biogeom (version 1.4.3)

fitsigmoid: Data-Fitting Function for the Sigmoid Growth Equation

Description

fitsigmoid is used to estimate the parameters of a sigmoid growth equation based on the integral of a performance equation or one of its simplified versions.

Usage

fitsigmoid(expr, x, y, ini.val, simpver = 1, 
           control = list(), par.list = FALSE, fig.opt = FALSE,
           xlim = NULL, ylim = NULL, xlab = NULL, ylab = NULL,         
           main = NULL, subdivisions = 100L,
           rel.tol = .Machine$double.eps^0.25, 
           abs.tol = rel.tol, stop.on.error = TRUE, 
           keep.xy = FALSE, aux = NULL)

Value

par

the estimates of the model parameters.

r.sq

the coefficient of determination between the observed and predicted \(y\) values.

RSS

the residual sum of squares between the observed and predicted \(y\) values.

sample.size

the number of data points used in the data fitting.

x

the observed \(x\) values.

y

the observed \(y\) values.

y.pred

the predicted \(y\) values.

Arguments

expr

a performance equation or one of its simplified versions that is used to build a sigmoid growth equation.

x

the observed investigation times.

y

the observed \(y\) values (i.e., biomass, height, body length, etc.).

ini.val

the initial values of the model parameters.

simpver

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

control

the list of control parameters for using the optim function in package stats.

par.list

the option of showing the list of parameters on the screen.

fig.opt

an optional argument to draw the observations and the predicted sigmoid curve.

xlim

the range of the \(x\)-axis over which to plot a sigmoid growth curve.

ylim

the range of the \(y\)-axis over which to plot a sigmoid growth curve.

xlab

the label of the \(x\)-axis when showing a sigmoid growth curve.

ylab

the label of the \(y\)-axis when showing a sigmoid growth curve.

main

the main title of the figure.

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

Here, ini.val only includes the initial values of the model parameters as a list. The Nelder-Mead algorithm (Nelder and Mead, 1965) is used to carry out the optimization of minimizing the residual sum of squares (RSS) between the observed and predicted \(y\) values. The optim function in package stats was used to carry out the Nelder-Mead algorithm. The performance equations denote MbetaE, MBriereE, MLRFE, MPerformanceE and their simplified versions. The arguments of P and simpver should correspond to expr (i.e., MbetaE or MBriereE or MLRFE or MPerformanceE). The sigmoid equation is the integral of a 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")

Nelder, J.A., Mead, R. (1965) A simplex method for function minimization. Computer Journal 7, 308\(-\)313. tools:::Rd_expr_doi("10.1093/comjnl/7.4.308")

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

areaovate, MbetaE, MBriereE, MLRFE, MPerformanceE, sigmoid

Examples

# The shrimp growth data(See the supplementary table in West et al., 2001)
# West, G.B., Brown, J.H., Enquist, B.J. (2001) A general model for ontogenetic growth. 
#     Nature 413, 628-631.
t0 <- c(3, 60, 90, 120, 150, 180, 384)
m0 <- c(0.001, 0.005, 0.018, 0.037, 0.06, 0.067, 0.07)

dev.new()
plot( t0, m0, cex.lab=1.5, cex.axis=1.5, col=4,
      xlab=expression(italic(x)), ylab=expression(italic(y)) )

xopt0   <- seq(100, 150, by=5)
ini.val <- list(0.035, xopt0, 200, 1)
resu1   <- fitsigmoid(MLRFE, x=t0, y=m0, ini.val=ini.val, simpver=1, fig.opt=TRUE, par.list=TRUE)

# \donttest{
  xopt0   <- seq(100, 150, by=5)
  ini.val <- list(0.035, xopt0, 200, 1)
  resu1   <- fitsigmoid(MbetaE, x=t0, y=m0, ini.val=ini.val, simpver=1, fig.opt=TRUE)

  m.ini   <- c(0.5, 1, 2, 3, 4, 5, 10, 20)
  ini.val <- list(1e-8, m.ini, 200, 1)
  resu2   <- fitsigmoid(MBriereE, x=t0, y=m0, ini.val=ini.val, simpver=1, 
             fig.opt=TRUE, control=list(reltol=1e-20, maxit=20000, trace=FALSE), 
             subdivisions=100L, rel.tol=.Machine$double.eps^0.25, 
             abs.tol=.Machine$double.eps^0.25, stop.on.error=TRUE, 
             keep.xy=FALSE, aux=NULL)

  delta0  <- c(0.5, 1, 2, 5, 10, 20)
  ini.val <- list(0.035, 150, -100, 200, delta0)
  resu3   <- fitsigmoid(MLRFE, x=t0, y=m0, ini.val=ini.val, simpver=NULL, 
               fig.opt=TRUE, control=list(reltol=1e-20, maxit=20000), 
               subdivisions = 100L, rel.tol=.Machine$double.eps^0.25, 
               abs.tol=.Machine$double.eps^0.25, stop.on.error=TRUE, 
               keep.xy=FALSE, aux=NULL)

  a.ini   <- c(0.1, 1, 10, 100, 200)
  b.ini   <- 200
  ini.val <- list(0.001, 0.02, 0.15, 0, 200, a.ini, b.ini)
  resu4   <- fitsigmoid(MPerformanceE, x=t0, y=m0, ini.val=ini.val, simpver=NULL, 
             fig.opt=TRUE, control=list(reltol=1e-20, maxit=20000, trace=FALSE), 
             subdivisions=100L, rel.tol=.Machine$double.eps^0.25, 
             abs.tol=.Machine$double.eps^0.25, stop.on.error=TRUE, 
             keep.xy=FALSE, aux=NULL)
  resu5   <- fitsigmoid(MPerformanceE, x=t0, y=m0, ini.val=resu4$par, simpver=NULL, 
               fig.opt=TRUE, control=list(reltol=1e-30, maxit=200000, trace=FALSE))

  ini.val <- list(0.001, 0.01, c(0.1, 1, 10), 0, 200)
  resu6   <- fitsigmoid(MPerformanceE, x=t0, y=m0, ini.val=ini.val, simpver=2, 
             fig.opt=TRUE, control=list(reltol=1e-20, maxit=20000, trace=FALSE), 
             subdivisions=100L, rel.tol=.Machine$double.eps^0.25, 
             abs.tol=.Machine$double.eps^0.25, stop.on.error=TRUE, 
             keep.xy=FALSE, aux=NULL)
# }

graphics.off()