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Carrying capacity is a commonly used concept for biologists when trying to better understand biological populations and the factors which affect them. [1] When addressing biological populations, carrying capacity can be seen as a stable dynamic equilibrium, taking into account extinction and colonization rates. [ 16 ]
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.
(Note that when the population size is greater than the carrying capacity then 1 - N/K is negative, which indicates a population decline or negative growth.) The choice of the letter K came from the German Kapazitätsgrenze (capacity limit), while r came from rate .
For instance, the use of β-lactam antibiotics has been shown for glutamate-producing bacteria to increase its transformation efficiencies. [13] [14] [15] Plasmid origin of replication – The origin of replication of the plasmid used in the transformation process can affect the efficiency in several ways. The copy number of the plasmid in the ...
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 ...
As resources become more limited, the growth rate tapers off, and eventually, once growth rates are at the carrying capacity of the environment, the population size will taper off. [6] This S-shaped curve observed in logistic growth is a more accurate model than exponential growth for observing real-life population growth of organisms.
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.
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 ...