General Ecology: Lecture 14
November 3, 2006
I.
II.
Predation defined
A.
An interaction in which one organism kills and eats another
1.
Examples: Classic predation, cannibalism and herbivory
Models of predation
A.
Lotka-Volterra equation for predation
1.
Assumptions of the model
a)
Exponential growth

Prey growth is exponential in absence of the predator

Predator decline is exponential in the absence of the prey
b)
Predators move randomly among prey.
c)
The proportion of encounters that result in prey capture and consumption are
the same at all predator and prey densities

May be true for some predators but not others (see section IV below.)
d)
No time lag for prey handling and consumption
2.
Prey equation.
a)
Continuous time equation: dV/dt = rV-a´CV

V = prey (I’m using this rather than P, because “P” could stand for
either predator or prey; think of “victim”)

r = intrinsic rate of growth (as in exponential growth equation)

a´ = kill rate

C = number of consumers (predators)
b)
Solve for equilibrium: dV/dt = 0

dV/dt = rV-a´CV = 0; so C = r/a´

This is the isocline for prey growth [Fig. 15.1a]

So, if the number of predators (C) is below this value, the
prey population (V) grows, but if above it, it shrinks.

Think intuitively about the values for r and a´ here
3.
B.
Predator equation
a)
Continuous time equation: dC/dt = fa´CV –qC

f is the efficiency at which prey is turned into offspring, multiplied
by a´CV, the total number of prey captured by the predator
population (see prey equation)

q is the per capita death rate
b)
Solve for equilibrium: dC/dt = 0

dC/dt = fa´CV –qC = 0; so V = q/fa´

This is the isocline for predator growth [Fig. 15.1b]

So if the number of prey (V) is above this value, the predator
population (C) grows, but if below it, it shrinks.

Think about intuitively
4.
Put the two equations together [Fig. 15.1c]
a)
Model predicts the cycling of predator and prey

Understand individual vectors for the predator and the prey here!

What this would look like through time? [Fig. 15.1d]
Rosenzweig-MacArthur model [Fig. 15.3]
1.
NOTE: We will not go through the mathematics of this model; focus on graphs.
2.
Similar to the Lotka-Volterra predation model, except that the prey population
grows according to the logistic growth model
a)
Hump shape of dV/dt = 0 (prey zero-growth) isocline) reflects the fact that
the lowest growth rates for the prey would be at its lowest and highest
densities, just as in the logistic growth equation
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
III.
At low prey densities, each act of predation results in a relatively
large loss of the population. Also, the population cannot recover as
quickly when there are a low number of individuals for reproduction.

At high prey densities, density-dependent factors (including
predation) decrease population growth.

Similar to dN/dt of logistic growth equation
b)
The predator population still grows (or shrinks) exponentially, and thus
dC/dt = 0 is a vertical line.
3.
The outcome of the predator-prey interaction depends upon where the prey and
predator isoclines intersect. You should work through the vectors to make sure you
understand the different outcomes!
a)
Intersection at peak of prey isocline  ?
b)
Intersection to right of peak of prey isocline (i.e. at relatively high prey
populations)  ?
c)
Intersection to left of peak of prey isocline (i.e. at relatively low prey
populations)  ?

Note that this situation corresponds with a predator that is relatively
efficient at converting prey eaten to offspring.

Can a predator be too efficient?
d)
Prey refuge

Explain the refuge in biological terms. What is meant by a refuge
and why does the outcome of the model change with a refuge?
Experimental predator-prey systems
A.
Gause’s studies of Didinium populations preying on Paramecium caudatum [Fig. 15.4]
1.
Basic experiment in a closed system [Fig. 15.4a]
a)
Predators consume all prey and then die
2.
Experiment with sediment as a refuge [Fig. 15.4b]
a)
NOTE: You should be able to explain what is happening for the predator
and prey populations in different parts of the graph.
b)
Harvest refugia

What is a harvest refugia? What role do they play in conservation
efforts?
3.
Experiment with continued immigration of both predator and prey [Fig. 15.4c]
a)
Added one Paramecium and one Didinium every 3rd day.

Stable oscillation!

Why would researchers strive to achieve stable oscillations?
Gause’s key conclusion: immigration and emigration are necessary to maintain a
balanced predator-prey relationship
a)
Note that these are not in any of the models.
Huffaker’s studies of mite populations
1.
Basics of experiments (study organisms and set-up)
a)
Prey is the six-spotted mite that feeds on plant material such as oranges.
Predator is a predatory mite.
b)
His goal: create a closed system where predator and prey oscillated
2.
Variations and results (see text pp. 267-269 for details)
a)
What did he start with ?
b)
Why did he keep adding complexity?

Concept of environmental heterogeneity: thought he could get a
stable oscillation if the environment was complex enough.
c)
What were his major results?

