Critical Points for Nonlinear Growth Models

Computes analytical critical points for nonlinear growth models from known parameter values.

NLIN

Overview

NLIN is an R package for computing critical points of nonlinear growth models from known parameter values.

The package does not estimate model parameters. Instead, it uses analytical expressions derived from the derivatives of nonlinear growth curves to calculate biologically relevant critical points.

Currently, the package provides functions for the following models:

• Gompertz;
• Logistic;
• Von Bertalanffy;
• Richards.

Depending on the model, the following critical points are calculated:

• PI: inflection point;
• PAM: maximum acceleration point;
• PDM: maximum deceleration point;
• PDA: asymptotic deceleration point.

For the Richards model, the PDA is obtained numerically from the biologically admissible root of the corresponding polynomial equation.

Installation

You can install the development version of NLIN from GitHub with:

# install.packages("remotes")
remotes::install_github("helleensilvaa/NLIN")

The GitHub repository address will be updated after the package is published.

Usage

First, load the package:

library(NLIN)

Gompertz model

gompertz_points(
  A = 100,
  B = 5,
  C = 0.1
)

Logistic model

logistic_points(
  A = 100,
  B = 5,
  C = 0.1
)

Von Bertalanffy model

vonbertalanffy_points(
  A = 100,
  B = 5,
  C = 0.1
)

Richards model

richards_points(
  A = 100,
  B = 4,
  C = 0.05,
  m = 0.5
)

Output

The functions return a data.frame containing:

• ponto: identification of the critical point;
• x: position of the critical point on the independent variable;
• estimativa: estimated response at the critical point.

For example:

gompertz_points(
  A = 100,
  B = 5,
  C = 0.1
)

Reference

Mischan, M. M., & Pinho, S. Z. de (2014). Modelos não lineares: funções assintóticas de crescimento. São Paulo: Cultura Acadêmica.

Author

Hellen Sonaly Silva Alves