Question

In the equation, $\dfrac{{dN}}{{dt}} = rN(\dfrac{{K - N}}{K})$ , r stands for
A.Intrinsic rate of natural increase
B.Death rate
C.Population density at time t
D.Carrying capacity
E.The base of natural logarithms

Answer 1

The above-given equation represents the sigmoid growth form of population growth. This equation is for the S-shaped or sigmoid growth form. In the equation, r is a value that is used to calculate the rate of a certain parameter in the population and it is obtained by the subtraction of two population characteristics.

Complete answer: 1. The given equation is part of the population growth form.
2. Populations have a characteristic pattern of growth with time. These patterns are termed as population growth form. There are two basic types of growth form, sigmoid or S-shaped growth form, and J-shaped growth form. These forms are explained by population growth curves.
3. The given equation is for S-shaped growth curves, which is shown by populations of most organisms. It has five phases: lag phase, positive acceleration phase, exponential phase, negative acceleration phase and stationary phase
4. S-shaped curve is also called Verhulst-pearl logistic curve. The sigmoid growth form is represented as:
$\dfrac{{dN}}{{dt}} = rN(\dfrac{{K - N}}{K})$
Where, $\dfrac{{dN}}{{dt}} =$ Rate of change in population size, r = Intrinsic rate of natural increase, N = Population size, $(\dfrac{{K - N}}{K}) =$ Environmental resistance.
5. The intrinsic rate of natural increase (r) can be understood as the birth rate minus the death rate $(b - d)$.
Hence, the correct answer is option A.

Note: The sigmoid population growth form is denoted by this equation in which r is the intrinsic rate of natural increase which is obtained by subtracting the birth rate and the death rate. It is the value used to calculate the rate of increase in population. It is also known as the Malthusian parameter.