REALISTIC MODELS IN POPULATION ECOLOGY
201
The process of constructing a mathematical model is itself instructive,
since it forces one to set down one’s thoughts clearly and it may indicate
areas in which basic understanding is lacking. Once the model is
constructed, it can be studied to exhibit sensitivities. Thus, one may
conclude that more precise information about some specific biological
process is required or that certain environmental effects are especially
critical in determining the population dynamics. This information may
suggest important experiments. It will also aid in designing experiments
or field studies by indicating what must be controlled or monitored. It is
equally important to discover which factors are not of importance so
that they need not be studied or controlled. Furthermore, such studies
of the model yield insight into complex dependences. Finally, a model
may be economically useful in optimizing pest control or harvesting and
it may be useful in predicting the effects of changing the environment or
of introducing new species (see Watt, 1968).
To construct a realistic model one begins by formulating submodels
for the individuals in the population (Watt, 1961; Holling, 1963, 1964).
The birth, death, and growth rates of individuals are formulated in
terms of their age, size, sex and other important characteristics. These
submodels are based on the life history studies of the individuals in the
laboratory or the field. They are combined into the model which is then
studied. Results are compared with experiments or observations of the
total population and, if they agree, one has some confidence in the
predictive validity of the model. If the results are at variance with
reality, this indicates that some basic mechanisms have been erroneously
described or overlooked. The above program may appear to require
more information than is available or readily obtainable. If information
for a submodel is lacking, one simply assumes a biologically reasonable
relationship with one or more unspecified parameters and checks the
model for some range of parameter values. If the response is insensitive
(robust), one need not obtain further information; however, if this is not
the case, further information is essential and absolutely must be
included.
It should be emphasized that a model is limited by the factors
included in the submodels. For example, if the presence of a toxic
substance is not included, the model cannot predict its effect. However,
to include its effect one makes statements in the submodels as to how it
influences births, deaths, individual growth etc., and then calculates the
effect on the total population. The latter information is determined by
the model and is not known a priori.
In this paper I discuss models as opposed to simulations; I distinguish
the latter by their one-to-one correspondence with individuals in a
population. Simulation studies rely heavily on statistical considerations,
201
The process of constructing a mathematical model is itself instructive,
since it forces one to set down one’s thoughts clearly and it may indicate
areas in which basic understanding is lacking. Once the model is
constructed, it can be studied to exhibit sensitivities. Thus, one may
conclude that more precise information about some specific biological
process is required or that certain environmental effects are especially
critical in determining the population dynamics. This information may
suggest important experiments. It will also aid in designing experiments
or field studies by indicating what must be controlled or monitored. It is
equally important to discover which factors are not of importance so
that they need not be studied or controlled. Furthermore, such studies
of the model yield insight into complex dependences. Finally, a model
may be economically useful in optimizing pest control or harvesting and
it may be useful in predicting the effects of changing the environment or
of introducing new species (see Watt, 1968).
To construct a realistic model one begins by formulating submodels
for the individuals in the population (Watt, 1961; Holling, 1963, 1964).
The birth, death, and growth rates of individuals are formulated in
terms of their age, size, sex and other important characteristics. These
submodels are based on the life history studies of the individuals in the
laboratory or the field. They are combined into the model which is then
studied. Results are compared with experiments or observations of the
total population and, if they agree, one has some confidence in the
predictive validity of the model. If the results are at variance with
reality, this indicates that some basic mechanisms have been erroneously
described or overlooked. The above program may appear to require
more information than is available or readily obtainable. If information
for a submodel is lacking, one simply assumes a biologically reasonable
relationship with one or more unspecified parameters and checks the
model for some range of parameter values. If the response is insensitive
(robust), one need not obtain further information; however, if this is not
the case, further information is essential and absolutely must be
included.
It should be emphasized that a model is limited by the factors
included in the submodels. For example, if the presence of a toxic
substance is not included, the model cannot predict its effect. However,
to include its effect one makes statements in the submodels as to how it
influences births, deaths, individual growth etc., and then calculates the
effect on the total population. The latter information is determined by
the model and is not known a priori.
In this paper I discuss models as opposed to simulations; I distinguish
the latter by their one-to-one correspondence with individuals in a
population. Simulation studies rely heavily on statistical considerations,