Question

The logistic population growth is expressed by the equation
A) ${\displaystyle \frac{dt}{dN}}=Nr(K-{\displaystyle \frac{N}{K}})$
B) ${\displaystyle \frac{dN}{dt}}=rN(K-{\displaystyle \frac{N}{K}})$
C) ${\displaystyle \frac{dN}{dt}}=rN$
D)${\displaystyle \frac{dN}{dt}}=rN(N-{\displaystyle \frac{K}{N}})$

Answer 1

Hint:Population growth can occur in different ways depending on the balance between available resources and the population density, the number of individuals in the reproductive age group, and so on.

Complete answer:
When a population has a larger amount of available resources, the growth will suddenly increase, and the graph will shoot straight up. This is known as exponential growth. It is very commonly seen in bacterial cultures, when a few cells are added to a fresh growth medium.
In natural populations, however, individuals have to compete for available resources, which put restrictions on the growth of the population. This is a part of the process of natural selection, and is known as logistic growth.
In the given equations, K stands for the carrying capacity of the land, and N is the number of individuals. ${\displaystyle \frac{dN}{dt}}$ is the basic population growth rate, expressed as the number of individuals with respect to time.
>Option A starts with ${\displaystyle \frac{dt}{dN}}$. option A is incorrect.
>For logistic growth, the correct equation is ${\displaystyle \frac{dN}{dt}}=rN({\displaystyle \frac{(K-N)}{K}})$. the correct answer is option B
>In option C, the carrying capacity of the land, or K, has not been considered on the right hand side. Option C is incorrect.
>Option D is incorrect as carrying capacity is being subtracted from the number of individuals.

Note:In a population of any given organisms, competition is not restricted to interspecific needs. In nature, ecosystems consist of several different organisms often competing for the same resources. This will also affect the growth curve of the organism under study.