Ecology 107 Midterm: I hereby pledge that my answers on this exam are entirely my own, & I only used materials provided by Dr. Kilpatrick in the course. I understand that doing otherwise constitutes cheating. Name:_______________________ See equations on page 5. 1) The graphs below show the classic research I showed in class by Gause from 1934 were he examined competition between two species of Paramecium. He started each species off with 5 individuals of in flasks of media alone. He next measured the nutrient use of both species. He found that P. aurelia used 2/3 of the resource that limits P. caudatum populations (nitrogen), whereas P. caudatum used 1.0 times as much of the resource that limit P. aurelia populations (phosphorus) (the different resources limiting Pa and Pc makes competition asymmetric). a) Use this information to construct a “state-space” graph (below). Draw isoclines for the two species using different colors and label them by putting a box around the name with the color for that species (6 pts). Remember that an isocline is a line where the population growth rate, dN/dt, for that species is 0. The endpoints of the isocline for a hypothetical species 1 (competing with species 2) are K1 and K1/21. The competition coefficient 21 measures the impact (or conversion) of species 2 on (or into) species 1 in terms of the resources that limit species 1 (& vice versa for 12). What are the values of these parameters: (4 pts) Kpa= pcpa= Kpc= papc= b) If we start with 50 Pa and 100 Pc, what will happen? Trace the path of the two populations through the state-space graph: Put a point at 50 Pa and 100 Pc, and move in the appropriate direction based on the isoclines. If you encounter an isocline or one of the axes, re-assess the correct direction. If you reach the intersection of both lines stop (both species co-exist at equilibrium). If you reach an intersection of an axis and an isocline and the correct direction is to go off the graph into negative space, stop (one species has gone extinct while the other is at equilibrium). Kpc Kpa Kpc/ Kpc/ c) Put a second point at 250 Pa, 100 Pc and repeat the same process as in (b) until you stop again. (4 pts) d) (4 pts) Interpret these results biologically. Can these two species co-exist together or does one go extinct? Does it depend on the starting population sizes? e) At equilibrium, what are the abundances of the two species and which species is more abundant? (2 pts) f) You wanted to grow the two paramecium species as fast as possible to send paramecium to biology classes all across the world. At what density should you grow them, and how long would this take, starting at a density of 5 (see top figs)? Density Pa (1pt): Day Pa (1pt): Density Pc (1pt): Day Pc (1pt): g) What is the fastest rate you could sustainably harvest each species? Show your work! Maximum harvest Pa (2pts): Maximum harvest Pc (2pts): h) What is the maximum per capita population growth ra.

1. Ecology 107 Midterm: I hereby pledge that my answers on this
exam are entirely my own, & I only used materials provided by
Dr. Kilpatrick in the course. I understand that doing otherwise
constitutes cheating.
Name:_______________________ See
equations on page 5.
1) The graphs below show the classic research I showed in class
by Gause from 1934 were he examined competition between two
species of Paramecium. He started each species off with 5
individuals of in flasks of media alone.
He next measured the nutrient use of both species. He found
that P. aurelia used 2/3 of the resource that limits P. caudatum
populations (nitrogen), whereas P. caudatum used 1.0 times as
much of the resource that limit P. aurelia populations
(phosphorus) (the different resources limiting Pa and Pc makes
competition asymmetric).
a) Use this information to construct a “state-space” graph
(below). Draw isoclines for the two species using different
colors and label them by putting a box around the name with the
color for that species (6 pts). Remember that an isocline is a
line where the population growth rate, dN/dt, for that species is
0. The endpoints of the isocline for a hypothetical species 1
(competing with species 2) are K1 and K1/21. The competition
coefficient 21 measures the impact (or conversion) of species 2
on (or into) species 1 in terms of the resources that limit species
1 (& vice versa for 12).
What are the values of these parameters: (4 pts)
Kpa= pcpa=
Kpc= papc=
b) If we start with 50 Pa and 100 Pc, what will happen? Trace
the path of the two populations through the state-space graph:
Put a point at 50 Pa and 100 Pc, and move in the appropriate
direction based on the isoclines. If you encounter an isocline or

2. one of the axes, re-assess the correct direction. If you reach the
intersection of both lines stop (both species co-exist at
equilibrium). If you reach an intersection of an axis and an
isocline and the correct direction is to go off the graph into
negative space, stop (one species has gone extinct while the
other is at equilibrium).
Kpc
Kpa
Kpc/
Kpc/
c) Put a second point at 250 Pa, 100 Pc and repeat the same
process as in (b) until you stop again. (4 pts)
d) (4 pts) Interpret these results biologically. Can these two
species co-exist together or does one go extinct? Does it depend
on the starting population sizes?
e) At equilibrium, what are the abundances of the two species
and which species is more abundant? (2 pts)
f) You wanted to grow the two paramecium species as fast as
possible to send paramecium to biology classes all across the
world. At what density should you grow them, and how long
would this take, starting at a density of 5 (see top figs)?
Density Pa (1pt): Day Pa (1pt):
Density Pc (1pt): Day Pc (1pt):
g) What is the fastest rate you could sustainably harvest each
species? Show your work!

