Unit17_LAB_Instructions_Competition
ECOL302 Unit 17 Lab Instructions: Two-Species Competition
LAB FORMAT: This is a computer-based lab.
BEFORE doing this lab, read the textbook excerpt that we have posted on D2L, and answe
question 1 below in your lab notebook.
OBJECTIVE: This week we are investigating competition between two species (interspecific
competition) under the Lotka‐Volte
a competition model. You will use the program Populus to
un these models. By using Populus to complete the exercises, you should gain a bette
understanding of the model, two‐species population dynamics in this system, and become
comfortable working with isoclines of zero growth in state space. Please take the time to
understand what all parts of the equations and plots mean. For example, why does adding
individuals of a competing species reduce the ca
ying capacity for both species? What factors
determine the outcome of the competition? How do the different model parameters need to change
to create each of the four possible outcomes of competition: both species coexist, species 1
excludes species 2, species 2 excludes species 1, or an unstable equili
ium (‘saddle point’ case)?
You should be able to comfortably answer these questions by the end of the lab. Feel free to use
your notes, textbook, your TA, Populus help screens, and each other for help as you work through
the exercises.
Before you start the lab, you should download the Populus program at
http:
www.cbs.umn.edu
esearch
esources/populus/download-populus.
We are working with an extension of the logistic growth model, using the following equations:
??
1
?? = ??1
?
1
−?
1
−∝?
2
?
1
( )
??
2
?? = ??2
?
2
−?
2
−β?
1
?
2
( )
1) a. Describe the elements of the first equation in your own words. Include explanations
for N1, K1, K2, α, and N2.
. What is β (in equation 2)?
Unit 17 Lab ~ Competition 1
http:
www.cbs.umn.edu
esearch
esources/populus/download-populus
Start Populus, select ‘Multi‐species Dynamics’, and choose ‘Lotka‐Volte
a Competition’.
Take a look at the Populus help sections for Lotka‐Volte
a Competition (F1 for DOS
program; page 14 of the Windows help file).
2) Enter the parameter values below, run the simulation until steady state,
and sketch the N vs. t graph.
Species 1 Species 2
No 10 20
.9 .5
K XXXXXXXXXX
α or β .6 .7
3) Describe the population dynamics you see. Does either species go extinct? Does the
population density of each species stabilize? What is the density of each species at this
point? What do these population densities represent for each species? How do they
compare to the values for this parameter that you entered into the model?
4) Now set the initial population size for species two to 0, run the simulation again and
sketch a graph. Describe the population dynamics for species one. At what density of
individuals does the population stabilize? Why is it different from the last simulation and
what does this value represent? How does it compare to the value for this parameter that
you entered into the model?
2
5) Enter the values below and run the simulation until steady state. Sketch the graph of N
vs. t and
iefly describe the population dynamics of each species over time. What
happens to species 2?
Species 1 Species 2
No 10 20
.9 .5
K XXXXXXXXXX
α or β 1.5 .7
6) Now switch to the state space graph, in the “Plot Type’ box check ‘N2 vs. N1’. What are
the units on the two axes? What does a point somewhere, anywhere, on the graph
epresent?
7) What do each of the two straight lines on the graph represent? What is the
population growth rate for each species on its line?
Recall that at population densities below a zero growth isocline, a species still has “room” for its
population to increase, so the population growth rate will be positive. Above a species’ zero growth
isocline, the density of the species has exceeded the available space (or resources) for population
growth, so the population growth rate will be negative.
Predict the population growth trajectories for each species and the ultimate changes in thei
combined abundances in each section of the state space graph. Check your predictions by doing a
trajectory (or vector analysis) in Populus. To do this in the old DOS versions of Populus, hit Alt‐ S,
use the a
ow keys to move the cursor around the graph and then hit enter. For the Windows and
Mac versions, you will need to change the initial population sizes to get points in each quadrant of
the state space. Compare the state space graph to a graph of N vs. t. Do the trajectories make sense?
8) What is the ultimate outcome of competition in this case? Why?
3
9 to 12) Using Populus, generate examples of each of the four outcomes of Lotka‐Volte
a
competitive interactions by changing the parameter values and draw them below. Pay
attention to which parameters affect the position and slope of the isoclines.
For each graph, do the following:
a. Draw and label the axes
. Draw and label the zero isocline for each species, using a solid line for Species 1 and a
dashed line for Species 2
c. Label all the points at which the isoclines cross the axes
d. For each region of the graph, draw an a
ow in the direction the population of each
species will move, and draw a diagonal a
ow for the “combination” of the two species’
a
ows. Use a solid line for the Species 1 a
ow, a dotted line for the Species 2 a
ow,
and a wavy line for the diagonal a
ow.
e. Label all equili
ia. Is each stable or unstable?
f. Title your graph (what case or outcome does the graph represent?)
g. List the values for r1, r2, K1, K2, α and β that you used to generate each case.
