| fitovate {biogeom} | R Documentation |
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)
Arguments
expr |
the simplified version 1 of the performance equations. |
x |
the |
y |
the |
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 |
control |
the list of control parameters for using the |
angle |
the angle between the major axis of the polygon and the |
fig.opt |
an optional argument to draw the observed and predicted polygons at an arbitrary angle
between the major axis and the |
index.xmax |
the specified index in parameters representing |
np |
the number of data points on the predicted ovate leaf-shape curve. |
xlim |
the range of the |
ylim |
the range of the |
unit |
the units of the |
main |
the main title of the figure. |
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.
Value
par |
the estimates of the model parameters. |
r.sq |
the coefficient of determination between the observed and predicted |
RSS |
the residual sum of squares between the observed and predicted |
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.stand.pred |
the predicted |
y.stand.obs |
the observed |
y.stand.pred |
the predicted |
x.obs |
the observed |
x.pred |
the predicted |
y.obs |
the observed |
y.pred |
the predicted |
Note
There are two types of parameters (i.e., three location parameters and model parameters)
for the value of par. The transferred
angle denotes the angle between the major axis and the x-axis. For the argument index.xmax,
the default is 3, which corresponds to the order of the model parameter of x_{\mathrm{max}} in
MbetaE, MBriereE, and MLRFE. However, in MPerformanceE,
index.xmax should be 4 rather than 3.
Author(s)
Peijian Shi pjshi@njfu.edu.cn, Johan Gielis johan.gielis@uantwerpen.be, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.
References
Jin, J., Quinn, B.K., Shi, P. (2022) The modified Brière equation and its applications. Plants 11, 1769. 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. 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. 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. doi:10.1007/s00468-023-02448-8
Nelder, J.A., Mead, R. (1965) A simplex method for function minimization.
Computer Journal 7, 308-313. 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. 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. 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. 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. 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")) )
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()