nlraa (version 1.2)

SSexplin: self start for the exponential-linear growth equation

Description

Self starter for an exponential-linear growth equation

Usage

explin(t, cm, rm, tb)
SSexplin(t, cm, rm, tb)

Value

a numeric vector of the same length as x containing parameter estimates for equation specified

explin: vector of the same length as x using a explin function

Arguments

t

input vector (time)

cm

parameter related to the maximum growth during the linear phase

rm

parameter related to the maximum growth during the exponential phase

tb

time at which switch happens

Details

J. GOUDRIAAN, J. L. MONTEITH, A Mathematical Function for Crop Growth Based on Light Interception and Leaf Area Expansion, Annals of Botany, Volume 66, Issue 6, December 1990, Pages 695–701, tools:::Rd_expr_doi("10.1093/oxfordjournals.aob.a088084")

The equation is: $$ (cm/rm) * log(1 + exp(rm * (t - tb)))$$

This function is described in Archontoulis and Miguez (2015) - (doi:10.2134/agronj2012.0506).

Examples

# \donttest{
require(ggplot2)
set.seed(12345)
x <- seq(1,100, by = 5)
y <- explin(x, 20, 0.14, 30) + rnorm(length(x), 0, 5)
y <- abs(y)
dat <- data.frame(x = x, y = y)
fit <- nls(y ~ SSexplin(x, cm, rm, tb), data = dat)
## plot
ggplot(data = dat, aes(x = x, y = y)) + 
  geom_point() + 
  geom_line(aes(y = fitted(fit)))
# }