3. Maximum harvest Pa (2pts): Maximum harvest
Pc (2pts):
h) What is the maximum per capita population growth rate, r,
for each species? Show your work!
Pop growth rate r Pa (2pts): Pop growth rate r
Pc (2pts):
2) An ornithologist studies two populations of birds called song
sparrows. One population is migratory and spends winters in
Santa Cruz and summers in Alaska. Migration, and variability
in the arctic environment make it so that over a long time
(decades), a quarter of the time the discrete-time annual
population growth rate is 4.0 (good conditions), a quarter of
the time is 1.0 (medium), and half the time is 0.5 (bad) (all
are based on just females). Amazingly, the other population
doesn’t migrate at all, but just lives in British Columbia (B.C.)
all year long. There the conditions are more stable and the
population growth rate in all years is 1.1.
a. If there were 50 female individuals in each population this
year, and conditions in Alaska were those given in the table
over the next 5 years, what would the population sizes be (fill
in the table)? (5pts)
Year
B.C. population
at beginning of this year
Alaska population
at beginning of year t
Alaska Conditions
in year t
Now (0)
50

4. 50
Good
1
Bad
2
Bad
3
Medium
4
b. What is the long-term trajectory of these two populations
(growing, shrinking, stable) and why (what is the average %
growth or decline each year over the long term)?
Alaska/Santa Cruz (1pt):
British Columbia (2 pts):
3) For this question, use the page with color maps of
temperature and precipitation and biomes.
a. What is the annual avg temperature, annual precipitation and
likely biome at the place indicated by the tip of the arrow in
South America?
Temperature (1pt):
Precipitation (1pt):
Likely Biome (1pt):
b. Why is it so cool at this location compared to Paraguay (the
small country to the southeast of the arrow that is all in red on

5. the Temperature map) (1pt)?
c. Why is it likely so dry at this location compared to areas to
the east? Explain. (2 pts)
d. If climate change warms this region by 3C, will this change
the biome in this location? Why? (2 pt)
4) a. Use the data in the table to make a plot of the rate of
photosynthesis of a plant species versus temperature. Label the
axes, plot the points and connect them with a line/curve. (3pts)
Temp (C)
Rate of Photosynthesis (μmol O2/m2s)
0
-1
5
5
10
12
15
18
20
20
25
-1
b. What range of temperatures does a plant in South America
experience, if mean annual temperature at its location is 10C,
and there is a 10C difference between the warmest month
(January) and coldest month (August), and a 20C difference
between the hottest hour of the day (3pm or 15:00 in military
time) and coldest hour of the night (5am or 5:00)? On the figure
to the left, draw two curves (with different colors), one for the

6. temperature (y-axis) vs time for one day during January and one
for one day during August (and label them!). You may want to
figure out what the maximum temperatures are in the hottest
month at the hottest hour, and the same for the coldest hour on
the coldest day before drawing the temperatures vs time. Put
numbers on the y-axis. (4 pts)
c. Will 3C of warming increase or decrease photosynthesis by
the plant at the location from part 4b? Will the effect be the
same across all months and times of the day? Explain. (3 pts)
d. If a plant of this species weighed 150g (including its roots!),
calculate the approximate metabolic rate of this plant at the
mean annual temperature before and after climate change.
Metabolic rate before climate change (2pts):
Metabolic rate with +3C warming (2pts):
What is the ratio of the metabolic rates (MR),
MRafter/MRbefore (1pt):
e. Using the figure above, what is the rate of photosynthesis at
the mean annual temperature before (10C) and after climate
change.
Photosynthetic rate before climate change (1 pt):
Photosynthetic rate with +3C warming (1 pt):

7. What is the ratio of the photosynthetic rates (PR),
PRafter/PRbefore (1 pt):
f. For most plants the rate of photosynthesis is about twice the
rate of respiration (the metabolic rate). Will warming be a net
benefit or a net cost to the plant, and is the net cost/benefit the
same at all times of year and all hours of the day? Explain. (3
pts)
g. If the plant grows additional leaves so that it doubles its
surface area from 0.10m2 to 0.2m2 and doubles its mass from
150g to 300g, will this make the plant more or less efficient,
and by how much? Efficiency is photosynthetic rate for the
whole plant/metabolic rate for the whole plant. Remember that
the rate of photosynthesis is given in units of O2/m2s, which
means that an increase in leaf area (m2) linearly increases the
whole plant rate of photosynthesis. At the average annual
temperature, what is the ratio of the metabolic rate of the bigger
plant to the smaller plant, and what is the ratio of the
photosynthetic rates of the bigger and smaller plant?
Ratio of metabolic rates, big/small (2pts):
Ratio of photosynthetic rates, big/small (2pts):
Is the bigger or smaller plant more efficient and why? (3 pts)

8. h. If the temperature on the leaf surface in the sun reached 30C
and the plant wanted to reduce its temperature to more
efficiently photosynthesize, what are two ways it could
“thermoregulate” (cool down) and what are tradeoffs that might
occur if the plant used these strategies?
Equations and other information
Nt=N0ert; Nt=tN0 if >1, then -1 = % increase per year; if
<1, then 1- = % decrease per year.
; K = carrying capacity, r = per capita pop growth rate, MSY =
rK/4
21 measures the impact of species 2 on population growth rate
of species 1 in terms of the resources that limit species 1, and
vice versa for 12.
Adiabatic cooling: -7C for each 1000m of elevation
Metabolic rate (in W) = c*M3/4e[-E/(kT)]; where c=e20, M is
mass in grams, E is activation energy, 0.63eV, k is Boltzmann’s
constant, 8.617x10-5 eV/K; and T is Temperature in K (0C =
273.15K)
For Question 3: The maps below show annual precipitation
(top), annual average temperature (middle) and likely biomes
given temperature and precipitation (bottom).

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1.2 12 30 60 90 120 180 240 360
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13. 05010015020025002468101214161820DensityTime (days)P.
aurelia
02040608010012014016018002468101214161820DensityTime
(days)P. caudatum
0
50
100
150
200
250
300
050100150200250300
P. aurelia
P. caudatum