Answer:
Explanation:
From the given information,
The first process is to determine the initial growth rate by using the formula:
where;
The initial growth rate(constant) = ; &
the doubling time = = 1 year
= 0.693 / year
Now, we move up to the net stage to find the growth constant by using the formula:
where;
= population of fish in the pond = 100
= The initial growth rate(constant) = 0.693 /year
K = carrying capacity = 2000
Then;
r = 0.730 / year
a)
Now, the maximum yield can be evaluated by using the expression:
= 365 fish per year
Also, the maximum sustainable yield is said to be half of the carrying capacity suppose that the population growth obeys logistic curve;
i.e.
N' = 1000 fish
b)
If the population is maintained at 1500 fish;
The sustainable yield can be calculated by using the formula:
The Sustainable yield =
The Sustainable yield =
The Sustainable yield = 1095 × 0.25
The Sustainable yield = 273.75 fish per year
The Sustainable yield ≅ 274 fish per year