rich: Richards equation

In nlraa: Non-linear regression for agricultural applications

Description

Richards equation (Richards, 1959) J Exp Bot 10: 290-300. This is equation 2.2 in Table 1 in the paper referenced below (Archontoulis and Miguez).

Usage

rich(time, tmax, theta, v, Yo)

Arguments

time	a numeric vector of values at which to evaluate the model.
tmax	tmax is the time when growth rate is maximum
theta	thetha determines the curvature. The relative growth rate is RGR = theta/(1+v).
v	v parameter determines the asymetrical growth.
Yo	Yo is the max Y

Details

Richards equation is an extension of the logistic to deal with asymmetrical growth.

Value

a numeric vector of length equal to the inputs

Note

Applied to describe water stress index, crop N-uptake, seed germination, crop growth, LAI development, etc. Remark at time = 0, Y is not zero Richards equation has often been criticized because the shape parameter v has no obvious biological interpretation

Author(s)

Fernando Miguez

References

Richards equation (Richards, 1959) J Exp Bot 10: 290-300

Nonlinear Regression Models and Applications in Agricultural Research. Sotirios V. Archontoulis and Fernando E. Miguez. Agronomy Journal. doi: 10.2134/agronj2012.0506

See Also

There used to be an R package called richards but it is no longer maintained.

Examples

require(lattice)
time <- seq(0, 150,5)
ans1 <- rich(time, tmax = 60, theta = 0.07, v=1.3, Yo=100)
ans2 <- rich(time, tmax = 60, theta = 0.07, v=0.6, Yo=100)
ans3 <- rich(time, tmax = 60, theta = 0.07, v=0.3, Yo=100)
ans4 <- rich(time, tmax = 60, theta = 0.07, v=1.0, Yo=100)
xyplot(ans1 + ans2 + ans3 + ans4 ~ time,
       type="l", auto.key=TRUE, ylab = "text", xlab = "time")

nlraa documentation built on May 2, 2019, 5 p.m.