Biol 463 Assignment 2 -- Interspecific Competition
How to complete this assignment. This assignment is divided into three sections. There
is an associated Excel spreadsheet file that you will be directed to use to complete the
assignment. There is one journal article that you will be asked to consult to complete
Section 3. Please type your answers into this file, save it with the file name described below,
adn submit them to me in the Homework 2 dropbox on the course ANGEL website. In
Sections 2 and 3, you will also be asked to save and submit a filled-in copy of the Excel
spreadsheet. Please name both the answer file and the Excel spreadsheet with your PSU ID
– e.g. ABC1234.doc and ABC1234.xls. This assignment must be uploaded to ANGEL by 5PM
on March 1.
As we discussed in class, the Lotka-Volterra interspecific competition model, while oversimplified, has had a powerful influence on the interpretation of the dynamic consequences
of interspecific competition in the structuring of ecological communities. The goal of this
assignment is to familiarize yourself with the predictions of the L-V model and to consider
the impact of variation in resource resources and conditions on the outcome of competitive
interactions. To that end, I will ask you to use the associated Excel spreadsheet to explore
the outcomes of the L-V model and to evaluate the results of two examples based on
empirical studies of competition in real ecological systems.
The Excel Spreadsheet consists of 3 interactive sheets, and a 4th sheet that performs the
associated calculations. The 3 interactive sheets are titled Plots, Section 2, Section 3 and
are described below.
Plots: This sheet contains two figures and two tables.
The figures give the abundance of two species projected by the L-V model (left panel) over
time (0-600) and the Zero Net Growth Isoclines for both species (right panel) with the
equilibrium abundance indicated by a red dot. (Note that the colors of the lines correspond
in the two plots).
The tables contain the parameters for the L-V model (left table) and the final abundance of
the two species (right table). Note that the final abundance is the abundance at time 600.
Depending on the parameters, 600 time steps may not be enough to attain the true
equilibrium. For example, there may be conditions where species 1 will out compete
species 2, but it will take longer than 600 time steps for that to happen – so the equilibrium
will be 0 of species 2, even though there may still be a few around at time 600.
Section 2: Contains a table with parameter values for the scenario described in Section 2 of
the homework and a figure that will be generated as you fill in the values.
Section 3: Contains a table with parameter values for the scenario described in Section 3 of
the homework and a figure that will be generated as you fill in the values.
Part 1: Theoretical predictions
Using the Plots sheet generate figures for each of the 7 scenarios in the table below (i.e. fill
in the parameter values listed for each row of the table). For each scenario, a new set of
figures will be generated. Fill in the final abundance values in the table based on the
simulation output and answer the questions below.
Parameters
1
2
3
4
5
6
7
r1
K1
α12
r2
K2
α21
N1
N2
.1
.1
.1
.1
.1
.08
.08
100
150
150
100
100
100
100
1
1
1
0.7
0.7
1.2
1.2
.1
.1
.5
.1
.1
0.1
0.1
110
110
110
120
120
100
100
1
0.75
0.75
0.5
0.5
1.2
1.2
1
1
1
1
50
25
50
1
1
1
1
25
50
25
Final
Abundance
Species Species
1
2
Questions:
1. What is the outcome of scenario 1?
2. What is the outcome of scenario 2?
3. Scenario 3 has the same competition and carrying capacity parameters as in
scenario 2, but the growth rate of species 2 is greater.
a. What is the same in the outcome of scenarios 2 and 3?
b. What is the different in the outcomes of scenarios 2 and 3?
4. What is the outcome of scenario 4?
5. In which of scenario 4 or 6 is inter-specific competition stronger relative to intraspecific competition?
6. Why does the outcome of scenario 7 differ from that of scenario 6?
Part 2: Competition and Eutrophication
In class we discussed the “paradox of enrichment” in which species diversity declines as
the available resources increase. One explanation for this phenomenon is that competitive
interactions may increase as resources become more abundant. Here we will explore this
process in the context of eutrophication. Eutrophication is the process by which
ecosystems receive excessive nutrients that stimulate excessive plant growth – this a
phenomenon common in lakes and ponds that receive fertilizer, or other nitrogen and
phosphorous rich, runoff. The nitrogen and phosphorous are often limiting to plant growth,
and the additions from human pollution can cause so-called “algal blooms” as the
additional nutrients raise the carrying capacity.
Passarge et al (2006) studied the limitation of several algal species by phosphorous and
speculated on the effect of additional phosphorous on the competitive interactions of 5
algal species (see figures at the end of this assignment). In their experiments, the authors
grew all 5 algal species in settings with the same phosphorous levels to assess their
carrying capacities and then grew them in competition to assess their competitive ability.
Note from Figure 2 of Passarge et al. that Synechocystis has the highest carrying capacity,
and from Figure 3 that Synechocystis excludes Chlorella when they are grown together.
TO DO: Consider that the addition of phosphorous increases the carrying capacity of
Synechocystis and Chlorella, but for each additional unit of phosphorous, the carrying
capacity of Chlorella increases faster. The table in the sheet Section 2 gives the carrying
capacities for 10 levels of phosphorous concentration (higher levels indicate increasing
pollution inputs).
