20
M. E. SOLOMON
one year (log N,) is plotted against that of the following year (log
and the points treated as a scatter diagram, a straight line can be fitted
(Fig. 8). The logarithmic scale has the effect of stabilizing the variance
over the range of densities involved, so that valid regression analysis
can be carried out. With reference to an artificial example based on
work with the fall webworm, Hyphntria cunea (Dru.), Morris (1963b)
writes ; “the slope, b = -5, which is a reasonably average value for forest
insects, provides an index .of the degree of density dependence in the
system. If the rate of increase in population did not decrease with
density, the slope would of course be 1.0.” Morris goes on to examine
how regression can be improved, and how the slope of the line is
altered, when the estimated effects of certain factors are eliminated,
but I do not propose to go into this. I do, however, wish to look more
closely at the implications of the slope in the graph of log N , against
log N,,,. Tt is not easy to do this with reference to either of the examples
given by Morris. I shall use simple artificial examples to show what may
be expected of the procedure with different sorts of density relationships.
In real examples, complicating factors would cause more or less scatter ;
this would make the fitting of a line a matter for statistical procedure,
but &s Morris (1963a) has shown, quite practicable in at least some
instances.
Fig. 9 will serve to show the difference between slopes for densityindependent, density-dependent and inversely density related population trends. Lines C and D in Fig. 9~ represent sustained unvarying
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Time, or generotions
log N”
(A)
(B)
FIQ. 9 ~ .
Curves ilustrating various density relationships: ‘ 2, D, constant, densityindependent geometric increase; E, F, density-dependent ; a, inverse.
B. C‘ to a’, corresponding slopes of log N,,, against log N,.