ANALYSIS O F PROCESSES IN CONTROL O F INSECTS
39
that it is by definition the percentage, killed by a density-independent
factor, that is independent of density - not the number killed.) For
example consider a density-independent mortality M of 50%, and a
constant-number mortality K killing 50 individaals :
KM: 200 - 50 = 150; 150 x 50/100 = 75 survive
MK : 200 x 50/100 = 100; 100 - 50 = 50 survive.
5. Constant-nurhber and Density-dependent Mortalities in Combination
Rule v: In a calculation of the final effect of one or more densitydependent mortalities and one killing an approximately constant
number of individuals, the greater reduction is achieved when the
density-dependent mortality comes first. This follows because densitydependent mortality kills a greater number of individuals when the
density is higher (to an even greater extent than in the case of densityindependent mortality).
For example, consider the density-dependent mortality B (Fig. 16)
and a constant-number mortality K killing 50 individuals :
KB : 200 - 50 = 150; 150 x 43-5/100 = 65 survive
BK: 200 x 25/100 = 50; 50 - 50 = 0 survive.
Obviously, much more complicated models could be built upon these
simple foundations, with mathematics taking over from intuition. This
would defeat the purpose of the present exercise, which is to show that
the effects of a succession of mortalities of different known types can
be calculated very easily - provided, of course, we know or can assume
how many, or what proportion, of the population will be killed by each
mortality at the level of density prevailing when it operates. It is
assumed in all this that variations in environmental conditions, if they
cannot be ignored, can be adequately allowed for in the calculations.
6. Assesszng the Signi$cance of Regulatory Mortalities
One reason for studying the effects of different mortalities acting in
combination is to learn something of the contributions they make to
regulation. Nicholson (1933) and many others since have emphasized
that a knowledge of the numbers or percentage killed by a factor cannot
by itself tell us whether the factor is making a great or small contribution to regulation; it is the ability to offset a rise in density that is
primarily important in this connection. Obviously, if a markedly
density-dependent factor (prompt or lagging) accounts for most of the
mortality in each generation, the case is clear - unusually so ! But a
factor that causes only a small fraction of the total mortality per
generation can play a dominant part in regulating abundance. Many
39
that it is by definition the percentage, killed by a density-independent
factor, that is independent of density - not the number killed.) For
example consider a density-independent mortality M of 50%, and a
constant-number mortality K killing 50 individaals :
KM: 200 - 50 = 150; 150 x 50/100 = 75 survive
MK : 200 x 50/100 = 100; 100 - 50 = 50 survive.
5. Constant-nurhber and Density-dependent Mortalities in Combination
Rule v: In a calculation of the final effect of one or more densitydependent mortalities and one killing an approximately constant
number of individuals, the greater reduction is achieved when the
density-dependent mortality comes first. This follows because densitydependent mortality kills a greater number of individuals when the
density is higher (to an even greater extent than in the case of densityindependent mortality).
For example, consider the density-dependent mortality B (Fig. 16)
and a constant-number mortality K killing 50 individuals :
KB : 200 - 50 = 150; 150 x 43-5/100 = 65 survive
BK: 200 x 25/100 = 50; 50 - 50 = 0 survive.
Obviously, much more complicated models could be built upon these
simple foundations, with mathematics taking over from intuition. This
would defeat the purpose of the present exercise, which is to show that
the effects of a succession of mortalities of different known types can
be calculated very easily - provided, of course, we know or can assume
how many, or what proportion, of the population will be killed by each
mortality at the level of density prevailing when it operates. It is
assumed in all this that variations in environmental conditions, if they
cannot be ignored, can be adequately allowed for in the calculations.
6. Assesszng the Signi$cance of Regulatory Mortalities
One reason for studying the effects of different mortalities acting in
combination is to learn something of the contributions they make to
regulation. Nicholson (1933) and many others since have emphasized
that a knowledge of the numbers or percentage killed by a factor cannot
by itself tell us whether the factor is making a great or small contribution to regulation; it is the ability to offset a rise in density that is
primarily important in this connection. Obviously, if a markedly
density-dependent factor (prompt or lagging) accounts for most of the
mortality in each generation, the case is clear - unusually so ! But a
factor that causes only a small fraction of the total mortality per
generation can play a dominant part in regulating abundance. Many