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At , a slightly higher harvest rate, however there is only one equilibrium point (at ), which is the population size that produces the maximum growth rate. With logistic growth, this point, called the maximum sustainable yield, is where the population size is half the carrying capacity (or =). The maximum sustainable yield is the largest yield ...
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 ...
The size of the ultimate resource was taken from a synthesis of estimates by well-known oil geologists and the US Geological Survey, which Hubbert judged to be the most likely case. upper-bound estimate: a logistic curve with a logistic growth rate equal to 6% and ultimate resource equal to 200 Giga-barrels and a peak in 1970.
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the family of models in 1959.
Assuming the logistic model, the MSY will be exactly at half the carrying capacity of a species, as this is the stage at when population growth is highest. In practice, the maximum sustainable yield is usually higher than the optimum sustainable yield. This logistic model of growth is produced by a population introduced to a new habitat or with ...
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation. where. , the value of the function's midpoint; , the supremum of the values of the function; , the logistic growth rate or steepness of the curve. [1] Standard logistic function where. For values of in the domain of real numbers from to , the S ...
K is the logistic growth rate or steepness of the curve and = / The logistic growth curve depicts how population growth rate and carrying capacity are inter-connected. As illustrated in the logistic growth curve model, when the population size is small, the population increases exponentially.
Sustainable yield is the amount of a resource that humans can harvest without over-harvesting or damaging a potentially renewable resource.. In more formal terms, the sustainable yield of natural capital is the ecological yield that can be extracted without reducing the base of capital itself, i.e. the surplus required to maintain ecosystem services at the same or increasing level over time.