biogeom (version 1.4.3)

sigmoid: Sigmoid Growth Equation

Description

sigmoid is used to calculate the \(y\) values (e.g., biomass, height, body length, and so on) at given investigation times.

Usage

sigmoid(expr, P, x, simpver = 1, subdivisions = 100L,
        rel.tol = .Machine$double.eps^0.25, 
        abs.tol = rel.tol, stop.on.error = TRUE, 
        keep.xy = FALSE, aux = NULL)

Value

The \(y\) values (i.e., biomass, height, body length, and so on) at given investigation times. The growth euqation is actually an integral of the performance equation or one of its simplified versions.

Arguments

expr

a performance equation or one of its simplified versions.

P

the parameters of the performance equation or one of its simplified versions.

x

the given investigation times.

simpver

an optional argument to use the simplfied version of the performance equation.

subdivisions

please see the arguments for the integrate function in package stats.

rel.tol

please see the arguments for the integrate function in package stats.

abs.tol

please see the arguments for the integrate function in package stats.

stop.on.error

please see the arguments for the integrate function in package stats.

keep.xy

please see the arguments for the integrate function in package stats.

aux

please see the arguments for the integrate function in package stats.

Author

Peijian Shi , Johan Gielis , Brady K. Quinn .

Details

The performance equations denote MbetaE, MBriereE, MLRFE, and their simplified versions. The arguments of P and simpver should correspond to expr (i.e., MbetaE, MBriereE, MLRFE, and MPerformanceE). The sigmoid curve is the integral of the performance equation or one of its simplified versions.

References

Jin, J., Quinn, B.K., Shi, P. (2022) The modified Brière equation and its applications. Plants 11, 1769. tools:::Rd_expr_doi("10.3390/plants11131769")

Lian, M., Shi, P., Zhang, L., Yao, W., Gielis, J., Niklas, K.J. (2023) A generalized performance equation and its application in measuring the Gini index of leaf size inequality. Trees \(-\) Structure and Function 37, 1555\(-\)1565. tools:::Rd_expr_doi("10.1007/s00468-023-02448-8")

Shi, P., Fan, M., Ratkowsky, D.A., Huang, J., Wu, H., Chen, L., Fang, S., Zhang, C. (2017) Comparison of two ontogenetic growth equations for animals and plants. Ecological Modelling 349, 1\(-\)10. tools:::Rd_expr_doi("10.1016/j.ecolmodel.2017.01.012")

Shi, P., Gielis, J., Quinn, B.K., Niklas, K.J., Ratkowsky, D.A., Schrader, J., Ruan, H., Wang, L., Niinemets, Ü. (2022) 'biogeom': An R package for simulating and fitting natural shapes. Annals of the New York Academy of Sciences 1516, 123\(-\)134. tools:::Rd_expr_doi("10.1111/nyas.14862")

See Also

fitsigmoid, MbetaE, MBriereE, MLRFE, and MPerformanceE

Examples

Pa1 <- c(3, 3, 10, 1)
xv1 <- seq(-5, 15, len=2000)
yv1 <- sigmoid(MBriereE, P=Pa1, x=xv1, simpver=1)
Pa2 <- c(3, 3, 2, 12, 1)
yv2 <- sigmoid(MBriereE, P=Pa2, x=xv1, simpver=NULL)
Pa3 <- c(200, 1.32, 0.85, 12, 3.7, 17)
yv3 <- sigmoid(MPerformanceE, P=Pa3, x=xv1, simpver=1)

dev.new()
plot( xv1, yv2, cex.lab=1.5, cex.axis=1.5, type="l", col=4,
      xlab=expression(italic(x)), ylab=expression(italic(y)) )
lines( xv1, yv1, col=2 )
lines( xv1, yv3, col=3 )

graphics.off()