Question 3. You are studying the predator-prey relationship between lizards (pre

Question

Question 3. 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, 200 changes in prey and predator population sizes are determined by the following equations: 150 100 50 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. 0 50 100 150 200

Explanation / Answer

By applying the formula ,

we get dNprey/dt= 0.2(Nprey) - 0.004 (Nprey) (Npred) and dNpred/dt= 0.25(NpreyNpred) - 0.1(Npred)

let us select the Npred and Nprey to be 50 at first

then we ge dNprey/dt= 0.2(50) - 0.004(50)(50) = 10 - 10 =0

dNpred/dt= 0.25(2500) - 0.1(50) = 625-5= 620

as we can see , if the inital population of both predator and the prey remains equal, then

dNpred/dt >>dNprey/dt ,

which means the chances of survival of predators is more, but ultimately they will extinct too due to shortage of food.

Increase in the atack rate (a )will decrease the rate of growth of the prey population and increase in the rate of growth in numbers in the predators.

In long terms , it will lead to a shortage of food for the predators and finally extinction of both predators and preys.

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