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The standard Hubbert curve.For applications, the x and y scales are replaced by time and production scales. U.S. Oil Production and Imports 1910 to 2012. In 1956, Hubbert proposed that fossil fuel production in a given region over time would follow a roughly bell-shaped curve without giving a precise formula; he later used the Hubbert curve, the derivative of the logistic curve, [6] [7] for ...
The formula can be read as follows: the rate of change in the population (dN/dt) is equal to growth (rN) that is limited by carrying capacity (1 − N/K). From these basic mathematical principles the discipline of population ecology expands into a field of investigation that queries the demographics of real populations and tests these results ...
[1] Malthusian models have the following form: = where 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]
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 Hubbert curve is an approximation of the production rate of a resource over time. It is a symmetric logistic distribution curve, [ 1 ] often confused with the "normal" gaussian function . It first appeared in "Nuclear Energy and the Fossil Fuels," geologist M. King Hubbert 's 1956 presentation to the American Petroleum Institute , as an ...
Along with mortality rate, natality rate is used to calculate the dynamics of a population. They are the key factors in determining whether a population is increasing, decreasing or staying the same in size. Natality is the greatest influence on a population's increase. Natality is shown as a crude birth rate or specific birth rate.
RGR is a concept relevant in cases where the increase in a state variable over time is proportional to the value of that state variable at the beginning of a time period. In terms of differential equations, if is the current size, and its growth rate, then relative growth rate is
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 popularity, the function initial rate of tumor growth is difficult to predetermine given the varying microcosms present with a patient, or varying ...