254
WILLIAM STREIFER
wasp; Bosch (1971) applied it to redwoods; Usher (1969) to single tree
species; O’Neill and Styron (1970) to collembola; Pennycuick (1969) to
birds. Pennycuick‘s model is particularly realistic3 in that births and
deaths are fitted to life-history studies. Crowding effects and food
supply are also included. Both Engstrom-Heg (1970) and Pennycuick
et al. (1968) studied such population models in general. Engstrom-Heg
includes results for single-species as well as two- and three-species
interactions, whereas Pennycuick et al. consider both single-species and
two-species interactions. A notable feature of the latter model is the
inclusion of time lags. Hughes and Gilbert (1968) and Gilbert and
Hughes (1971) have modeled the infestation of plants by the cabbage
aphid (Brevicoryne brassicae). Their model, specifically formulated for a.
digital computer, is algebraic, age-specific, and includes the effects of
temperature, predators and parasites. Each of these effects is realistically modeled, including time delays, when needed. The 6rst paper
(1 968) illustrates how several separately observed ecological relationships can be combined to understand their composite effects. The
second paper (1971) considers stochastic variations, parasite (Diaeretus
rapw Curtis) strategy, and a field test of biological control. A study of
the model indicates that the parasite adjusts various aspects of its
behavior so as to maximize the total number of aphids per plant.
Specifically, the optimum number of eggs laid per female parasite, the
optimum number of immigrant parasites per immigrant aphid, and the
optimum age (instar periods) of the parasite at maturity are just those
values observed in nature. These two outstanding papers present an
excellent example of the utility of realistic models.
Other authors report modeling work in which similar individuals in a
population are grouped (or placed in compartments). Lefkovitch (1965)
discusses such grouping; Niven (1970) applies such models to Quokka;
Coulman et aZ. (1972) to the amphipod HyaZeZZa azteca. In the last model
the amphipods are grouped according to instars. Niven (1967, 1969) and
Taylor (1967, 1968) used models of this type to study Tribolium, both
single species and in competition. The animals are grouped according to
stages; eggs, small larvae, large larvae, pupae, young adults and mature
adults. Taylor’s models include cannibalistic phenomena, and agedependent birth and death rates.
Several other models warrant mention. Craig and Oertel (1966, 1967)
formulated and studied age-size specific computer models to determine
the relations between size distributions of species and their fossil
remains. Their models assume three possible growth rates and three
possible death rates. They obtain and plot many size-frequency and agefrequency histograms of the living and corresponding fossil populations.
Bella (1971) modeled the competitive interaction between trees, taking
WILLIAM STREIFER
wasp; Bosch (1971) applied it to redwoods; Usher (1969) to single tree
species; O’Neill and Styron (1970) to collembola; Pennycuick (1969) to
birds. Pennycuick‘s model is particularly realistic3 in that births and
deaths are fitted to life-history studies. Crowding effects and food
supply are also included. Both Engstrom-Heg (1970) and Pennycuick
et al. (1968) studied such population models in general. Engstrom-Heg
includes results for single-species as well as two- and three-species
interactions, whereas Pennycuick et al. consider both single-species and
two-species interactions. A notable feature of the latter model is the
inclusion of time lags. Hughes and Gilbert (1968) and Gilbert and
Hughes (1971) have modeled the infestation of plants by the cabbage
aphid (Brevicoryne brassicae). Their model, specifically formulated for a.
digital computer, is algebraic, age-specific, and includes the effects of
temperature, predators and parasites. Each of these effects is realistically modeled, including time delays, when needed. The 6rst paper
(1 968) illustrates how several separately observed ecological relationships can be combined to understand their composite effects. The
second paper (1971) considers stochastic variations, parasite (Diaeretus
rapw Curtis) strategy, and a field test of biological control. A study of
the model indicates that the parasite adjusts various aspects of its
behavior so as to maximize the total number of aphids per plant.
Specifically, the optimum number of eggs laid per female parasite, the
optimum number of immigrant parasites per immigrant aphid, and the
optimum age (instar periods) of the parasite at maturity are just those
values observed in nature. These two outstanding papers present an
excellent example of the utility of realistic models.
Other authors report modeling work in which similar individuals in a
population are grouped (or placed in compartments). Lefkovitch (1965)
discusses such grouping; Niven (1970) applies such models to Quokka;
Coulman et aZ. (1972) to the amphipod HyaZeZZa azteca. In the last model
the amphipods are grouped according to instars. Niven (1967, 1969) and
Taylor (1967, 1968) used models of this type to study Tribolium, both
single species and in competition. The animals are grouped according to
stages; eggs, small larvae, large larvae, pupae, young adults and mature
adults. Taylor’s models include cannibalistic phenomena, and agedependent birth and death rates.
Several other models warrant mention. Craig and Oertel (1966, 1967)
formulated and studied age-size specific computer models to determine
the relations between size distributions of species and their fossil
remains. Their models assume three possible growth rates and three
possible death rates. They obtain and plot many size-frequency and agefrequency histograms of the living and corresponding fossil populations.
Bella (1971) modeled the competitive interaction between trees, taking