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The rate of population growth (or decline) of a closed population depends on the combined effects of the birth rate and the death rate. If the population is not closed, we must also include immigration with births and emigration with deaths. Providing we use instantaneous rates, there is a very simple relationship between the growth rate and birth and death rates, namely:
Using the instantaneous rate of increase we can describe exponential population growth with the following equation.
If birth and death rates remain constant, r will also be constant, and a stable age distribution will develop. The maximum rate of increase that is possible for a species in an unlimited environment, for given climatic conditions, is known as the intrinsic rate of natural increase (rm). This measure is used extensively by applied ecologists as a means of describing the growth potential of an organism.
We can readily convert the instantaneous rate of increase to a finite rate. For a single time period we can rewrite the equation above as follows:
Estimating rate of growth/decline
From reproductive parameters
We can predict the maximum potential rate of increase (rm) from the age specific birth and death rates.
By direct observation
We often want to assess the actual rate of increase (or decrease) of a population, for comparison with its potential rate of increase.
This is done by simply plotting the natural log (loge) of the number of individuals against time. The slope of the line is equal to the instantaneous rate of increase per unit time.