A Flexible Growth Function for Empirical Use

By F. J. Richards. 1959

Subfields: Statistics and Probability, Time-Series & Forecasting

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Finely-grained annotated datasets for image-based plant phenotyping (2016, background): “This growth curve usually follows an exponential relationship with time (Richards, 1959; Walter and Schurr, 1999), and frequent imaging can capture small di ﬀ erences.”
Height-diameter models for Scots pine and birch in Finland (2005, methodology): “For both tree species, an appropriate trend function for parameter A was the Chapman-Richards function (Richards 1959)”
Mechanical and microstructural testing of wire and arc additively manufactured sheet material (2020, methodology): “An S-shaped logistic curve, similar to Richards curve [55], was then fitted to the data between bands A and B using the”
A best practices guide for generating forest inventory attributes from airborne laser scanning data using an area-based approach (2013, unknown): “The heights of the unmeasured trees can then be estimated through species-specific dbh–height regression models developed from the measured subsample (e.g., Richards 1959; Sharma and Parton 2007).”
Height-diameter models with random coefficients and site variables for tree species of Central Maine (2008, methodology): “inary study using weighted OLS, fits of the data with a 3-parameter form of the Chapman-Richards function [7, 33, 39] were slightly better and converged more often than 3-parameter Weibull [44], mod-”
Protein aggregation kinetics, mechanism, and curve-fitting: a review of the literature. (2009, background): “Richards' function is itself a generalized form of the logistic function [143], and is commonly used in botany to determine both the growth period length and the ultimate weight of plants [144].”
Site quality curves for birch stands in north-western Spain (2006, methodology): “The first model tested is based on the function proposed by Bertalanffy (1949, 1957) and studied by Richards (1959), whose integral form can, for simplicity, be represented as Y = a1[1 – exp(–a2t)]a3 (1) where a1 is an asymptote or limiting value, a2 is often called a ‘rate parameter’, and a3 is…”
SEX DIFFERENCES IN PARENTAL INVESTMENT AND CHICK GROWTH IN WANDERING ALBATROSSES: FITNESS CONSEQUENCES (2000, background): “The period of mass increase up to peak mass belongs to the family of sigmoid growth curves best described by the Richards (1959) equation M 5 A/(1 1 l exp[2K(t 2 Ti)])1/l where A is the asymptotic or maximum mass, K is the growth rate, and Ti is the time of inflection of the growth curve or time of…”
Ecological Models and Data in R (2008, background): “The – The theta-logistic or generalized logistic model (Nelder, 1961; Richards, 1959; Thomas et al., 1980; Sibly et al., 2005) generalizes the logistic equation by adding a power (θ) to the logistic growth equation given above (3.”