Problem statement: The Lotka-Volterra equations are used to model competition and predation. You may use web resources for some questions. For two competing species, use what you know about Lotka-Volterra to make a sketch and describe the outcomes for each of the following scenarios: 1. What would be the ultimate outcome for both competitors under the following set of conditions? (15 points total) - K = 200, r = 100, alpha = 12 - K = 100, r = 10, alpha = 20 - K = 160, r = 20, alpha = 2 Remember, your book uses alpha (α) instead of r. It's just a matter of saying the same thing. Lotka-Volterra equations consider the following assumptions: - The population size of Species A has been approximately 100 individuals per km² - The population size of Species B has been approximately 50 individuals per km² - Species A has experienced a sudden increase in population size due to the decline of Species B. Answer the following questions based on the information provided. You'll need your critical thinking skills! 16. Now imagine a case where the values above are the carrying capacities of the populations. Do not simply assume that the populations are stable. Use this information to determine the competition coefficients (alpha and beta). Sketch the phase diagram that describes this new scenario. Which species should win? (10 points) 17. BONUS points: What would the population sizes of each species be in the absence of their competitors? In other words, if a female individual of Species A had no competitors, how many individuals of Species A could exist? Likewise, if a male individual of Species B had no competitors, how many individuals of Species B could exist? (Hint: It might be helpful to first consider the effect of removing a single individual) 18. Explain how the figures below relate to each other in terms of predator-prey relationships. Label the axes and put missing directional arrows. (5 points)