In order to define growth limit logistic equation was given by Verhulst. In a given ecosystem, the maximum population that can exit is called carrying capacity (k). The factors which affect carrying capacity are food, habitat and water present in that particular ecosystem.
The change in population with time is represented by following logistic equation.
Where
N = Change in size of growing population
N =Initial population
T =Time
R =growth rate
K =carrying capacity
1. The Difference between maximum population (K) and that which already exists is equal to (K-N).
2. As existing population approaches maximum the value of (K-N) will become smaller. More resistance would be encountered because of less available space and resources in that ecosystem. Therefore according to Logistic equation the intrinsic rate of natural increase (r) would reduce progressively as population increases towards carrying capacity (K)
From above equation it is clear that factor acts against the rate of increase of population (rN).
Case 1: When value of N is negligible, the value of = 1 and population will grow rapidly.
Case 2: When value N ~ K (assuming r to be constant). The value of ≈ 0. Hence,
There will not be any growth in population and population will become stable of stationary.