Biology · Organisms and Populations · NEET
N = population density at time t (the number of individuals right now). r = intrinsic rate of natural increase (how fast the population can grow per individual under the given conditions). K = carrying capacity (the maximum number the habitat can support with its limited resources). dN/dt = the rate of change of population size (how fast the population is growing at that instant). NCERT lists exactly these three meanings for N, r and K, so learn them word for word.
It is the 'environmental resistance' or the fraction of resources still available. (K-N) is the room left before the habitat is full; dividing by K makes it a fraction between 0 and 1. When the population is small, (K-N)/K is close to 1, so growth is almost exponential. When N gets close to K, (K-N)/K drops toward 0, so growth slows down. This bracket is the only difference from the exponential equation dN/dt = rN.
The growth rate dN/dt becomes zero when the bracket (K-N)/K becomes zero. That happens only when K - N = 0, i.e. when N = K. At that point the population has reached the carrying capacity, the curve flattens into an asymptote, and the population stops growing. This is a very common one-mark question in NEET.
Yes. rN[(K-N)/K] and rN(1 - N/K) are the same equation written differently, because (K-N)/K = K/K - N/K = 1 - N/K. NEET has used both forms in different years, so do not get confused if the paper shows 1 - N/K instead of (K-N)/K. They give identical results.
Because in nature resources like food and space are finite, no population can grow forever. The (K-N)/K brake makes growth slow down and level off, giving the S-shaped (sigmoid) curve, which matches what actually happens in real habitats. NCERT directly states that since resources become limiting sooner or later, the logistic model is considered the more realistic one.
The equation of Verhulst-Pearl logistic growth is dN/dt = rN[(K-N)/K]. From this equation, K indicates:
When does the growth rate of a population following the logistic model equal zero? The logistic model is given as dN/dt = rN(1 - N/K):
Which one of the following equations represents the Verhulst-Pearl Logistic Growth of population?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It was given by Verhulst and Pearl, so it is called the Verhulst-Pearl logistic growth equation. NEET has repeatedly asked to name them, so do not confuse them with G. F. Gause, who gave the competitive exclusion principle.
It produces an S-shaped or sigmoid curve. The curve shows a lag phase, then an acceleration phase, then a deceleration phase, and finally an asymptote when N equals K.
If N is greater than K, then (K-N) becomes negative, so dN/dt becomes negative and the population declines back toward K. The carrying capacity acts like a ceiling the population settles at.
r is the intrinsic rate of natural increase, a per-individual growth speed. K is the carrying capacity, the maximum number of individuals the habitat can hold. r controls how fast growth happens; K controls where growth stops.
Both are important, but the logistic equation is asked more often because of its symbols (N, r, K) and the exact condition for zero growth (N = K). Learn the equation form and the meaning of each term precisely.
