ANALYSIS O F PROCESSES I N CONTROL O F INSECTS
37
Another necessary preliminary is to distinguish the following types
of mortality. (i) Density-independent : killing a percentage of the total
population, irrespective of density. (ii) Promptly density-dependent :
killing a higher percentage at high density, a lower percentage at low
density. Fig. 16 shows three relationships of this sort, which will be
used in the numerical examples. (iii) Killing a more or less constant
number of animals, irrespective of density. In the context of one
generation, this is an inverse density-relationship (the higher the
density, the lower the proportion killed). But it is introduced here as a
simplified representation of what may happen in certain parasite-host
interactions (delayed density-dependent), in the early upswing of each
cycle. It is assumed that the parasites have a more or less constant
capacity each to attack a certain number of hosts over the range of
densities involved (cf. Morris, 1957). Whether or not it is widely
representative, the implications of this “constant-number” type of
mortality are worth consideration.
For the numerical examples, a hypothetical population of 200 young
insects is taken, and the mortalities are considered to operate in succession on the juvenile stages. This figure could also represent the egg
output per female under favourable conditions, and reductions in this
output could be treated like mortalities.
1. Density-independent Mortalities in Combination
Rule i : The calculated final effect of a succession of density-independent mortalities is not affected by the order in which they operate.
This is generally recognized (e.g. Morris, 1957). For example, if 70%
mortality is followed by 90% mortality of those remaining, or vice versa,
in either case we have 200 x 3/10 x 1/10 = 6 survivors.
2. Density-dependent Mortalities in Combination
Rule ii : The calculated final survival from two density-dependent
mortalities acting in succession is lower when the more powerful
mortality operates first. This follows because the greatest effect is
achieved if the more potent factor has the advantage of high density
to act upon.
Consider, for example, mortality A in Fig. 16 followed by mortality C.
The percentage reduction in current density inflicted by each will
depend on the level of that density at the time ; the appropriate values
are read off from Fig. 16 :
200 x 2.5/100 = 5 ; then 5 x lOO/lOO = 5 survive.
In reverse order (CA) :
200 x 60/100 = 120; 120 x 22.5/100 = 27 survive.
37
Another necessary preliminary is to distinguish the following types
of mortality. (i) Density-independent : killing a percentage of the total
population, irrespective of density. (ii) Promptly density-dependent :
killing a higher percentage at high density, a lower percentage at low
density. Fig. 16 shows three relationships of this sort, which will be
used in the numerical examples. (iii) Killing a more or less constant
number of animals, irrespective of density. In the context of one
generation, this is an inverse density-relationship (the higher the
density, the lower the proportion killed). But it is introduced here as a
simplified representation of what may happen in certain parasite-host
interactions (delayed density-dependent), in the early upswing of each
cycle. It is assumed that the parasites have a more or less constant
capacity each to attack a certain number of hosts over the range of
densities involved (cf. Morris, 1957). Whether or not it is widely
representative, the implications of this “constant-number” type of
mortality are worth consideration.
For the numerical examples, a hypothetical population of 200 young
insects is taken, and the mortalities are considered to operate in succession on the juvenile stages. This figure could also represent the egg
output per female under favourable conditions, and reductions in this
output could be treated like mortalities.
1. Density-independent Mortalities in Combination
Rule i : The calculated final effect of a succession of density-independent mortalities is not affected by the order in which they operate.
This is generally recognized (e.g. Morris, 1957). For example, if 70%
mortality is followed by 90% mortality of those remaining, or vice versa,
in either case we have 200 x 3/10 x 1/10 = 6 survivors.
2. Density-dependent Mortalities in Combination
Rule ii : The calculated final survival from two density-dependent
mortalities acting in succession is lower when the more powerful
mortality operates first. This follows because the greatest effect is
achieved if the more potent factor has the advantage of high density
to act upon.
Consider, for example, mortality A in Fig. 16 followed by mortality C.
The percentage reduction in current density inflicted by each will
depend on the level of that density at the time ; the appropriate values
are read off from Fig. 16 :
200 x 2.5/100 = 5 ; then 5 x lOO/lOO = 5 survive.
In reverse order (CA) :
200 x 60/100 = 120; 120 x 22.5/100 = 27 survive.