Competition Problems (10C)

1. Draw a joint abundance graph, with Lotka-Volterra isoclines consistent with the results of competition in the experiment on Paramecium illustrated in Figure 10.4.
   

   
2. Assume the maximum density of harvester ants in a desert region is eight colonies per hectare in the absence of honeypot ants. Five colonies of honeypot ants move into the area, and as a result of interference competition, the number of harvester ant colonies falls to six colonies per hectare. What is the competition coefficient representing the effect of honeypot colonies on harvester colonies
   • The competition coefficient is 0.4
3. Use the Lotka-Volterra equations to predict the equilibrium population sizes of these two competing species, elk and bison, in a Kansas prairie reserve. Draw a joint abundance graph with isoclines to illustrate your answer.
   

   
   • The equilibrium populations are predicted to be 54 bison and 103 elk.
4. In the Kansas preserve described in problem 3, if the bison herd is culled every year and maintained at a constant number of 50 individuals by the park staff, predict the equilibrium number of elk. Explain your answer by referencing isoclines on the joint abundance graph.
   • I predict the number of elk to be 126 using the competition coefficient of bison on elk (.45) and multiplying it by 50, and then adding that number (22.5) to the equilibrium number of elk (103.5).
5. Assume that Species 1 (cattails) and Species 2 (rushes) compete for space around a pond in such a way that K₁= 80 shoots per m² and K₂= 115 shoots per m². Competition coefficients are α= 0.8 and β= 1.6, indicating a high level of niche overlap. Draw a joint abundance graph with isoclines, adding arrows to indicate the direction of change within each area of your graph. In theory, if the populations were at the point of intersection of the two isoclines in your drawing, both cattails and rushes would demonstrate zero growth, and the system would be in equilibrium. Is the population likely to remain at this point? What biological factors might determine the actual outcome for this pond? 
   

   
   • The population is unlikely to remain at this point because cattails and rushes probably have different reproductive patterns, which may give one of them an advantage over the other. Growth rates may play a role in determining the outcome for the pond if one species grows faster, taking up more space and possibly creating more shade, which could hurt the other species.