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In the study of age-structured population growth, probably one of the most important equations is the Euler–Lotka equation.Based on the age demographic of females in the population and female births (since in many cases it is the females that are more limited in the ability to reproduce), this equation allows for an estimation of how a population is growing.
P 0 = P(0) is the initial population size, r = the population growth rate, which Ronald Fisher called the Malthusian parameter of population growth in The Genetical Theory of Natural Selection, [2] and Alfred J. Lotka called the intrinsic rate of increase, [3] [4] t = time. The model can also be written in the form of a differential equation:
Using these techniques, Malthus' population principle of growth was later transformed into a mathematical model known as the logistic equation: = (), where N is the population size, r is the intrinsic rate of natural increase, and K is the carrying capacity of the population. The formula can be read as follows: the rate of change in the ...
For example, with an annual growth rate of 4.8% the doubling time is 14.78 years, and a doubling time of 10 years corresponds to a growth rate between 7% and 7.5% (actually about 7.18%). When applied to the constant growth in consumption of a resource, the total amount consumed in one doubling period equals the total amount consumed in all ...
The Leslie matrix is a discrete, age-structured model of population growth that is very popular in population ecology named after Patrick H. Leslie. [1] [2] The Leslie matrix (also called the Leslie model) is one of the most well-known ways to describe the growth of populations (and their projected age distribution), in which a population is closed to migration, growing in an unlimited ...
Thus, the figures after the 1960 column show the percentage annual growth for the 1955-60 period; the figures after the 1980 column calculate the same value for 1975–80; and so on. The formulas used for the annual growth rates are the standard ones, used both by the United Nations Statistics Division and by National Census Offices worldwide.
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The UN Population Division report of 2022 projects world population to continue growing after 2050, although at a steadily decreasing rate, to peak at 10.4 billion in 2086, and then to start a slow decline to about 10.3 billion in 2100 with a growth rate at that time of -0.1%.