Question

Several years ago, a pond had 200 perch and increased by 20 fish that year. This year, the pond has 600 fish and it did not exhibit a net increase in number at all. Assuming that the population of fish is growing according to the logistic growth model, please answer the following questions.

a) What is carrying capacity of the population?

b) What is the intrinsic rate of increase?

c) What is the maximum sustainable harvest of perch from this pond?

d) By how many individuals did the school increase when there were 400 fish in the pond?

Answer 1

a) The maximum population size that can be sustained in an environment is called its carrying capacity.

In this case the carrying capacity is 600

b) The rate of increase of population when density dependent regulatory forces are absent is called as the intrinsic rate of population increase.

r= (dN/Dt) x  1/N

=20 x 1/600

= 20 x 0.0016

= 0.032

c) maximum sustainable harvest of perch = 1/2 (carrying capacity)

=1/2 x (600)

=300

d) logistic growth rate= dN/dT= rmax (K-N/ K) x N where , K= carrying capacity, N= number of individuals

=0.032 {(600-400)/ 600} x 400

=0.032 x 0.33 x 400=4.224