Fish Population Dynamic and Stock Assessment

2.2.4.4 Density dependent model for populations which breeds continuously 

the equation is (density dependent model)

$$N_t= {K \over 1+e^{-(rmax.t)}}$$

Logistic population increase of the continuous density dependent model (N_t with time and attains asymptotic to K )

In the above graph, the population size follows the logistic pattern. It increases slowly and at a certain interval of time, it increases rapidly and once it attains K (the carrying capacity of the system) the line gets almost becomes stationary.