Chapter 35
Herbivore-Algae Predator–Prey Dynamics
That the carnivore may live herbivores must die.
(H. Spencer Data of Ethics, 1879)
35.1 Herbivore-Algae Predator–Prey Model
Let us return to the simple predator–prey model to see that even without migration
the system can exhibit a wide range of responses, not just a simple population crash.
Assume that the prey are algae in a pond on which an herbivore grazes. The data for
this problem has been invented. Its input data, parameters, and initial conditions
would normally be determined by experiment.
The model consists of two main parts, one for the change in the algae population,
one for the herbivore. The algae-growth portion of the model we have seen before
in various forms. The growth rate is a function of the algal density, ALGAE. This
function is monotonic and declining (Fig. 35.1). Algal growth is calculated as the
product of the density and the growth rate.
The algae density is reduced through consumption by the herbivore. The consumption per head is a nonlinear function of the algal density: the greater the
density, the higher the consumption per head. The consumption rate is simply the
product of the number of herbivore and the consumption per head (Fig. 35.2).
The herbivore death rate is determined by their average life span, which is a
nonlinear function of the consumption per head: the higher the consumption per
head, the longer the life span, within limits (Fig. 35.3). Indirectly, the denser the
algae, the lower the herbivore death rate.
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_35,
© Springer International Publishing Switzerland 2014
305
Herbivore-Algae Predator–Prey Dynamics
That the carnivore may live herbivores must die.
(H. Spencer Data of Ethics, 1879)
35.1 Herbivore-Algae Predator–Prey Model
Let us return to the simple predator–prey model to see that even without migration
the system can exhibit a wide range of responses, not just a simple population crash.
Assume that the prey are algae in a pond on which an herbivore grazes. The data for
this problem has been invented. Its input data, parameters, and initial conditions
would normally be determined by experiment.
The model consists of two main parts, one for the change in the algae population,
one for the herbivore. The algae-growth portion of the model we have seen before
in various forms. The growth rate is a function of the algal density, ALGAE. This
function is monotonic and declining (Fig. 35.1). Algal growth is calculated as the
product of the density and the growth rate.
The algae density is reduced through consumption by the herbivore. The consumption per head is a nonlinear function of the algal density: the greater the
density, the higher the consumption per head. The consumption rate is simply the
product of the number of herbivore and the consumption per head (Fig. 35.2).
The herbivore death rate is determined by their average life span, which is a
nonlinear function of the consumption per head: the higher the consumption per
head, the longer the life span, within limits (Fig. 35.3). Indirectly, the denser the
algae, the lower the herbivore death rate.
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_35,
© Springer International Publishing Switzerland 2014
305