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A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation. where. is the carrying capacity, the supremum of the values of the function; is the logistic growth rate, the steepness of the curve; and. is the value of the function's midpoint.
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.
The von Bertalanffy growth function (VBGF), or von Bertalanffy curve, is a type of growth curve for a time series and is named after Ludwig von Bertalanffy. It is a special case of the generalised logistic function. The growth curve is used to model mean length from age in animals. [ 1 ] The function is commonly applied in ecology to model fish ...
Allee effects are classified by the nature of density dependence at low densities. If the population shrinks for low densities, there is a strong Allee effect. If the proliferation rate is positive and increasing then there is a weak Allee effect. The null hypothesis is that proliferation rates are positive but decreasing at low densities.
where is the binary entropy function [1] In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier ...
This is the logistic growth curve and it is calculated with: = + (), where e is the natural logarithm base (also known as Euler's number), x 0 is the x value of the sigmoid's midpoint, L is the curve's maximum value, K is the logistic growth rate or steepness of the curve [19] and
A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of the earliest and most ...
The logistic growth equation is an effective tool for modelling intraspecific competition despite its simplicity, and has been used to model many real biological systems. At low population densities, N(t) is much smaller than K and so the main determinant for population growth is just the per capita growth rate.