Population growth: exponential (J) and logistic (S)
"Population growth: exponential (J) and logistic (S)" is a free, interactive Class 12 Biology simulation for NEET, built on the lesson "Logistic growth and life history" in Organisms and Populations. Both curves start from 10 individuals. The dashed curve has unlimited resources; the solid one lives in a habitat that can hold at most K. Change r and K and watch the two curves. Exponential: dN/dt = rN, J-shaped. Logistic: dN/dt = rN (K − N)/K, sigmoid, with lag, acceleration, deceleration and an asymptote at K. The logistic model is the more realistic one.
From the lesson Logistic growth and life history in Organisms and Populations. Change the values and watch what happens.
The idea behind it
NCERT §11.1.2 (ii), §11.1.3
- No population in nature has unlimited resources. Individuals compete for what there is, and the 'fittest' survive and reproduce.
- A habitat can support only a maximum number of a species, beyond which the population cannot grow. This limit is the carrying capacity, K.
- With limited resources a population shows a lag phase, then acceleration, then deceleration, and finally an asymptote when density reaches K.
- N plotted against time then gives a sigmoid (S-shaped) curve. This is Verhulst-Pearl logistic growth: dN/dt = rN (K − N)/K.
- Because resources for most animal populations are finite and sooner or later limiting, the logistic model is considered the more realistic one.
- Populations evolve to maximise reproductive fitness, also called Darwinian fitness (a high r value), in their habitat.
- Some organisms breed only once in a lifetime (Pacific salmon, bamboo); others breed many times (most birds and mammals).
- Some produce many small offspring (oysters, pelagic fishes); others produce a few large ones (birds, mammals).
- Ecologists suggest these life history traits evolved under the limits set by the abiotic and biotic parts of each habitat.
Questions
2 answers
- What does the "Population growth: exponential (J) and logistic (S)" simulation show?
- Both curves start from 10 individuals. The dashed curve has unlimited resources; the solid one lives in a habitat that can hold at most K. Change r and K and watch the two curves.
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Logistic growth and life history" in Organisms and Populations (Class 12 Biology).
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