255
H . KLOMP
higher or lower than Et independent of the size of Et, and in that case
the coefficient of regression of log Et+l on log Et tends to equal unity.
As shown in Table XXV this coefficient is 0.13 only and deviates significantly from unity (P < O-Ol), indicating that there is a strong tendency for Et+l to be smaller than Et a t the higher values of the latter,
as a result of density related generation mortality.
These facts make it appear extremely likely that the population of
Bupalus is stabilized by one or more regulating processes, and in the
following sections we shall have to give further consideration to the way
in which these processes operate.
B. DENSITY DEPENDENT FECUNDITY
In Chapter IV-B it was pointed out that larval density has an influence on larval growth through mutual interference. It was shown that
high density inhibits growth, resulting in small pupae and giving rise to
moths with a relatively low fecundity (Figs. 24 and 26). The regression
line in Fig. 26 shows that, on average, the fecundity decreases by 20
eggs when larval density increases by 10 individuals/mZ. Within the
density range observed in the field this means a 25% overall reduction
going from minimum to maximum density levels. At first sight this may
seem to be considerable, but the power of regulation resulting from this
reduction is small. This can be illustrated in various ways.
One of these methods makes use of the effect of the density dependent
factor (in this case fecundity) on the net rate of reproduction R ( = the
index of population trend, being the quotient of successive densities of
the same stage, e.g. Et+JEt), assuming for the sake of simplicity the
resultant fraction (s) surviving the mortality factors to be constant. If
we indicate the mean density level by p , and the deviations of this mean
by up, then R roughly equals l / q a .
This can be illustrated as follows. Let us assume the population to be i n balance
a t the mean density of Fig. 26 (p = 10 larvae/m'). Then the mean fecundity is
182, and consequently 8 = 1/182.
If the population increases to 2p = 20, then fecundity decreases to 163, and
If density decreases to 1/2 p = 5, then fecundity increases to 193 and
This means that without 'the action of other density related mechanisms the population tends to approach asymptotically and slowly to
the mean level as a result of the density governed fecundity, the successive densities being e.g. 5p, 3.6p, 2.513, 2 . 3 ~ ~
1 . 9 ~ ~
and so on.
It might be supposed that the regulation of numbers in the Bupalus
population is realized in this way, but that in the field the gradual return to the mean level is distorted by density independent variation of
R = 163 x 1/182 = 0.90 Z 1/+2.
R = 193/182 = 1.06 Z 1/+(1/2).
H . KLOMP
higher or lower than Et independent of the size of Et, and in that case
the coefficient of regression of log Et+l on log Et tends to equal unity.
As shown in Table XXV this coefficient is 0.13 only and deviates significantly from unity (P < O-Ol), indicating that there is a strong tendency for Et+l to be smaller than Et a t the higher values of the latter,
as a result of density related generation mortality.
These facts make it appear extremely likely that the population of
Bupalus is stabilized by one or more regulating processes, and in the
following sections we shall have to give further consideration to the way
in which these processes operate.
B. DENSITY DEPENDENT FECUNDITY
In Chapter IV-B it was pointed out that larval density has an influence on larval growth through mutual interference. It was shown that
high density inhibits growth, resulting in small pupae and giving rise to
moths with a relatively low fecundity (Figs. 24 and 26). The regression
line in Fig. 26 shows that, on average, the fecundity decreases by 20
eggs when larval density increases by 10 individuals/mZ. Within the
density range observed in the field this means a 25% overall reduction
going from minimum to maximum density levels. At first sight this may
seem to be considerable, but the power of regulation resulting from this
reduction is small. This can be illustrated in various ways.
One of these methods makes use of the effect of the density dependent
factor (in this case fecundity) on the net rate of reproduction R ( = the
index of population trend, being the quotient of successive densities of
the same stage, e.g. Et+JEt), assuming for the sake of simplicity the
resultant fraction (s) surviving the mortality factors to be constant. If
we indicate the mean density level by p , and the deviations of this mean
by up, then R roughly equals l / q a .
This can be illustrated as follows. Let us assume the population to be i n balance
a t the mean density of Fig. 26 (p = 10 larvae/m'). Then the mean fecundity is
182, and consequently 8 = 1/182.
If the population increases to 2p = 20, then fecundity decreases to 163, and
If density decreases to 1/2 p = 5, then fecundity increases to 193 and
This means that without 'the action of other density related mechanisms the population tends to approach asymptotically and slowly to
the mean level as a result of the density governed fecundity, the successive densities being e.g. 5p, 3.6p, 2.513, 2 . 3 ~ ~
1 . 9 ~ ~
and so on.
It might be supposed that the regulation of numbers in the Bupalus
population is realized in this way, but that in the field the gradual return to the mean level is distorted by density independent variation of
R = 163 x 1/182 = 0.90 Z 1/+2.
R = 193/182 = 1.06 Z 1/+(1/2).