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The carrying capacity of an environment is the maximum population size of a biological species that can be sustained by that specific ... increase carrying capacity ...
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 standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
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 ...
At intermediate population densities, also represented by half the carrying capacity, individuals are able to breed to their maximum rate. At this point, called the maximum sustainable yield, there is a surplus of individuals that can be harvested because growth of the population is at its maximum point due to the large number of reproducing ...
In this way humans are currently exceeding the carrying capacity of Earth as we increase the ecological overshoot each year. The IPAT equation attempts to quantify the environmental impact ("I") of the human population ("P"), their affluence ("A") and technology ("T").
(b-d) is called the 'intrinsic rate of natural increase' and is a parameter chosen for assessing the impacts of any biotic or abiotic factor on population growth. [5] As the population approaches its carrying capacity, the rate of growth decreases, and the population trend will become logistic. [6]
There also exists density-independent inhibition, where other factors such as weather or environmental conditions and disturbances may affect a population's carrying capacity. [citation needed] An example of a density-dependent variable is crowding and competition.