PREDATION I - INTRODUCTION AND MODELS
I. Differences in the ways predation and competition are studied
A. Occurrence in nature
1. Competition may or may not occur and if it does it may be of limited importance in
communities.
2. Predation - in the broad sense- is the mechanism by which all energy and material pass
through food chains.
3. Some models of competition have the potential to increase species diversity
B. Laboratory tests of the concepts
1. The competitive exclusion principle is very easy to demonstrate in laboratory situations
2 The balance between predator and prey is very difficult to simulate with laboratory
experiments.
II. The mathematical modeling of predator prey relationships.
A. Assumptions of the model
1 Population growth can be modeled by the Lotka-Volterra equations.
2 The intensity of predation increases as the number of predators increases.
This implies that the mortality of prey increases as the number of predators increases.
i.e. the prey are limited by predation
3 In the two species system being modeled, the prey are the only food source for the
predators.
This implies that the birth rate of the predators increases as the density of prey increases.
i.e. the predators are food limited
4 Interactions between predator and prey are multiplicative.
That is the intensity of predation is a function of the encounters between predators and prey.
THEN:
dN/dt = rN - a'CN
where N is the number of prey organisms
C is the number of predators
r is the intrinsic rate of population increase for the prey
a' is the effect of each encounter with a predator on the prey
and
dC/dt = fa'CN-qC
where fa' is the benefit that each encounter with a prey organism brings a predator
q is the mortality rate of the predators
Then at equilibrium for the prey (dN/dt = 0);
the density of the predators is a constant (!)
C=r/a'
And at equilibrium for the predators (dC/dt = 0);
N=q/fa'
the density of the prey is a constant (!)
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