REALISTIC MODELS IN POPULATION ECOLOGY
22 1
D. O T H E R I N D I V I D U A L A T T R I B U T E S
The specification of individual age and size in some populations will
be an incomplete or unsuitable description. It might be necessary to
include other characteristics which affect survival, e.g. intelligence,
speed, visual accuity, protective coloration, bodily accumulation of
toxic substances, state of health etc. (Oldfield, 1966; Rubinow, 1968;
Weiss, 1968). If one or more of these characteristics is included, a
numerical measure must be assigned. Let c represent a measure of a
particular characteristic and unless otherwise noted, larger values of c
are assumed to be more desirable.
Individual characteristics are separable into two types: those for
which c cannot change in time for a particular individual (e.g. protective
coloration) and those for which c can change for an individual (e.g.
learned traits). I n both cases the density function r](a, m, t ) is replaced
by $a, m, c, t ) , but if c for an individual does not change in t, dc/dt = 0
and Eqn (20) for r] is unchanged. Consider this case first. In general, the
submodels for growth, death and birth require modification in that they
become functions of c. For example, if a predator species is being
modeled and the characteristic c is related to its success in capturing
prey, the growth function should be an increasing function of c. This
increase in c might act in the model to increase the relative size of
individuals with larger values of c and thus indirectly influence their
death and birth rates. Such indirect influences would not be included in
the death and birth functions, except in that larger individuals would be
less liable to die and would produce more neonates. I n the case of a prey
species, if c measured the degree of protective coloration, then individuals with higher values of c would experience lower death rates. Thus
these individuals would survive to produce more neonates than those
with lower value of c. The more fundamental problem of relating the
value of c for neonates to those of the parent involves genetic considerations which will not be pursued here (Levin, 1969; Crow and Kimura,
1970).
The resulting model perhaps is suitable for studying problems in
evolutionary ecology (Levins, 1968; Pimentel, 1968; Anderson and
King, 1970; Chabora and Pimentel, 1970; Istock, 1970). Consider, for
example, c to be the average litter size of an adult female of age a and
mass m. Here large c does not necessarily imply a more favorable
characteristic since a parent of a large litter may suffer a higher death
rate. Also, neonates in large litters may experience high death rates for
various reasons such as small size or insufficient maternal protection or
food supply. Thus, the population may evolve toward smaller litters of
larger individuals and the resultant population may be composed of few
22 1
D. O T H E R I N D I V I D U A L A T T R I B U T E S
The specification of individual age and size in some populations will
be an incomplete or unsuitable description. It might be necessary to
include other characteristics which affect survival, e.g. intelligence,
speed, visual accuity, protective coloration, bodily accumulation of
toxic substances, state of health etc. (Oldfield, 1966; Rubinow, 1968;
Weiss, 1968). If one or more of these characteristics is included, a
numerical measure must be assigned. Let c represent a measure of a
particular characteristic and unless otherwise noted, larger values of c
are assumed to be more desirable.
Individual characteristics are separable into two types: those for
which c cannot change in time for a particular individual (e.g. protective
coloration) and those for which c can change for an individual (e.g.
learned traits). I n both cases the density function r](a, m, t ) is replaced
by $a, m, c, t ) , but if c for an individual does not change in t, dc/dt = 0
and Eqn (20) for r] is unchanged. Consider this case first. In general, the
submodels for growth, death and birth require modification in that they
become functions of c. For example, if a predator species is being
modeled and the characteristic c is related to its success in capturing
prey, the growth function should be an increasing function of c. This
increase in c might act in the model to increase the relative size of
individuals with larger values of c and thus indirectly influence their
death and birth rates. Such indirect influences would not be included in
the death and birth functions, except in that larger individuals would be
less liable to die and would produce more neonates. I n the case of a prey
species, if c measured the degree of protective coloration, then individuals with higher values of c would experience lower death rates. Thus
these individuals would survive to produce more neonates than those
with lower value of c. The more fundamental problem of relating the
value of c for neonates to those of the parent involves genetic considerations which will not be pursued here (Levin, 1969; Crow and Kimura,
1970).
The resulting model perhaps is suitable for studying problems in
evolutionary ecology (Levins, 1968; Pimentel, 1968; Anderson and
King, 1970; Chabora and Pimentel, 1970; Istock, 1970). Consider, for
example, c to be the average litter size of an adult female of age a and
mass m. Here large c does not necessarily imply a more favorable
characteristic since a parent of a large litter may suffer a higher death
rate. Also, neonates in large litters may experience high death rates for
various reasons such as small size or insufficient maternal protection or
food supply. Thus, the population may evolve toward smaller litters of
larger individuals and the resultant population may be composed of few