4
XXXXXXXXXXa. Which parameters (of N1, N2, K1, K2, r1, r2 ,α , β ) affect
the position of species 1's isocline?
. Species 2's isocline?
14. How do r‐values affect the behavior of trajectories?
15. What direction do trajectories have when they begin on isoclines?
16. How do initial conditions affect the outcome of the unstable, "saddle point" case?
17. Is the model we used in this lab (two‐species Lotka‐Volte
a competition) deterministic
or stochastic? Why?
5
Competition 281
(A) Competition in green light
Figure 12.12 Do Cyanobacteria Partition Their Use of
Light? Two types of cyanobacteria, BS1 and BS2, were
grown together under (A) green light (550 nm), (B) red light
(635 nm), and (C) "white" light (the full spectrum, which
includes both green and red light). BS1 abso
s green light
more efficiently than it abso
s red light; the reverse is true for
BS2. Only BS1 persists when the two types are grown together
under green light, and only BS2 persists when they are grown
under red light. However, both types persist under white light,
suggesting that BS1 and BS2 coexist by partitioning their use
ot light. Population densities are expressed in biovolumes.
(Ater Stomp et al. 2004.)
U.b
Red cyanobacterium BS1 (abso
s green light)Green cyanobacterium BS2 (abso
s red light) J.4
0.2
30
Days
(B) Competition in red light
0.6 r
grown alone under green or red light. However, when
they were grown together under green light, the red cya-
nobacterium BS1 drove the green cyanobacterium BS2 to
extinction (Figure 12.12A)as might be expected, since
BSI uses green light more efficiently than does BS2. Con-
versely, under red light, BS2 drove BS1 to extinction (Fig
ure 12.12B), as also might be expected. Finally, when
grown together under "white light" (the full spectrum
of light, including both green and red light), both BS1
and BS2 persisted (Figure 12.12C). Taken together, these
esults suggest that BS1 and BS2 coexist under white
light because they differ in which wavelengths of light
they use most efficienty in photosynthesis.
Following up on their laboratory experiments, Stomp
et al XXXXXXXXXXanalyzed the cyanobacteria present in 70
aquatic environments that ranged from clear ocean wva-
ters (where green light predominates) to highly tu
id
lakes (where red light predominates). As could be pre-
dicted from Figure 12.12, only red cyanobacteria were
found in the clearest waters and only green cyanobacte
ia were found in highly tu
id watersbut both types
were found in waters of intermediate tu
idity, where
oth green and red light were available. Thus, the labo-
atory experiments and field surveys conducted by Stomp
and colleagues suggest that red and green cyanobacteria
coexist because they partition the use of a key limiting
esource: the underwater light spectrum.
Evidence for resource partitioning has been found in
many other species, including protists, birds, fishes, crus
taceans, and plants. Overall, studies of resource partition-
ing suggest that species can coexist if they use resources
in different ways-an inference that is also supported by
esults from mathematical models of competition.
Competition can be modeled by modifying
the logistic equation
0.2
0 15 30
Days
(C) Competition in white light
0.6
0.4
.2
e
30 45
Days
In a marine example, Stomp et al XXXXXXXXXXstudied re-
source partitioning in two types of cyanobacteria col-
lected from the Baltic Sea. The species identities of these
cyanobacteria are unknown, so we will refer to them as
BS1 and BS2 (standing for Baltic Sea 1 and Baltic Sea
2). BS1 abso
s green wavelengths of light efficiently,
which it uses in photosynthesis. However, BS1 reflects
most of the red light that strikes its surface; hence, it
uses red wavelengths inefficiently (and is red in color).
In contrast, BS2 abso
s red light and reflects green light;
hence, B$2 uses green wavelengths inefficiently (and is
green in color).
Stomp and colleagues explored the consequences
of these differences in a series of competition experi-
ments. They found that each species could survive when
Working independently of each other, A. J. Lotka (1932)
and Vito Volte
a XXXXXXXXXXboth modeled competition by
modifying the logistic equation that we discussed in Con-
282 Chapter 12
use a graphical approach to examine
the conditions unde
which each species would be expected
to increase or de-
crease in abundance.
We begin by determining when
the population of
each species would stop changing in size, using the ap-
proach described in Web Extension
12.4. This approach
is