Question

Explain why a constant per capita rate of growth (r) for a population produces a curve that is J-shaped.

Short answer

The population size (N) is not constant. It is either decreasing or increasing. The development of the population shows acceleration and produces a J-shaped curve when the per capita rate of growth is applied to a population that is growing exponentially.

Step-by-step solution

Change in population size

The number of resources available for members of the population determines the increase and decrease in the population size. For example, a population living in an unlimited and ideal environment shows an increase in population size.

They have all access to energy and ability to grow and reproduce. A population living with limited resources does not show rapid growth.

Exponential growth

Exponential growth is the pattern of growth that shows a constant increase in the size of the population at each instant time. This type of growth pattern is seen in a population that lives in an unlimited and ideal environment. The equation that represents exponential growth is \(\frac{{dN}}{{dt}} = rN\)

Exponential growth curve

In the equation \(\frac{{dN}}{{dt}} = rN\), the rate of increase of population size is denoted by \(\frac{{dN}}{{dt}}\) and \(rN\) represents current population size (N) multiplied with constant (r). The population, which shows exponential growth, increases at a constant rate per member.

Therefore, when population size is compared with time, it shows a J-shaped growth curve even though the per capita rate of population growth is constant. Over time, more individuals are added to the population, which results in progressively steeper curves.