J curve can be defined as the j shaped growth curve that graphically represents a situation in a new environment where the population density of an organism increases at an exponential rate. This logarithmic growth abruptly halts due to some environmental resistance, such as changes in seasonal patterns, cessation of the breeding season of the organism concerned, etc.
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What is a J Curve?
A rapid increase in growth is witnessed in a population when the organism experiences a favourable condition. The j curve effect can be mathematically expressed by the following equation:
dN/dT=r
Where N= number of individuals present in the population;
T= time required;
r= the biotic potential constant of the organism under study.
And finally, the dN/dT represents the rate of change in the population size.
Examples of J Curve
One of the j curve examples can be observed in the boost and boom cycle represented by algal bloom and some insects such as fruit flies. Many insects show logarithmic growth during the rainy season, which is followed by a sudden decrease in the insect population by the end of the season.
Corresponding to the J-shape, the population achieves a peak value and ultimately crashes. The population tends to increase till a sufficient amount of food is present in the environment of the organism, which in turn helps in the continuation of breeding. An overwhelming increase in population causes the extinction of food materials originally present in the environment. This cessation of food supply results in abruptly stopping the exponential population growth. Two distinct phases are observed in a j shaped curve:
- Lag phase: Witnessed at the lower end of the graphical representation;
- Log phase: This is the spike in population growth.
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The j Curve Effect
The j curve can be observed in human population growth or other activity, for instance, energy use in a population. The j curve is also referred to as the ‘hockey stick curve’ due to the flat portion of the graph followed by a rapid spike. The dramatic rise in the population may is not indicative of any recent acceleration of the growth rate in the concerned population.
Another significant curve that graphically represents population growth is the ‘s-shaped curve’ or ‘sigmoid curve’. The s-shaped curve is represented by three distinct phases:
- The lag phase: When the population is increasing very slowly after the introduction of a few organisms into the environment, the curve rises positively, marking the lag phase.
- The logarithmic phase: The population increase becomes very rapid during the middle phase.
- A phase of negative acceleration: the population increase is slowed down, and equilibrium is attained in the last phase.
The sigmoid growth in a population can be represented by the following mathematical formula:
dN/dT= rN(K-N/K)
Where K-N/K represents environmental resistance.
Both types of population growth curves occur over a period of time. The prime point of difference between the j curve and the sigmoid curve is as follows:
- The j-shaped growth is observed in populations with an abundance of food supply and favourable environmental conditions; on the other hand, sigmoid or logistic growth is observed in populations with a scarcity of food materials.
- An abrupt halt is observed in the j curve, and thus no stationary phase is obtained. A stationary phase, however, is seen in the sigmoid curve.
- The j curve keeps into account the carrying capacity, though it is not the case with the s-shaped curve.
The j curve effect will be observed in an ideal environment with unlimited resources and zero competition among the organisms. Due to the absence of competition, there is no limit on the geometric growth rate. The lag phase of the j shape occurs due to a shortage of reproducing organisms. The increase in the number of organisms in the curve attains a dramatic rise. The biotic potential determines the maximal growth rate for the concerned population.
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Frequently Asked Questions on the J Curve
In what kind of environment can we observe the j curve?
J shaped growth curves are witnessed in a population with an abundant food supply and favourable environmental conditions. The environment should not elicit any form of competition among the organisms that may result in an unnatural decrease in the population size.
What are the major differences between a j curve and a sigmoid curve?
Sigmoid curves are observed in a population facing scarcity of food materials. The s-shaped curves obtain a stationary phase after a peaked growth, but no stationary growth occurs in j curves.
Where can we observe j shaped growth in a population?
Such growths are observed in very small regions or areas that are newly colonised by a species. For instance, the growth of fruit flies on bananas attains maximum growth and then abruptly falls at the end.
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