Question

I need help with parts a-c if possible, thank you!

5. Assume a predator and its prey are interacting according to the basie Lotka-Volterra model. The prey population size is 1000, the predator population size is 10, the prey population's intrinsic rate of growth is 0.1, the predator's capture efficiency is 0.01, the predator's assimilation efficiency is 0.2, and the predator's mortality rate is 0.3. a. Under these conditions, what are the instantaneous growth rates of the prey and predator populations? b. Ifr, c, a, and m remain stable, which population (predator or prey) would you expect to decline over time? c. If a disease swept through the predator population and reduced each predator's assimilation efficiency to 0.1, capture efficiency to 0.001, and increased the predator's mortality rate to 0.6, which population (predator or prey) would you expect to decline over time?

Answer 1

Qn a.

The prey popu.Size = 1000 (m) Predator popu. Size = 10 (P) Prey's intrinsie growth rolo z o.1 (8) Predator's capture efficieney = 0.01 (€) Predators assimilation n = 0.2 (a) Predator's mortality rate = 0.3 (m) Instantaneous rake of change in prey pouplations ON = YN-END = 0.1(1000) – 0.01(1000x10) = 100 - 100 Instantaneous rate of change in predator population a = ae NP - nn = 0.28 0.01 (loooxto) – 0.3x10 z 20 -3. 217

b.

If all parameters (r,c,a,m) remains stable, prey population will decline overtime.

c.

Predator's assimilation efficieneyz o.1 (a) capture efficiency = o.ool (e) Predators mortality rate 20.6 cm) Livet de dp = 0.1*0.001 x 1000x10 - 0.6 X10 = 1-6 - z-5 == 0.1*1000 -0.001 (1000 x 10) E too - 10 Ego

Predator population would expected to decline overtime.