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This template quickly calculates the population growth rate given two pairs of years and populations using the formula from Population growth:
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.
This template calculates the per annum compound growth rate given two pairs of years and populations (or other time periods and units) using: P A G R = [ ( P 2 P 1 ) 1 t 2 − t 1 − 1 ] × 100 % {\displaystyle PAGR=\left[\left({\frac {P_{2}}{P_{1}}}\right)^{\frac {1}{t_{2}-t_{1}}}-1\right]\times 100\%}
The function also adheres to the sigmoid function, which is the most widely accepted convention of generally detailing a population's growth. Moreover, the function makes use of initial growth rate, which is commonly seen in populations of bacterial and cancer cells, which undergo the log phase and grow rapidly in numbers. Despite its ...
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:
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.
This model can be generalized to any number of species competing against each other. One can think of the populations and growth rates as vectors, α 's as a matrix.Then the equation for any species i becomes = (=) or, if the carrying capacity is pulled into the interaction matrix (this doesn't actually change the equations, only how the interaction matrix is defined), = (=) where N is the ...
The table below shows annual population growth rate history and projections for various areas, countries, regions and sub-regions from various sources for various time periods. The right-most column shows a projection for the time period shown using the medium fertility variant. Preceding columns show actual history.