Posted: December 10th, 2024

Answer the Following Questions Related to Ecology

Question description

CompetitionAssignment(1).doc  1. Select"Multi-Species Interactions" from the Model tab on the menu. 2. Select"Lotka-Volterra Competition" from the pop-up menu.  Variables you control: In the Lotka-Volterra competitionequations, there are 4 variables controlling the population growth rate (dN/dt): 1. N - the current size ofthe population. In Populus, this is labelled N0, the population size atsome arbitrary time zero. 2. r - the intrinsic rate of increase (rmax = per capita birthrate - per capita death rate under optimal conditions) 3. K - environmental carryingcapacity (which reflects the strength of intraspecific competition) 4. α and β − competitioncoefficients. α is the effect on species 2 ofspecies 1 (α12).β =effect on species 1 of species 2 (α21). These reflect the strength of interspecificcompetition.  The input panel allows you to changeeach of these variables, for each of the two competing species. When you run the simulation "Tosteady state", it will run until population size is no longer changing foreither species. Steady state means dN/dt = 0 for both species. This can occurwith competitive coexistence (both species persist), or competitive exclusion (onespecies is driven extinct).   The goal of this exercise is tounderstand:  1. How differences between the twospecies in each of these 4 variables affects the outcome of competition,and  2. How the 4 variables affect the trajectorythrough which N1 and N2 change to reach that outcome.   Displays: For each run of the simulation,there are two output displays. Look at both displays for each simulation run, and understandhow they relate to each other.  From the input panel, run thesimulation with the default settings and look at the displays as you read the followingexplanation. "N vs T" plots populationsize for each species against time. "N2 vs N1" plotspopulation size for species 2 against population size for species 1 (this iscalled a phase-plane). On the N2 vs N1, there are three lines: · atrajectory that shows how the numbers of the two species change through time (green), · thezero-isocline for species 1 (red) · thezero-isocline for species 2 (blue) Remember that zero-isoclines show
where population growth is zero. An isocline is a line that connects points
with equal growth rates (dN/dt): a zero-isocline connects points with dN/dt =
0. On one side of the isocline, the population grows; on the other side, it shrinks.
With a plot of N2 vs N1: · Forspecies 1, population growth is positive LEFT of the (red) isocline, andnegative RIGHT of the isocline. The red isocline refers to the X axis, andgives information about changes in N1. · Forspecies 2, population growth is positive in areas BELOW the (blue) isocline,and negative in areas ABOVE the isocline. The blue isocline refers to the Yaxis, and gives information about changes in N2. · Foreither species, the arrows are parallel to the axis that plots the numbers ofthat species.  Stability Analysis: This is very useful for testing howwell you understand the Lotka-Volterra competition model! Select the N2 vs N1 “phase-plane”plot. Rather than running to steady state, run until time 1, then time 2, 3,etc, seeing if the trajectory follows the path you predicted ahead of time. Twovaluable ways of going about this are: · Leaveeverything else the same but change the initial population sizes. See if you canpredict the trajectory correctly. · Changeone variable (r, K, α, β) and see how the trajectory changes.  SIMULATIONS: The default values for variablesare: Species 1  Species 2 N0   10   20 r   0.9   0.5 K   500   700 α,β   0.6   0.7  A. Effect of initial population size(N1 and N2). 1.  Accept the default values for allvariables (if you've changed values, the defaults are given above so you canreset them). Re-set the simulation to run until steady state. QUESTION1: Before running any of the simulations, look at the phase plane. Mentallydraw in the carrying capacity connector and see where it lies in relation tothe equilibrium point. Do you expect the outcome of this simulation to becoexistence or competitive exclusion? 2.  Run the simulation and examine bothoutput displays. In the N2 vs N1 display, select different pairs of initialpopulation sizes, and understand the trajectory of changes in population sizesthrough time from that starting point. 3.  Use this approach to check outcomesfrom a wide range of initial population sizes. 4.  Now set the input values to: Species 1  Species2 N0   10   10 r   0.5   0.5 K   700     700 α,β   0.7     0.7 5.  