Question

You are studying the predator-prey relationship between lizards (predator) and beetles (prey). The intrinsic growth rate of beetles in the absence of lizards (r) is 0.2 per week, and the mortality rate of lizards in the absence of beetles (m) is 0.1 per week. The attack rate (a) is 0.004, and the efficiency at which beetle biomass is converted into lizard biomass (b) is 0.25.

Assuming the interaction follows Lotka?Volterra dynamics, changes in prey and predator population sizes are determined by the following equations:

dN_prey/dt = rN_prey – aN_preyN_pred

dN_pred/dt = b(aN_preyN_pred) – mN_pred

1. If there are 35 lizards and 160 beetles in the two populations, approximately how many beetles will be killed per week? Show your work.

2. Complete the above phase plane by adding the zero growth isoclines for each species, such that dN_prey/dt = 0 when N_pred = r/a and dN_pred/dt = 0 when N_prey = m/ba. Label the axes and lines; show your work.

3. Given initial population sizes of N_prey = 160 beetles and N_predator = 35 lizards, what are the expected short-term (one time step) dynamics for each population (i.e., do they increase, decrease, or stay the same)? Explain.

4. What are the expected long-term dynamics for the two populations described above (i.e., do they go extinct, reach carrying capacity, or coexist in some way)? Be specific.

5.. In the Lotka?Volterra predator?prey model, an increase in the attack rate (a) should have what effect on the long-term average number of predators and prey? Explain.

Answer 1

Answer.

4.

According to the given data for Lotka-Voltera equation, both population will coexist as shown in d picture showing circle in anticlockwise direction. Predators kill prey and thus prey population size depends on the number of predators. With few predators, prey population grows and with many predators, prey population shrinks. With many prey, predator population grows and with few prey, predator population shrinks and thus coexit in a cyclic way as shown in the d. picture.