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Bacterial growth curve\Kinetic Curve. In autecological studies, the growth of bacteria (or other microorganisms, as protozoa, microalgae or yeasts) in batch culture can be modeled with four different phases: lag phase (A), log phase or exponential phase (B), stationary phase (C), and death phase (D).
The red curve describes the growth of such a market as the first derivative of the market volume. The yellow curve illustrates the growth weighted by the size of the market. As for logistic growth, the yellow curve shows that even a large market size cannot strengthen growth when approaching saturation. Logistic growth never is negative, but in ...
Logarithmic dose–response curves are generally sigmoidal-shape and monotonic and can be fit to a classical Hill equation. The Hill equation is a logistic function with respect to the logarithm of the dose and is similar to a logit model. A generalized model for multiphasic cases has also been suggested. [7]
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 ...
They can be used for longitudinal studies, as with growth studies, to separate changes within one individual and differences between individuals. Cross-level interactions may also be of substantive interest; for example, when a slope is allowed to vary randomly, a level-2 predictor may be included in the slope formula for the level-1 covariate.
One of the most basic and milestone models of population growth was the logistic model of population growth formulated by Pierre François Verhulst in 1838. The logistic model takes the shape of a sigmoid curve and describes the growth of a population as exponential, followed by a decrease in growth, and bound by a carrying capacity due to ...
After dividing both sides of the equation by the population size N, in the logistic growth the left hand side of the equation represents the per capita population growth rate, which is dependent on the population size N, and decreases with increasing N throughout the entire range of population sizes.
In logistic populations however, the intrinsic growth rate, also known as intrinsic rate of increase (r) is the relevant growth constant. Since generations of reproduction in a geometric population do not overlap (e.g. reproduce once a year) but do in an exponential population, geometric and exponential populations are usually considered to be ...