biogeom (version 1.4.3)

fitovate: Data-Fitting Function for the Ovate Leaf-Shape Equation

Description

fitovate is used to estimate the parameters of a simplified performance equation.

Usage

fitovate(expr, x, y, ini.val, 
         par.list = FALSE, stand.fig = TRUE, control = list(), 
         angle = NULL, fig.opt = FALSE, index.xmax = 3, np = 2000, 
         xlim = NULL, ylim = NULL, unit = NULL, main = 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 on the polygon's boundary in the data fitting.

scan.length

the observed length of the polygon's boundary.

scan.width

the observed width of the polygon's boundary.

scan.perimeter

the observed perimeter of the polygon's boundary.

scan.area

the observed area of the polygon's boundary.

pred.length

the predicted length of the polygon's boundary.

pred.width

the predicted width of the polygon's boundary.

pred.perimeter

the predicted perimeter of the polygon's boundary.

pred.area

the predicted area of the polygon's boundary.

x.stand.obs

the observed \(x\) coordinates at the standard state.

x.stand.pred

the predicted \(x\) coordinates at the standard state.

y.stand.obs

the observed \(y\) coordinates at the standard state.

y.stand.pred

the predicted \(y\) coordinates at the standard state.

x.obs

the observed \(x\) coordinates at the transferred angles defined by the user.

x.pred

the predicted \(x\) coordinates at the transferred angles defined by the user.

y.obs

the observed \(y\) coordinates at the transferred angles defined by the user.

y.pred

the predicted \(y\) coordinates at the transferred angles defined by the user.

Arguments

expr

the simplified version 1 of the performance equations.

x

the \(x\) coordinates of a polygon's boundary.

y

the \(y\) coordinates of a polygon's boundary.

ini.val

the initial values of the simplified version 1 of a performance equation.

par.list

an optional argument to show the list of parameters on the screen.

stand.fig

an optional argument to draw the observed and predicted polygons' boundaries at the standard state (i.e., the origin is located at (0, 0), and the major axis overlaps with the \(x\)-axis).

control

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

angle

the angle between the major axis of the polygon and the \(x\)-axis, which can be defined by the user.

fig.opt

an optional argument to draw the observed and predicted polygons at an arbitrary angle between the major axis and the \(x\)-axis.

index.xmax

the specified index in parameters representing \(x_{\mathrm{max}}\).

np

the number of data points on the predicted ovate leaf-shape curve.

xlim

the range of the \(x\)-axis over which to plot the ovate leaf-shape curve.

ylim

the range of the \(y\)-axis over which to plot the ovate leaf-shape curve.

unit

the units of the \(x\)-axis and the \(y\)-axis when showing the ovate leaf-shape curve.

main

the main title of the figure.

Author

Peijian Shi , Johan Gielis , Brady K. Quinn .

Details

ini.val is a list for two types of parameters: three location parameters, and model parameters. This means that expr is limited to being the simplified version 1 (where \(x_{\mathrm{min}} = 0\)) in MbetaE, MBriereE, MLRFE, and MPerformanceE. The initial values for the first three parameters in ini.val are location parameters, among which the first two are the planar coordinates of the transferred origin, and the third is the angle between the major axis of the polygon and the \(x\)-axis. 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 \(y\)-axis. The optim function in package stats was used to carry out the Nelder-Mead algorithm. When angle = NULL, the observed polygon will be shown at its initial angle in the scanned image; when angle is a numerical value (e.g., \(\pi/4\)) defined by the user, it indicates that the major axis is rotated by the amount (\(\pi/4\)) counterclockwise from the \(x\)-axis.

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")

Huey, R.B., Stevenson, R.D. (1979) Integrating thermal physiology and ecology of ectotherms: a discussion of approaches. American Zoologist 19, 357\(-\)366. tools:::Rd_expr_doi("10.1093/icb/19.1.357")

Li, Y., Zheng, Y., Ratkowsky, D.A., Wei, H., Shi, P. (2022) Application of an ovate leaf shape model to evaluate leaf bilateral asymmetry and calculate lamina centroid location. Frontiers in Plant Science 12, 822907. tools:::Rd_expr_doi("10.3389/fpls.2021.822907")

