bertarich.fx: A function having the mathematical expression of the...

In biometrics: A Package for Biometrics and Modelling

A function having the mathematical expression of the Bertalanffy-Richards model.

Description

Function of the Bertalanffy-Richards model, based upon three parameters and a single predictor variable as follows

y_i= \alpha \left(1-\mathrm{e}^{-\beta {x_i}}\right)^{1/\gamma},

where: y_i and x_i are the response and predictor variable, respectively for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

bertarich.fx(x, alpha, beta, gamma, upsilon = 0)

Arguments

x	is the predictor variable.
alpha	is the coefficient-parameter \alpha.
beta	is the coefficient-parameter \beta.
gamma	is the coefficient-parameter \gamma.
upsilon	is an optional constant term that force the prediction of y when x=0. Thus, the new model becomes y_i = \Upsilon+ f(x_i,\mathbf{\theta}), where \mathbf{\theta} is the vector of coefficients of the above described function represented by f(\cdot). The default value for \Upsilon is 0.

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Richards FJ. 1959. A flexible growth function for empirical use. J. of Experimental Botany 10(29):290-300.

• von Bertalanffy L. 1957. Quantitative laws in metabolism and growth. The Quarterly Review of Biology 32(3):217-231.

• Salas-Eljatib C. 2020. Height growth-rate at a given height: a mathematical perspective for forest productivity. Ecological Modelling 431:109198. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.ecolmodel.2020.109198")} https://eljatib.com/myPubs/2020hgrate_ecoModelling.pdf

• Salas-Eljatib C, Mehtatalo L, Gregoire TG, Soto DP, Vargas-Gaete R. 2021. Growth equations in forest research: mathematical basis and model similarities. Current Forestry Reports 7:230-244. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s40725-021-00145-8")}

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-bertarich.fx(x=time,alpha=23,beta=0.08,gamma=0.89)
plot(time,y,type="l")
 

biometrics documentation built on March 20, 2026, 5:09 p.m.