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 () 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. 200 Assuming the interaction follows Lotka-Volterra dynamics, changes in prey and predator population sizes are determined by the following equations: 150 100 50 Given initial population sizes of Nowey 160 beetles and Npmodatsic0 -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. 0 50 100150 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)

the Npred=35 and Nprey=160

then we ge dNprey/dt= 0.2(160) - 0.004(160)(35) = 32 - 22.4 =9.6

dNpred/dt= 0.25(5600) - 0.1(35) = 1400-3.5=

as we can see ,

dNpred/dt >>dNprey/dt

So for short period of time ,The predator population will increase in the number, but the prey population will decrease in number, none of them are extinct though.

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