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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 ...
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.
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. However, as population size nears carrying capacity, the growth decreases and reaches zero at K.
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.
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 ...
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 tails (higher kurtosis ).
An explanation of logistic regression can begin with an explanation of the standard logistic function. The logistic function is a sigmoid function, which takes any real input , and outputs a value between zero and one. [2] For the logit, this is interpreted as taking input log-odds and having output probability.
Biological exponential growth. Biological exponential growth is the unrestricted growth of a population of organisms, occurring when resources in its habitat are unlimited. Most commonly apparent in species that reproduce quickly and asexually, like bacteria, exponential growth is intuitive from the fact that each organism can divide and ...