28
M. E. SOLOMON
values of r gives 0.86 and 0.45, suggesting that 45% of the variance in
larval density is accounted for when log N , is used for prediction, as
compared to 86% when log S, is used. The regression formula is
log N,,, = 0.53 + 0.92 log s,,
in which the estimated slope of b = 0.92 is not significantly different from
the value b = 1 to be expected for a perfect key factor accounting for
all the variation. It is concluded that larval parasitism was a key
factor and that the insect was remarkably unresponsive to variations
that must have occurred in other factors. This is in marked contrast
to what was found for the spruce budworm, in which effects of weather
accounted for most of the variability (Morris, 1963a).
This short account omits many aspects of the paper, but should make
at least brief reference to Morris’ insistence that “the single-factor
approach should be recognized as a useful lead to more complete
studies but certainly not as a substitute for them”. A final point that
should be noted is that the black-headed budworm population was
involved in a parasite-host oscillation, i.e. in a delayed type of densitydependent relationship ; inspection of the data shows that the percentage
parasitism was correlated with the host population density of the
previous generation rather than with current density.
Varley and Gradwell (1960), in a note on key factors as defined by
Morns (Zoc. cit.), described a graphical method of demonstrating them.
They compared killing powers of a series of successive mortality
factors acting on a population of the winter moth, Operophtera brumata
(L.), on oaks in Wytham Wood near Oxford. They estimated the
numbers at two stages in each life cycle of this insect, which has one
generation per year. For each generation they took the difference
between the logarithms of the two estimates. This value (k-value) is
equivalent to the logarithm of the factor by which the population has
been reduced; e.g. if the density is 50 on the first occasion and 10 on
the second, the k-value is log 50 -log 10 = 0.699, or log (50/10).
Further, with the aid of additional information, the mortality was
subdivided into 6 parts according to the developmental stages and
causal agents, and each part was treated as above, giving values of
k,, k, . . . k6 which in sum are equal to K .
When the process was repeated with the data for each of 10 successive
years, and the values plotted against time (Fig. 13), two different sorts
of k-values were distinguishable. That for “winter disappearance’’ (kl)
followed the same fluctuating course as K , only the fluctuations tended
to be greater, But the k-value for pupal predation (k5) ran counter to
the fluctuations of k,, and so partly offset them. Clearly, k, represents
the “key factor”. The second type (kS) apparently tends to compensate
M. E. SOLOMON
values of r gives 0.86 and 0.45, suggesting that 45% of the variance in
larval density is accounted for when log N , is used for prediction, as
compared to 86% when log S, is used. The regression formula is
log N,,, = 0.53 + 0.92 log s,,
in which the estimated slope of b = 0.92 is not significantly different from
the value b = 1 to be expected for a perfect key factor accounting for
all the variation. It is concluded that larval parasitism was a key
factor and that the insect was remarkably unresponsive to variations
that must have occurred in other factors. This is in marked contrast
to what was found for the spruce budworm, in which effects of weather
accounted for most of the variability (Morris, 1963a).
This short account omits many aspects of the paper, but should make
at least brief reference to Morris’ insistence that “the single-factor
approach should be recognized as a useful lead to more complete
studies but certainly not as a substitute for them”. A final point that
should be noted is that the black-headed budworm population was
involved in a parasite-host oscillation, i.e. in a delayed type of densitydependent relationship ; inspection of the data shows that the percentage
parasitism was correlated with the host population density of the
previous generation rather than with current density.
Varley and Gradwell (1960), in a note on key factors as defined by
Morns (Zoc. cit.), described a graphical method of demonstrating them.
They compared killing powers of a series of successive mortality
factors acting on a population of the winter moth, Operophtera brumata
(L.), on oaks in Wytham Wood near Oxford. They estimated the
numbers at two stages in each life cycle of this insect, which has one
generation per year. For each generation they took the difference
between the logarithms of the two estimates. This value (k-value) is
equivalent to the logarithm of the factor by which the population has
been reduced; e.g. if the density is 50 on the first occasion and 10 on
the second, the k-value is log 50 -log 10 = 0.699, or log (50/10).
Further, with the aid of additional information, the mortality was
subdivided into 6 parts according to the developmental stages and
causal agents, and each part was treated as above, giving values of
k,, k, . . . k6 which in sum are equal to K .
When the process was repeated with the data for each of 10 successive
years, and the values plotted against time (Fig. 13), two different sorts
of k-values were distinguishable. That for “winter disappearance’’ (kl)
followed the same fluctuating course as K , only the fluctuations tended
to be greater, But the k-value for pupal predation (k5) ran counter to
the fluctuations of k,, and so partly offset them. Clearly, k, represents
the “key factor”. The second type (kS) apparently tends to compensate