Question

Pigs are invading a ranch in California. Estimates of logistic model parameters for this population suggest that the instantaneous rate of population growth is 0.4 year-1 and the carrying capacity is 50 pigs km-2. The area of the ranch is 40 km2.
The island’s owner applies for a permit to allow recreational shooting of up to 60 pigs per year. If the logistic equation is valid for this species, would the hunting program be likely to cause a decline in population if the shooting were permitted? Explain your reasoning briefly.

Answer 1

Maximum carrying capacity is the number of individuals that can accomodate in the existing ecosystem.

in the logistic model the growth :- dN/dt = rN ( 1- N/K) where N is the number of individuals in the population, r = intrinsic rate of natural increase, k is carrying capacity.

here we have r = 0.4, K = 50 x 40 = 2000 individuals

According to the logistic model the maximum growth of population occur at Ko= 1/2 Km

so N = 1/2 x 2000 = 1000

now the growth = 0.4x1000( 1- 1000/2000)

= 400 x 1/2

= 200 individual per annum

As the growth is of 200 pigs per annum so , it can be permitted to the owner for recreational shooting of 60 pigs per annum