Question

I need everyone question please!!

Predator prey model captures the dynamics of the both organisms using the following equation: dN -=rN - ANP 4 = baNP-mP dt 1) What is the meaning of the parameters r, a, b and m in this model? (20pts) 2) In the first equation dN/dt=rN-aNP, explain what is the logic behind multiplying the abundances of the prey and the predator (NP). (10pts) Using this model and posing each equation equals to zero and solving this, one obtains the equilibrium points and associated zero-growth isocline for both the predator (P) and the prey (N). 3) Find the non-trivial (where P#0 and N70) equilibrium point for this model. Make sure you show your work and how you solve the equations. (30pts: 10pts for answer and 20 pts for showing your work correctly) The figure below shows the interaction between predator abundance and prey abundance. Populations of predator (P) and prey (N) are located at the green star on this figure. 4) Based on the Lotka-Volterra predator-prey model, we would expect the number of prey to __(10pts) and the number of predators to (10pts) Pisocline a. increase, increase b. increase, decrease C. decrease; increase d. decrease; stay the same Predator abundance (P) N isocline Prey abundance (N) 5) Explain your answer for question #4 by showing mathematically the conditions for predator- prey coexistence; and use your graph to explain why current abundances of prey and predator you indicated in #4 indicate coexistence or not (20pts).

Answer 1

1. r- intrinsic rate of prey population growth

a- predator capture efficiency

b- rate at which prey are converted to predator offspring

m-mortality rate of predators.

2. the abundance of prey and predator are multiplied to know the rate of prey by predators .