Explore the effects of differentinitial population sizes for this set of conditions, using the same approach asbefore.  QUESTION 2: How do the initialpopulation sizes for species 1 and species 2 affect the outcome of competition?Why? When looking at the N vs t graph, what is the final total population size(for both species combined)? Does this change as you alter the initialpopulation sizes? Does this match what you would expect from the N2 vs N1graph?  B. Effect of intrinsic rate ofincrease (r): 1.  Set the input values to: Species 1  Species 2 N0   100   100 r  0.5   0.5 K  700   700 α,β   0.7   0.7 2.  Run the simulation and examine theoutcome. In particular, note the shape of the trajectory in the N2 vs N1 plot(equivalently, note the shapes of the two population growth curves vs time inthe other plot… understand how the two plots relate). 3.  Run the simulation several times,varying the intrinsic rate of increase (r) for species 1 (be sure toinclude 0 and 1) and leaving everything else constant. Notice that the competitionis symmetric, with only r differing between the species. The carrying capacitiesand competition coefficients are the same for each species…so competition itselfis symmetrical in its effects on the two. 4.  Restore the input values from step1. Now re-run the simulation several times, varying the intrinsic rate ofincrease for species 2 (be sure to include 0 and 1)  QUESTION 3: How does variation inthe intrinsic rate of increase affect the outcome of competition? How does itaffect the trajectory (rate of increase) of population sizes? What happens tothe equilibrium number of individuals when r = 0 for either species (but notboth at the same time)? Why does this happen?  C. Effects of competitioncoefficients (α & β)and carrying capacities (K): 1.  Set the input values to: Species 1  Species 2 N0   100   100 r   0.5   0.7 K   500   300 α,β   0.7   0.9 2.  Run the simulation and inspect theoutcome. 3.  Rerun the simulation, decreasing thecarrying capacity (K) for species 1 by 100 each time (500, 400, 300, 200& 100), and noting the outcome. Leave everything else constant.   QUESTION 4: What effect does K haveon the outcome of competition (all else equal)? How small does K1 have to be soswitch the outcome from competitive exclusion to stable coexistence? How smalldoes K1 have to get to switch the outcome to competitive exclusion by species2? Demonstrate this mathematically by using the relationships between K1, K2,a12 and a21. 4.  Set the inputs to values in shown inbelow: Species1   Species 2 N0   100   100 r   0.5   0.5 K   500   500 α,β   0.5   0.5 5.  Rerun the simulation, increasing thecompetition coefficient for the effect of species 1 on species 2 (β)by 0.1 each time, and noting the changes. Run β values from0.5 to 1.0 Leave everything else constant. 6.  Now run β =1.1. What happens? Why? 7.  Next set β =1.0, and change the carrying capacity (K) for species 2 to 600. How doesthis result compare with the previous one?  QUESTION 5: Whatdoes a competition coefficient greater than one mean? As you increase β from 0.5 to1, how does the equilibrium number of each species in the community and thetotal number of individuals in the community change? Why? What effect does changing the carryingcapacity have on equilibrium population values? Growth of species 1 is zerowhen N1 = K or N1 = K2/a21. Explain in a sentence or two how K1 is related toK2/a21.   Practice Problems –Do these by handbut you can check your answers in Populus.  Youhave both green sunfish (Lepomis cyanellus) and bluegill (L.macrochirus) available for stocking in a 10 ha impoundment. These twospecies compete to some degree; pertinent population data are:  Greensunfish K1 =600, a12 = 1.50; Bluegill K2 = 600, a21 =0.90 6.  Is there some level ofcompetition between these 2 species? How do you know? 7.  Would you classify thesespecies as weak, moderate, or strong competitors?   8.  Which species appears tobe the stronger competitor? Why? 9.  Draw the phase-planediagram for this situation and predict the outcome if you start with 100 ofeach species. 10.  What would happen if youused the same initial population sizes but changed the following data: Greensunfish: K1 = 600, a12=0.50; Bluegill: K2=600,a21=0.90 · Draw the phase plane diagram and describe the outcome. 11.  What would happen if wetook the input parameters from question #10 and changed the initial populationsizes to N1=700 and N2=600?    

Tags: Academic Paper Assistance, Assignment Help Australia, Cheap Essay Writing Service, Dissertation Writing Services