Call Synechocystis species 1, and Chlorella species 2, and use the Plots sheet to calculate the
outcome of competition as the different levels of phosphorous addition. Assume the
following parameters for both species (NOTE: they are on the excel sheet as well):
Intrinsic growth rate for both species is 0.1
α 12 is 1 and α 21 is 0.8 – Chlorella is larger and darker than Synechorcycstis so it has a larger
impact due to competition for light.
The initial population sizes are 1 for both species.
Fill in the above parameter values for each species in the Plots sheet. Then fill in each of
the carrying capacities that result from each of the 10 phosphorous addition levels. In the
Section 2 sheet, fill in resulting final densities of Synechocystis and Chlorella after 600 time
steps. NOTE: this will automatically fill in the figure below that plots the final abundance of
each species, and the total algal abundance as a function of the phosphorous levels.
Questions:
1. What kind of competition is this: interference or exploitation?
2. How does the total abundance of algae change as phosphorous increases?
3. How does the diversity in this “pond” change as phosphorous increases? (Note: for
simplicity, consider that diversity is simply the number of species present.)
4. How does the pattern in Question 2 relate to the “paradox of enrichment”?
Part 3: Competition and Climate Change
Climate change is expected to affect the conditions that species face – notably increased
temperatures and earlier springs may affect seasonal breeding. Ahola et al (2007) studied
the impact of climate on the seasonal breeding of two birds (great tits and pied flycatchers)
that compete for nesting sites. Both species breed in Finland and use holes in trees (and
manmade structures) for nesting. Great tits are resident species and pied flycatchers are
migrants (spending the winters in tropical Africa) – as a consequence, great tits often get
the first pick of nesting sites and flycatchers are limited to unoccupied sites or must
physically displace great tits from their nests. If great tits begin their nests early, relative to
the arrival of flycatchers, then they better able to fend off take-over attempts by flycatchers.
There is speculation that global warming will affect northern areas more than equatorial
areas. As a consequence, one might expect that over time, great tits may begin their nests
earlier as global temperatures rise. Thus, as global temperatures rise, we would expect
great tits to be increasingly strong competitors for nest sites.
TO DO: Consider that global warming will result in earlier nest building by great tits,
resulting in lower ability of flycatchers to displace nests, and ultimately lower competitive
ability. The sheet Section 3 gives values for the competition coefficient of each bird on the
other as the temperature increases.
Call great tits species 1, and pied flycatchers species 2 and use the Plots sheet to calculate
the outcome of competition as function of the temperature increase. Assume the following
parameters for both species (NOTE: they are on the excel sheet as well):
Intrinsic growth rate is 0.1.
Carrying capacity is 100 for both species.
Initial population size is 1 for both species.
Fill in the above parameter values for each species in the Plots sheet. Then fill in each of
the competitive abilities that result as temperature increases. In the Section 3 sheet, fill in
the resulting final densities of great tits and pied flycatchers. NOTE: this will automatically
fill in the figure below that plots the final abundance of each species.
Questions:
1. What type of competition is this: interference or exploitation?
2. Describe your prediction for the impact of climate warming on the abundance of
great tits and pied flycatchers.
3. Though this was a very simplified example of the story presented in Ahola et al
(2007), the results were designed to replicate one of the patterns presented in that
paper. Which figure illustrates the same pattern as that seen in the figure in the
Section 3 sheet?
http:/ / www.esajournals.org - ESA Online Journals Display Figures
Close
2/ 21/ 13 12:11 AM
Print
[previous] [next]
High-Resolution Image (82KB)
http:/ / www.esajournals.org - ESA Online Journals Display Figures
2/ 21/ 13 12:11 AM
FClose
IG. 2. Monoculture
experiments under phosphorus-limited conditions: (A) Synechocystis (gray squares), (B) Chlorella (“plus”
Print
symbols), (C) Monoraphidium (triangles up), (D) Selenastrum (black squares), and (E) Monodus (triangles down). Open diamonds
[previous] [next]
indicate the external phosphorus concentration. Solid lines indicate the population densities predicted by the model (Eqs. 1–4), and
dotted lines
indicate the predicted
external phosphorus concentrations. For parameter values, see Table 1.
High-Resolution
Image (82KB)
[previous] [next]
http:/ / www.esajournals.org.ezaccess.libraries.psu.edu/ action/ showFullPopup?id= i0012- 9615- 76- 1- 57- f02&doi= 10.1890%2F04- 1824
Page 1 of 1
FIG. 5. Competition experiments under phosphorus-limited conditions: (A) Synechocystis (gray squares) displaces Chlorella (“plus”
symbols); (B) Chlorella (“plus” symbols) displaces Monoraphidium (up-pointing triangles); (C) Monoraphidium (up-pointing triangles)
displaces Selenastrum (black squares); (D) Selenastrum (black squares) displaces Monodus (down-pointing triangles). Open diamonds
indicate the external phosphorus concentration. Solid lines indicate the population densities predicted by the model (Eqs. 1–4), and
dotted lines indicate the predicted external phosphorus concentrations. For parameter values, see Table 1.
[previous] [next]