For a given community, the initial prey population size is growth rate of the pr

Question

For a given community, the initial prey population size is growth rate of the prey is 0.9, the of pr rate at which capt predator populations at the next time step (Q.e. after 50, the initial predator population size is 3, the intrinsic the mortality rate of predators is 0.2, the capture efficiency of predators is 0.2, and the ured prey are made into predator babies is 0.4. What will be the approximate size of the prey and one year)?" 55 prey, 4 predators 50 prey, 4 predators 70 prey, 100 predators 65 prey, 14 predators Pred c pop= 3 grouth mortal 0,2 rate Capp. o pre Question 7 of 1 Moving to another question will save this response.

Explanation / Answer

We have, Prey pop.= 50, Pred. pop.= 3, Prey growth rate = 0.9, Pred. death rate = 0.2, Capture eff. of Pred. = 0.2, Rate of captured prey making pred babies = 0.4. Let predation rate = 0.3

Now, we know Prey population growth = (Prey pop size*growth rate) - predation....eq 1

here predation = (predation rate)*( prey pop) *( pred pop)

Therefore, predation = 0.3*50*3 = 45, now 40% of these captured pray survive(as captured prey making into pred babies is 0.4). Hence the actual predation will be 45 -0.4*45=18

Now, putting the values in eq 1, we get Prey population growth = (50*0.9) - 27 = 45 - 27 = 18

Also, we know population growth of predators = ((Pred pop)*(growth rate)) - predator deaths....eq 2

here, growth rate = predation rate*predator efficiency*prey population = 0.3*0.2*150 = 3

and predator deaths = death rate * pred. pop. = 0.2*3 = 0.6

Now putting values in eq 2, we get population growth of predators = 3*3 - 0.6 = 8.(approx)

Now, cosidering the population growth in prey pop and pred pop calculated above for one cycle, the approximate ppopulation of prey and predator will be 70 and 10 respectively.

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