Richardsmodel
The Richards model, also known as the Richards growth model, is a flexible sigmoidal growth function used to describe growth processes in biology, ecology, agronomy, and related fields. It generalizes the logistic and other S-shaped models by introducing a shape parameter that controls the curve’s asymmetry, enabling better fits to empirical data with varying growth dynamics.
A common form of the Richards function is:
N(t) = K / [1 + A e^{-B t}]^{1/ν},
where N(t) is the size at time t, K is the carrying capacity or upper asymptote, B
N(t) = K [1 + ((K^{1/ν} − N0^{1/ν}) / N0^{1/ν}) e^{-r t/ν}]^{-ν},
with r related to the growth rate.
Relation to other models: when ν = 1, the Richards function reduces to the logistic growth model. For
Applications: the model has been used to fit growth curves of plants and animals, microbial populations, tumor
Estimation and interpretation: parameters are typically estimated by nonlinear regression or maximum likelihood methods. Challenges include
See also: logistic function, Gompertz function, growth curves, nonlinear regression.