Study the image given below and identify the equation that correctly represents the curve shown in the diagram.
Study the image given below and identify the equation that correctly represents the curve shown in the diagram.
The correct option is B dNdt= rN[(K−N)K
The growth of population in a habitat shows a logistic growth model or exponential growth model depending on the availability of resources (food, mating, shelter, etc.). The given diagram represents the growth curves of a population following the logistic growth model.
In a logistic growth model, a population in a habitat has limited resources. It initially shows slow growth (lag phase of growth curve), followed by phases of accelerated growth (log phase of growth curve) and then deceleration. Once the population density reaches the carrying capacity, the growth curve reaches the last phase (stationary phase). Carrying capacity is the maximum number of individuals of a population that can be sustained indefinitely in a given habitat. When the number of individuals in the population reaches the carrying capacity, population growth slows down or stops altogether. This is represented by a sigmoid growth curve as represented by the curve in the given diagram. The logistic growth curve can be expressed as
dNdt= rN[(K−N)K
Where, N - Population density at time t. (It is the number of individuals per unit geographic area, for example, number per square meter)
r - Intrinsic rate of natural increase (It shows the number of births minus the number of deaths per generation)
K- Carrying capacity
dN - Change in population density
dt - Change in time
The growth of population in a habitat shows a logistic growth model or exponential growth model depending on the availability of resources (food, mating, shelter, etc.). The given diagram represents the growth curves of a population following the logistic growth model.
In a logistic growth model, a population in a habitat has limited resources. It initially shows slow growth (lag phase of growth curve), followed by phases of accelerated growth (log phase of growth curve) and then deceleration. Once the population density reaches the carrying capacity, the growth curve reaches the last phase (stationary phase). Carrying capacity is the maximum number of individuals of a population that can be sustained indefinitely in a given habitat. When the number of individuals in the population reaches the carrying capacity, population growth slows down or stops altogether. This is represented by a sigmoid growth curve as represented by the curve in the given diagram. The logistic growth curve can be expressed as
dNdt= rN[(K−N)K
Where, N - Population density at time t. (It is the number of individuals per unit geographic area, for example, number per square meter)
r - Intrinsic rate of natural increase (It shows the number of births minus the number of deaths per generation)
K- Carrying capacity
dN - Change in population density
dt - Change in time
