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.
 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 “statespace” 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 K_{1} and K_{1}/a_{2}_{®}_{1}. The competition coefficient a_{2}_{®}_{1 }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 b_{1}_{®}_{2}).
What are the values of these parameters: (4 pts)
K_{pa}= a_{pc}_{®}_{pa}=
K_{pc}= b_{pa}_{®}_{pc}=




 b) If we start with 50 Pa and 100 Pc, what will happen? Trace the path of the two populations through the statespace 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, reassess the correct direction. If you reach the intersection of both lines stop (both species coexist 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).
 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 coexist 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 rate, r, for each species? Show your work!
Pop growth rate r Pa (2pts): Pop growth rate r Pc (2pts):
 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 discretetime annual population growth rate l is 4.0 (good conditions), a quarter of the time l is 1.0 (medium), and half the time l is 0.5 (bad) (all l 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 l in all years is 1.1.
 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  50  Good 
1  Bad  
2  Bad  
3  Medium  
4 
 What is the longterm 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):
 For this question, use the page with color maps of temperature and precipitation and biomes.
 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):
 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 the Temperature map) (1pt)?
 Why is it likely so dry at this location compared to areas to the east? Explain. (2 pts)
 If climate change warms this region by 3°C, will this change the biome in this location? Why? (2 pt)
 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 O_{2}/m^{2}s) 
0  1 
5  5 
10  12 
15  18 
20  20 
25  1 
 What range of temperatures does a plant in South America experience, if mean annual temperature at its location is 10°C, and there is a 10°C difference between the warmest month (January) and coldest month (August), and a 20°C 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 temperature (yaxis) 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 yaxis. (4 pts)
 Will 3°C 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)
 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 +3°C warming (2pts):
What is the ratio of the metabolic rates (MR), MR_{after}/MR_{before} (1pt):
 Using the figure above, what is the rate of photosynthesis at the mean annual temperature before (10°C) and after climate change.
Photosynthetic rate before climate change (1 pt):
Photosynthetic rate with +3°C warming (1 pt):
What is the ratio of the photosynthetic rates (PR), PR_{after}/PR_{before }(1 pt):
 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)
 If the plant grows additional leaves so that it doubles its surface area from 0.10m^{2} to 0.2m^{2} 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 O_{2}/m^{2}s, which means that an increase in leaf area (m^{2}) 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)
 If the temperature on the leaf surface in the sun reached 30°C 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
N_{t}=N_{0}e^{rt}; N_{t}=l^{t}N_{0} if l>1, then l1 = % increase per year; if l<1, then 1l = % decrease per year.
; K = carrying capacity, r = per capita pop growth rate, MSY = rK/4
a_{2}_{®}_{1 }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 b_{1}_{®}_{2}.
Adiabatic cooling: 7°C for each 1000m of elevation
Metabolic rate (in W) = c*M^{3/4}e^{[E/(kT)]}; where c=e^{20}, M is mass in grams, E is activation energy, 0.63eV, k is Boltzmann’s constant, 8.617×10^{5} eV/°K; and T is Temperature in °K (0°C = 273.15°K)
For Question 3: The maps below show annual precipitation (top), annual average temperature (middle) and likely biomes given temperature and precipitation (bottom).