# 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

 `1` ```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

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

 ```1 2 3 4 5 6 7 8``` ```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") ```