This attached is an ecology lab assignment.
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 answer question 1 below in your lab notebook. OBJECTIVE: This week we are investigating competition between two species (interspecific competition) under the Lotka‐Volterra competition model. You will use the program Populus to run these models. By using Populus to complete the exercises, you should gain a better 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 carrying 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 equilibrium (‘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/research/resources/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. b. What is β (in equation 2)? Unit 17 Lab ~ Competition 1 http://www.cbs.umn.edu/research/resources/populus/download-populus Start Populus, select ‘Multi‐species Dynamics’, and choose ‘Lotka‐Volterra Competition’. Take a look at the Populus help sections for Lotka‐Volterra 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 r .9 .5 K 500 700 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 briefly describe the population dynamics of each species over time. What happens to species 2? Species 1 Species 2 No 10 20 r .9 .5 K 500 200 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 represent? 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 their 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 arrow 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‐Volterra 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 b. 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 arrow in the direction the population of each species will move, and draw a diagonal arrow for the “combination” of the two species’ arrows. Use a solid line for the Species 1 arrow, a dotted line for the Species 2 arrow, and a wavy line for the diagonal arrow. e. Label all equilibria. 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 13. a. Which parameters (of N1, N2, K1, K2, r1, r2 ,α , β ) affect the position of species 1's isocline? b. 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‐Volterra 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 absorbs green light more efficiently than it absorbs 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 (absorbs green light)Green cyanobacterium BS2 (absorbs 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 results 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. (2007) analyzed the cyanobacteria present in 70 aquatic environments that ranged from clear ocean wva- ters (where green light predominates) to highly turbid 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 ria were found in highly turbid watersbut both types were found in waters of intermediate turbidity, where both green and red light were available. Thus, the labo- ratory 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 resource: 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 results 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. (2004) studied 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 absorbs 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 absorbs 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 Volterra (1926) both modeled competition by modifying the logistic equation that we discussed in Con- 282 Chapter 12 use a graphical approach to examine the conditions under 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