REALISTIC MODELS IN POPULATION ECOLOGY
253
probability of a tail being eaten were expressed as a function of the
number of feeding individuals and the food supply.
V I I I . OTHER APPLICATIONS
The applications discussed in the previous section were based on the
partial differential equation model, Eqn (20). That equation was solved
numerically in discrete approximations on a digital computer. Only two
of the applications discussed below employ models of this type (Gentry,
1971; and Saidel, 1968); the others utilize either discrete (matrix)
equations directly formulated for the digital computer or computer
models in the form of flow charts. These approaches do not differ greatly.
The advantages of analytic formulations are that one can be certain the
problem is mathematically “well set”, i.e. a unique solution exists.
Furthermore, special cases can occasionally be solved analytically to
provide checks of the final numerical computer solutions (Beyer, 1970).
Some researchers may, however, find computer models easier to formulate. It should be noted that there are available powerful computer
programs for solving systems of differential equations (King and Paulik,
1967; Brennan et al., 1970), which require little or no knowledge of
numerical methods on the part of the user.
The applications to particular species and the general population
models discussed below are limited to those in which individuals are
classified (or equivalently, compartmentilized) by age, size or other
attribute (instar, for example). Furthermore, only very recent English
language articles are referenced. Several excellent books and review
papers contain extensive bibliographies of the less recent literature
(Watt, 1961, 1962, 1968; Pielou, 1969; Gulland, 1971).
Gentry (1971) and Saidel (1968) both employ partial differential
equations in their models. Gentry applies Eqn (13) to the study of rat
eradication programs. Death rates are dependent on age, poisoning,
overcrowding and food supply; birth rates on the age structure and the
percentage of fertile females. The various strategies utilizing poison
and/or sterilizing chemicals are studied. A second density function for
sterile rodents is introduced for the case in which treated females produce
sterile offspring. Saidel (1968) disregards age in his models of bacterial
populations and employs an equation similar to (94). The growth
function is dependent on cell surface area and nutrient concentration,
the birth rate (binary fission) on cell volume, and the death rate on the
concentration of nutrient and toxic substances. Both Gentry and Saidel
have formulated quite realistic models.
Many researchers have employed various versions of the age-specific
matrix model. Rabinovich (1969) applied the model to the pteromalid
253
probability of a tail being eaten were expressed as a function of the
number of feeding individuals and the food supply.
V I I I . OTHER APPLICATIONS
The applications discussed in the previous section were based on the
partial differential equation model, Eqn (20). That equation was solved
numerically in discrete approximations on a digital computer. Only two
of the applications discussed below employ models of this type (Gentry,
1971; and Saidel, 1968); the others utilize either discrete (matrix)
equations directly formulated for the digital computer or computer
models in the form of flow charts. These approaches do not differ greatly.
The advantages of analytic formulations are that one can be certain the
problem is mathematically “well set”, i.e. a unique solution exists.
Furthermore, special cases can occasionally be solved analytically to
provide checks of the final numerical computer solutions (Beyer, 1970).
Some researchers may, however, find computer models easier to formulate. It should be noted that there are available powerful computer
programs for solving systems of differential equations (King and Paulik,
1967; Brennan et al., 1970), which require little or no knowledge of
numerical methods on the part of the user.
The applications to particular species and the general population
models discussed below are limited to those in which individuals are
classified (or equivalently, compartmentilized) by age, size or other
attribute (instar, for example). Furthermore, only very recent English
language articles are referenced. Several excellent books and review
papers contain extensive bibliographies of the less recent literature
(Watt, 1961, 1962, 1968; Pielou, 1969; Gulland, 1971).
Gentry (1971) and Saidel (1968) both employ partial differential
equations in their models. Gentry applies Eqn (13) to the study of rat
eradication programs. Death rates are dependent on age, poisoning,
overcrowding and food supply; birth rates on the age structure and the
percentage of fertile females. The various strategies utilizing poison
and/or sterilizing chemicals are studied. A second density function for
sterile rodents is introduced for the case in which treated females produce
sterile offspring. Saidel (1968) disregards age in his models of bacterial
populations and employs an equation similar to (94). The growth
function is dependent on cell surface area and nutrient concentration,
the birth rate (binary fission) on cell volume, and the death rate on the
concentration of nutrient and toxic substances. Both Gentry and Saidel
have formulated quite realistic models.
Many researchers have employed various versions of the age-specific
matrix model. Rabinovich (1969) applied the model to the pteromalid