statforbiology (version 0.9.9)

SSYL: Yield loss equation (Rectangular hyperbola)

Description

These functions provide the yield loss equation, based on a rectangular hyperbola, supporting a higher asymptote and no inflection points. These functions provide the equation (YL.fun), the equation with self-starters for the nls function (NLS.YL) and equation with self-starters for the drm function in the drc package (DRC.YL)

Usage

YL.fun(predictor, i, A)
NLS.YL(predictor, i, A)
DRC.YL(fixed = c(NA, NA), names = c("i", "A"))

Value

YL.fun and NLS.YL return a numeric value, while DRC.YL returns a list containing the nonlinear function and the self starter function

Arguments

predictor

a numeric vector of values at which to evaluate the model

i

model parameter (initial slope)

A

model parameter (maximum percentage yield loss)

fixed

numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.

names

a vector of character strings giving the names of the parameters. The default is usually reasonable.

Author

Andrea Onofri

Details

The Yield-loss equation is parameterised as: $$ f(x) = \frac{i \, x}{1 + (i \, x)/A} $$, it is convex and asymptotically increasing, while the predictor increases. The response is zero when the predictor is also zero and it was mainly used to describe yield losses (in percentage) due to weed competition, expressed as plant density (Cousens, 1985)

References

Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.

Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/

Cousens, R., 1985. A simple model relating yield loss to weed density. Annals of Applied Biology 107, 239–252. https://doi.org/10.1111/j.1744-7348.1985.tb01567.x

Examples

library(statforbiology)
WeedDens <- c(0, 5, 10, 20, 25)
YieldLoss <- c(0, 17.9, 21.5, 27.4, 29.5)

# nls fit
mod.nls <- nls(YieldLoss ~ NLS.YL(WeedDens, i, A) )
summary(mod.nls)
# drm fit
mod.drc <- drm(YieldLoss ~ WeedDens, fct = DRC.YL() )
summary(mod.drc)