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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 individual growth model published by Ludwig von Bertalanffy in 1934 is widely used in biological models and exists in a number of permutations. In its simplest version the so-called Bertalanffy growth equation is expressed as a differential equation of length (L) over time (t):
The individual growth model, published by von Bertalanffy in 1934, can be used to model the rate at which fish grow. It exists in a number of versions, but in its simplest form it is expressed as a differential equation of length ( L ) over time ( t ): L ′ ( t ) = r B ( L ∞ − L ( t ) ) {\displaystyle L'(t)=r_{B}\left(L_{\infty }-L(t ...
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.
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.
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[11] [21] [22] Under constant environmental conditions (constant food and temperature) the standard DEB model can be simplified to the von Bertalanffy (or better, Putter's [23]) growth model, but its mechanistic process-based setup enables incorporating fluctuating environmental conditions, as well as studying reproduction and maturation in ...