4. (10 points, 46 points cumulative) Suppose that a population of voles is growi

Question

4. (10 points, 46 points cumulative) Suppose that a population of voles is growing according to a logistic equation. The carrying capacity is K 1200 and the exponential growth rate is r 0.5 individuals per individual per month. a. At what population size is the maximum growth rate of the population reached (circle one)? 200 250 400 600 800 b. What is the maximum growth rate (individuals per month) of the population at this point (circle one)? 75 87.5 120 150 240 c. If this were a discrete population model with reproduction at monthly intervals, and you release it from harvesting, you might expect this population to (check one): O increase gradually up to the carrying capacity O overshoot the carrying capacity and initiate a series of damped oscillations overshoot the carrying capacity and enter a limit cycle a become chaotic 5. (8 points, 54 points cumulative) Can density-independent factors regulate a population at a stable size in the absence of density-dependent factors? (a brief response)

Explanation / Answer

1. Here population of the growth of voles is according to the logistic equation, which is,

dN/dt=rN(K-N/K)

so a value of N is population over time so as N is increased the growth rate is increased which is maximum at 800 so answer is 800

2.The maximum growth rate per month is 120

3.overshoot the carryin capacity and enter limit cycle

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