 in the case of the density-independent lines H‘. There
are two lines because of the difference between the rates of increase and
decrease in H , but both have the same slope. Similarly, there are two
lines J’, representing the density-independent increases and decreases
in J . Their slope is 0.625 and 0.60 respectively; the similarity is
accidental, since the rules governing the density-dependent increases
and decreases in J were separately and arbitrarily invented. The lines
K’ representing the increase and decrease of K have slopes of 1.33 and
1.44 respectively, the values above unity indicating the inverse density
relationship embodied in K . In brief, Fig. 10 demonstrates that the
method can be used to assess the degree of density-dependence in
populations that are fluctuating mainly under the influence of densityindependent factors ; also, it shows that phases of increase and decrease
tend to require separate treatment, a point not dealt with by Morris
(1963a,b).
As already mentioned, Nicholson (1933) envisaged populations as
being regulated towards an equilibrium level which continually
changed. While acknowledging the value of this idea on a theoretical
level, I have objected that it would be difficult in practice to distinguish
movement towards an equilibrium, on the one hand, from changes in the
equilibrium level, on the other (Solomon, 1949). Another difficulty that
might often arise is the imposition of sudden reductions by densityindependent influences that have no reference to any equilibrium level.
I believe the method outlined above might in certain circumstances be
used to distinguish between (i) movement towards an equilibrium,
(ii) a change in the equilibrium level, and (iii) density-independent
changes. Fig. 11 illustrates a simple hypothetical example embodying
these features. As before, the graphs of logN,,, against logN have
separate lines for the rising and falling approaches to equilibrium. The
M. 1. SOLOMON
the influence of weather, etc. Can the method be used to detect densitydependence in such populations? Figure 10 shows three curves, H , J and
K , representing the density of three hypothetical populations increasing
and decreasing in unison as if under the influence of common environmental changes. They differ however in that H increases at the same
geometric rate at all the levels of density involved, whereas J increases
at a slower rate as density becomes greater, and K increases at a faster
rate as density becomes greater. Correspondingly, H declines at a constant proportionate rate as density falls, whereas J declines more slowly
as density falls, and K more rapidly. In H and J the rate of decrease
is greater than the rate of increase (there is of course no reason to expect
rates of increase and decrease to be equal, and sustained increase
followed by a relatively rapid decrease is characteristic of many insect
populations, and others). The graphs of log N,,, against log N , again
show a slope of 1 in the case of the density-independent lines H‘. There
are two lines because of the difference between the rates of increase and
decrease in H , but both have the same slope. Similarly, there are two
lines J’, representing the density-independent increases and decreases
in J . Their slope is 0.625 and 0.60 respectively; the similarity is
accidental, since the rules governing the density-dependent increases
and decreases in J were separately and arbitrarily invented. The lines
K’ representing the increase and decrease of K have slopes of 1.33 and
1.44 respectively, the values above unity indicating the inverse density
relationship embodied in K . In brief, Fig. 10 demonstrates that the
method can be used to assess the degree of density-dependence in
populations that are fluctuating mainly under the influence of densityindependent factors ; also, it shows that phases of increase and decrease
tend to require separate treatment, a point not dealt with by Morris
(1963a,b).
As already mentioned, Nicholson (1933) envisaged populations as
being regulated towards an equilibrium level which continually
changed. While acknowledging the value of this idea on a theoretical
level, I have objected that it would be difficult in practice to distinguish
movement towards an equilibrium, on the one hand, from changes in the
equilibrium level, on the other (Solomon, 1949). Another difficulty that
might often arise is the imposition of sudden reductions by densityindependent influences that have no reference to any equilibrium level.
I believe the method outlined above might in certain circumstances be
used to distinguish between (i) movement towards an equilibrium,
(ii) a change in the equilibrium level, and (iii) density-independent
changes. Fig. 11 illustrates a simple hypothetical example embodying
these features. As before, the graphs of logN,,, against logN have
separate lines for the rising and falling approaches to equilibrium. The