Question

Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1100 fish. Absent constraints, the population would grow by 230% per year. If the starting population is given by Po = 200, then after one breeding season the population of the pond is given by P1= P2=

Answer 1

For a population rate of change r and a total capacity of the pond C, the logistic growth is given by:

$P_n=P_{n-1}\lbrack1+r(1-\frac{P_{n-1}}{C})\rbrack$

For r = 2.3, P0 = 200 fish and C = 1100 fish, we have:

$\begin{gathered} P_1=200\cdot\lbrack1+2.3(1-\frac{200}{1100})\rbrack\approx576\text{ fish} \\ P_2=576\cdot\lbrack1+2.3(1-\frac{576}{1100})\rbrack\approx1207\text{ fish} \end{gathered}$