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., Ge, F., Sun, Y., Chen, C. (2011) A simple model for describing the effect of temperature on insect developmental rate. Journal of Asia-Pacific Entomology 14, 15\(-\)20. tools:::Rd_expr_doi("10.1016/j.aspen.2010.11.008")

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")

Shi, P., Yu, K., Niklas, K.J., Schrader, J., Song, Y., Zhu, R., Li, Y., Wei, H., Ratkowsky, D.A. (2021) A general model for describing the ovate leaf shape. Symmetry 13, 1524. tools:::Rd_expr_doi("10.3390/sym13081524")

See Also

areaovate, curveovate, MbetaE, MBriereE, MLRFE, MPerformanceE

Examples

data(Neocinnamomum)

uni.C <- sort( unique(Neocinnamomum$Code) )
ind   <- 2
Data  <- Neocinnamomum[Neocinnamomum$Code==uni.C[ind], ]
x0    <- Data$x
y0    <- Data$y

Res1 <- adjdata(x0, y0, ub.np=200, len.pro=1/20)
x1   <- Res1$x
y1   <- Res1$y

dev.new()
plot( Res1$x, Res1$y, asp=1, cex.lab=1.5, cex.axis=1.5, 
      xlab=expression(italic("x")), ylab=expression(italic("y")) ) 

# \donttest{
  x0.ini    <- min( x1 )
  y0.ini    <- min( y1 )
  theta.ini <- pi/4
  len.max   <- max( max(y1)-min(y1), max(x1)-min(x1) ) *2/sqrt(2)
  a.ini     <- c(0.1, 0.01, 0.001, 0.0001)
  m.ini     <- c(0.1, 0.5, 1, 2)
  x2.ini    <- len.max
  delta.ini <- c(0.5, 1)
  ini.val   <- list(x0.ini, y0.ini, theta.ini, a.ini, m.ini, x2.ini, delta.ini)

  Res1 <- fitovate(MBriereE, x=x1, y=y1, ini.val=ini.val,            
            par.list=FALSE, fig.opt=TRUE, angle=pi/6, 
            control=list(reltol=1e-20, maxit=20000), 
            np=2000, unit=NULL)
  Res1$RSS

  x0.ini    <- min( x1 )
  y0.ini    <- min( y1 )
  theta.ini <- pi/4
  len.max   <- max( max(y1)-min(y1), max(x1)-min(x1) ) *2/sqrt(2)
  yc.ini    <- len.max/3 
  xc.ini    <- 1/4*len.max
  x2.ini    <- len.max
  delta.ini <- c(0.5, seq(1, 5, by=5))
  ini.val   <- list(x0.ini, y0.ini, theta.ini, yc.ini, xc.ini, x2.ini, delta.ini)

  Res2 <- fitovate( MbetaE, x=x1, y=y1, ini.val=ini.val,            
                    par.list=TRUE, fig.opt=TRUE, angle=pi/3, 
                    control=list(reltol=1e-20, maxit=20000), 
                    np=2000, unit=NULL )
  Res2$RSS

  Res3 <- fitovate( MLRFE, x=x1, y=y1, ini.val=ini.val, 
                    unit=NULL, par.list=FALSE, fig.opt=TRUE, 
                    angle=NULL, control=list(reltol=1e-20, 
                    maxit=20000), np=2000)
  Res3$RSS


  x0.ini    <- min( x1 )
  y0.ini    <- min( y1 )
  theta.ini <- pi/4
  len.max   <- max( max(y1)-min(y1), max(x1)-min(x1) ) *2/sqrt(2)
  c.ini     <- 1/5*len.max
  K1.ini    <- c(0.1, 1, 5, 10)
  K2.ini    <- 1
  x2.ini    <- len.max
  a.ini     <- 1
  b.ini     <- 1
  ini.val   <- list(x0.ini, y0.ini, theta.ini, c.ini, K1.ini, K2.ini, x2.ini, a.ini, b.ini)

  Res4 <- fitovate( MPerformanceE, x=x1, y=y1, ini.val=ini.val,            
                    par.list=TRUE, fig.opt=TRUE, index.xmax=4, angle=pi/3, 
                    control=list(reltol=1e-20, maxit=20000), 
                    np=2000, unit=NULL )
  Res4$RSS
# }

graphics.off()