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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:
Thomas Robert Malthus, after whom Malthusianism is named. Malthusianism is a theory that population growth is potentially exponential, according to the Malthusian growth model, while the growth of the food supply or other resources is linear, which eventually reduces living standards to the point of triggering a population decline.
The Limits to Growth (LTG) is a 1972 report [2] that discussed the possibility of exponential economic and population growth with finite supply of resources, studied by computer simulation. [3] The study used the World3 computer model to simulate the consequence of interactions between the Earth and human systems.
At first, the population growth rate is fast, but it begins to slow as the population grows until it levels off to the maximum growth rate, after which it begins to decrease (figure 2). The equation for figure 2 is the differential of equation 1.1 ( Verhulst's 1838 growth model ): [ 13 ]
The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the Malthusian growth model. According to Malthus, assuming that the conditions (the environment) remain constant ( ceteris paribus ), a population will grow (or decline) exponentially .
Inbreeding in a population reduces fitness by causing deleterious recessive alleles to become more common in the population, and also by reducing adaptive potential. The so-called "50/500 rule", where a population needs 50 individuals to prevent inbreeding depression, and 500 individuals to guard against genetic drift at-large, is an oft-used ...
The population growth in Rule 90 starting from a single live cell, measured by Gould's sequence. The number of alive cells plotted versus the number of elapsed generations for the first sawtooth discovered in the Game of Life Example of a sawtooth pattern living through several drops below the maximum live cell count. Click on the image to see ...
Liebig's law states that growth only occurs at the rate permitted by the most limiting factor. [2] For instance, in the equation below, the growth of population is a function of the minimum of three Michaelis-Menten terms representing limitation by factors , and .