36
M. E. SOLOMON
mortality tables is of course valuable, indeed indispensable for a
thorough investigation. The crux of the matter, however, is how to
assess the real significance of the different mortalities, since the ultimate
effect of each depends on the contributions of the others, and the degree
of responsiveness of each mortality factor to difference% in population
density is also an essential consideration.
One line of thought, with various branches, is represented by the
papers of Thompson (1928, 1955), Bess (1945), Morris (1957), and some
others. The earlier ones were reviewed by Morris (Zoc. cit.) who discussed
the significance and limitations of the proposals of Thompson and Bess,
and indicated some general principles governing the effects of mortalities
in combination.
Another line of thought on the subject was developed by Nicholson
(1933) and Nicholson and Bailey (1935). They were primarily concerned
with the elaboration of their model representing parasite-host interactions. They gave some consideration to the effects of several species
of parasites attacking a common host, and to the effects of densityindependent mortality impinging on a parasite-host system, in the terms
of the model. Varley (1947) applied their theory to the interpretation
of field observations on the knapweed gall-fly , including a consideration
of the effects on its abundance when density-independent mortality
acted before or after a major parasite.
Neither of these lines can be easily summarized, and I do not propose
t o attempt it. It seems more useful to state clearly some simple principles concerning the combination of mortalities. These rules or relationships are self-evident when clearly understood, and do not need
mathematical proof. The numerical examples are for illustration, not
proof.
In calculations of this sort, it is generally more convenient to combine survival rates than mortality rates. For example, ifa 70% mortality
is followed by a 90% mortality of the survivors, the simplest way of
calculating the result is to consider the survival rate, 10% of 30%, i.e.
3% of the original numbers. The fact that successive survival ratios in
a life-cycle can be combined by multiplying together has been used as
the basis of models and calculations by the investigators of the spruce
budworm (Morris, ed., 1963). They use ratios instead of percentages, so
that if N , animals are reduced by one mortality to N , and by a later
one to N,, one writes N , / N , x N J N , = N,/N,, which is convenient for
dealing with population counts. It makes no difference to the calculation, of course, what numbers one writes in one of these fractions, e.g.
N,/N,, so long as the ratio is preserved. It is often convenipnt to convert
a percentage reduction to this ratio form, e,g. 3/10 for the survival ratio
from a 70% mortality.
M. E. SOLOMON
mortality tables is of course valuable, indeed indispensable for a
thorough investigation. The crux of the matter, however, is how to
assess the real significance of the different mortalities, since the ultimate
effect of each depends on the contributions of the others, and the degree
of responsiveness of each mortality factor to difference% in population
density is also an essential consideration.
One line of thought, with various branches, is represented by the
papers of Thompson (1928, 1955), Bess (1945), Morris (1957), and some
others. The earlier ones were reviewed by Morris (Zoc. cit.) who discussed
the significance and limitations of the proposals of Thompson and Bess,
and indicated some general principles governing the effects of mortalities
in combination.
Another line of thought on the subject was developed by Nicholson
(1933) and Nicholson and Bailey (1935). They were primarily concerned
with the elaboration of their model representing parasite-host interactions. They gave some consideration to the effects of several species
of parasites attacking a common host, and to the effects of densityindependent mortality impinging on a parasite-host system, in the terms
of the model. Varley (1947) applied their theory to the interpretation
of field observations on the knapweed gall-fly , including a consideration
of the effects on its abundance when density-independent mortality
acted before or after a major parasite.
Neither of these lines can be easily summarized, and I do not propose
t o attempt it. It seems more useful to state clearly some simple principles concerning the combination of mortalities. These rules or relationships are self-evident when clearly understood, and do not need
mathematical proof. The numerical examples are for illustration, not
proof.
In calculations of this sort, it is generally more convenient to combine survival rates than mortality rates. For example, ifa 70% mortality
is followed by a 90% mortality of the survivors, the simplest way of
calculating the result is to consider the survival rate, 10% of 30%, i.e.
3% of the original numbers. The fact that successive survival ratios in
a life-cycle can be combined by multiplying together has been used as
the basis of models and calculations by the investigators of the spruce
budworm (Morris, ed., 1963). They use ratios instead of percentages, so
that if N , animals are reduced by one mortality to N , and by a later
one to N,, one writes N , / N , x N J N , = N,/N,, which is convenient for
dealing with population counts. It makes no difference to the calculation, of course, what numbers one writes in one of these fractions, e.g.
N,/N,, so long as the ratio is preserved. It is often convenipnt to convert
a percentage reduction to this ratio form, e,g. 3/10 for the survival ratio
from a 70% mortality.