State whether the following statements are true (T) or false (F).
I. Carrying capacity of a population is represented by ‘r’.
II. A population growing in a habitat with limited resources shows initially a lag phase.
III. Logistic growth model is represented by a J- shaped curve.
State whether the following statements are true (T) or false (F).
I. Carrying capacity of a population is represented by ‘r’.
II. A population growing in a habitat with limited resources shows initially a lag phase.
III. Logistic growth model is represented by a J- shaped curve.
The correct option is C I - F, II - T, III - F
Statement I is false: Carrying capacity is the maximum number of individuals of a population that can be sustained indefinitely in a given habitat. It is represented by the letter K.
Statement II is true: In a logistic growth model, a population in a habitat has limited resources. It initially shows slow growth (lag phase), followed by phases of acceleration (log phase) and then deceleration and ultimately reaches a stationary phase as the population density reaches the carrying capacity. In the lag phase, the population tries to adjust with the new habitat, which is why the birth rate is slow.
Statement III is false: The logistic growth of a population is represented by a S- shaped sigmoid growth curve as is represented by the curve in the diagram below. The logistic growth curve can be expressed as
dN/dt= 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
Statement I is false: Carrying capacity is the maximum number of individuals of a population that can be sustained indefinitely in a given habitat. It is represented by the letter K.
Statement II is true: In a logistic growth model, a population in a habitat has limited resources. It initially shows slow growth (lag phase), followed by phases of acceleration (log phase) and then deceleration and ultimately reaches a stationary phase as the population density reaches the carrying capacity. In the lag phase, the population tries to adjust with the new habitat, which is why the birth rate is slow.
Statement III is false: The logistic growth of a population is represented by a S- shaped sigmoid growth curve as is represented by the curve in the diagram below. The logistic growth curve can be expressed as
dN/dt= 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