Heterogeneity did help sustain the populations, but the populations
eventually crashed [Fig. 15.6]
3.
Huffaker’s key conclusions: Like Gause, he concluded that immigration was
required…
4.
B.
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C.
IV.
Pimentel et al. (1963): (see text p. 270)
1.
Created a “metapopulation” with host flies and parasitic wasps. This model
allowed for movement between distinct cells. At 16 cells, the populations died out,
but at 30 he was able to get predator-prey oscillations in the system as a whole.
a)
Some “cells” (a.k.a. individual populations) would die out but would be
replenished by other cells (so really, immigration also matters here…)
b)
30 cells were enough to keep the populations dispersed so that parasite
numbers wouldn’t overwhelm the prey.
What factors contribute to the impact of a predator on prey abundance?
A.
The responses of the predator to prey
1.
Functional response of individual predators. Three models [Fig. 15.7]
a)
Type 1: Predator responds linearly to prey concentration up to a max value.
b)
Type 2: The rate of prey capture decreases with more prey present

Caused by a finite “handling time” for each prey.
c)
Type 3: At low prey levels, the predator is ineffective. (Why?) At high
prey levels, the predator is satiated (as for type 2).

The type 3 curve may also be seen due to prey-switching by
generalist predators [Fig. 15.10]

In this case, the relatively low rate of capture is due to the
predator feeding on a different, more abundant prey.

Can have effect of stabilizing prey populations.

Might also reduce impact of competition in similar species
that both serve as prey.
2.
Numerical response of the predator
a)
Short term: Aggregative response (i.e. feeding aggregations of birds on
fish)
b)
Long term

Immigration into an area with abundant prey

Increased reproductive rates (think about Lotka-Volterra equations)
B.
The population size of the prey
1.
If the prey pop. is at high densities, the loss due to predation may be insignificant
Study questions
1.
What are the basic assumptions of the Lotka-Volterra model for predation? How do the
assumptions of the Rosenzweig-MacArthur model differ?
2.
Are the Lotka-Volterra equations based on exponential growth or logistic growth? What about the
Rosenzweig-MacArthur model? (HINT: Think carefully about the R-M model—answer not
straightforward!)
3.
Be able to recognize and write out the Lotka-Volterra equations for both the prey and the predator.
We will focus on the continuous time model. You should be able to define all the terms in both
equations and state what each equation means in words.
4.
Make a sketch of the Lotka-Volterra predator-prey graph. Be sure you:
a.
label your axes,
b.
Identify and label both the predator and prey isoclines. Know what these lines actually
mean (state in words).
c.
Identify and label the x and y-intercepts and solve for from the basic equations. Show your
work!
5.
What pattern of predator and prey populations does the Lotka-Volterra model predict? Be able to
draw prey, predator and “net” vectors in each quadrant.
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6.
Why is the zero-growth isocline for the prey drawn as a hump in the Rosenweig-MacArthur
model?
7.
Given any of the graphs shown in Fig. 15.3 (that illustrate the Rosenzweig-MacArthur model), be
able to
a.
Label the axes
b.
Label the lines
c.
Draw the proper vectors in each of the regions
d.
Describe and explain the outcome of each situation (i.e. will the population oscillate, reach
a stable equilibrium, etc…) and why, based on the biological interactions (don’t just reexplain the math?)
e.
Be able to match each graph on the right with the phase-plane diagram on the left.
f.
Be sure you understand the difference between Fig. 15.3 b and 15.3 c. In which is the
predator more efficient? In practical terms, why might that be ultimately problematic for
the predator as well as the prey?
8.
Discuss the three different outcomes obtained by Gause in his predator-prey experiments with
ciliates (Fig. 15.4). Be sure you know the differences in the experimental conditions that led to
the different outcomes.
9.
What general conclusion did Gause reach after he completed his experiments? Are these
conclusions consistent with the Lotka-Volterra models? Do they match any of the models?
10.
What is a “harvest refugium” Describe the simple experiment Gause did to show the potential
value of harvest refugia to prey species. What is the ecological value of harvest refugia in the real
world?
11.
What did Huffaker think was necessary for creating a stable, oscillating predator-prey system in
the lab? Was he successful? Explain. What general conclusion did Huffaker reach?
12.
Compare the experiments and results of Pimentel et al. (1963) to those of Gause and Huffaker.
Did the Pimentel results support the hypotheses developed by Gause and Huffaker based on their
experiments? Explain.
13.
Sketch the three types of functional responses and provide a basic explanation as to what each
curve means in terms of the ability of a predator to find and eat its prey.
14.
Which of these functional response curves (could be more than one):
a.
Takes predator satiation into account?
b.
Would help a rare prey item from going extinct?
15.
What makes small prey populations more vulnerable to predator limitation than larger ones?
16.
What is meant by the “numerical response” by predators? Give examples of both short and longterm numerical response.
17.
Is generalist or specialist predator more likely to create stability in its prey populations? Explain.
18.
Is a generalist or specialist predator more likely to wipe out/create oscillations in its prey
populations? Explain.
19.
NOTE: See also questions posed in the body of the outline itself.
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