Predation
One of the first predator-prey relationships to be closely studied as to their population dynamics
was the snowshoe hare - Canadian lynx association. One of the most striking characteristics of
this dynamic is the oscillations in both populations (Figure 1). Since then, the predator-prey
oscillations have routinely been seen. For this simulation we'll make the prey and predator
populations totally dependent on one another.
There are four possible oscillation scenarios (the predators are always shown in RED, the prey in BLUE for all the
diagrams in this exercise.
1.
Either the predator or prey could go extinct. If the prey go extinct, the predator will soon follow.
Figure 4.
Predator
goes extinct
followed by
explosive prey growth (A), Prey goes extinct
followed by predator (B)
2.
A stable oscillation (Figure 5; The prey continues to grow under the blue line for the left graph. The
predator grows in the gray area. The arrows show the population trajectory).
Figure 5. Stable Oscillation.
3.
A convergent oscillation (Figure 6).
Figure 6. Convergent oscillation.
4.
A divergent oscillation (Figure 7). Divergent oscillations may eventually lead to extinction of one or both
species (The predator in this case).
Figure 7 Divergent oscillation
Logistic Growth; Natural Regulation of Population Size
The physical environment is always fluctuating, sometimes in a predictable way (but often not). While
seasons and climate patterns are clearly predictable, short term weather patterns often are not. Carrying
capacity, K, for example, describes the resources that are available in the environment, and resource
availability obviously changes over time.
Regular changes in the environment can cause a species to go extinct.
The logistic growth map shows that a population will continue
with a density of K in a constant environment as long as the
reproductive rate, r, is positive.
If the population does not go extinct, but the environment
fluctuates, the population will sometimes be above (or below) K
and there will a discrepancy between the available resources and
the population size. When 2 populations interact we may see a
stable oscillation as in figure 5.
Dispersion
The dispersion of a population may also be affected by fluctuating resources. Populations are not usually
evenly distributed over their range so that members are concentrated in particular areas. The surprising
fact is that areas of high population density do not necessarily correspond to high quality habitat. A patch
is an area where population densities are higher than normal. These patches may be places where
historically the habitat was favorable (so that the animals chase around the favorable habitats and are
often a step behind.
Uniform/Even
3 possible dispersion patterns:
Limiting factors to Population Growth
Several other agents can work to control population sizes and keep them permanently below the carrying
capacity:
 Density Dependent limiting factors control population size by exerting more influences when the
population density increases and less when the density is low. Parasitism and disease would be
examples of facultative agents.

Density Independent limiting factors: Catastrophic Agents are independent of population size.
Storms, drought, and temperature extremes are examples of catastrophic agents. Predation also
takes a constant number no matter how large the population gets. Many long-lived predators, for
example show little change in population density from year to year. No matter how large the prey
population gets, they'll continue to take the same number of prey.
Questions:
1. Describe how this predator prey interaction represents Negative Feedback.
2. Describe your graph and identify the lag phase, exponential growth, logarithmic growth and
estimate what the carrying capacity of the environment might be if you extended the number of
generations to 100.
3. Is positive feedback happening at any point in the graph?
4. What density dependent limiting factors might also play a role in the populations of wolves?
Rabbits?
5. Provide 2 other examples of negative feedback interactions.