ETE | R Documentation |
ETE
is used to calculate the y-value for an arbitrary point on the Troscianko curve
that was generated by the explicit Troscianko equation.
ETE(P, x)
P |
the parameters of the explicit Troscianko equation, including |
x |
the x-value used in the explicit Troscianko equation. |
The explicit Troscianko equation is recommended as:
y = a\,\exp\left\{\alpha_{0}+\alpha_{1}\,\left(\frac{x}{a}\right)+\alpha_{2}\, \left(\frac{x}{a}\right)^2\right\}\sqrt{1-\left(\frac{x}{a}\right)^2},
where x
and y
represent the abscissa and ordinate of an arbitrary point on the explicit Troscianko curve;
a
, \alpha_{0}
, \alpha_{1}
, and \alpha_{2}
are parameters to be estimated.
The y
values predicted by the explicit Troscianko equation.
We only considered the upper part of the egg-shape curve in the above expressions because
the lower part is symmetrical to the upper part around the x-axis.
The mid-line of an egg's profile in ETE
is aligned to
the x-axis. The argument, P
, in the ETE
function has the same parameters,
\alpha_{0}
, \alpha_{1}
, and \alpha_{2}
, as those in the TE
function.
However, the former has an additional parameter a
than the latter, which represents half
the egg's length. The lmTE
function is based on the TE
function, while
the fitETE
function is based on the ETE
function here.
In addition, the values in x
> a
(i.e., the first element in P
)
are forced to be a
, and the values in x
< -a
will be forced to be -a
.
Peijian Shi pjshi@njfu.edu.cn, Johan Gielis johan.gielis@uantwerpen.be, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.
Biggins, J.D., Montgomeries, R.M., Thompson, J.E., Birkhead, T.R. (2022) Preston’s universal formula for avian egg shape. Ornithology 139, ukac028. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/ornithology/ukac028")}
Biggins, J.D., Thompson, J.E., Birkhead, T.R. (2018) Accurately quantifying
the shape of birds' eggs. Ecology and Evolution 8, 9728-
9738. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/ece3.4412")}
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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/nyas.14862")}
Shi, P., Wang, L., Quinn, B.K., Gielis, J. (2023) A new program to estimate the parameters of Preston's equation, a general formula for describing the egg shape of birds. Symmetry 15, 231. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3390/sym15010231")}
Troscianko, J. (2014). A simple tool for calculating egg shape, volume and surface area from digital images.
Ibis, 156, 874-
878. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/ibi.12177")}
curveETE
, fitETE
, SurfaceAreaETE
, VolumeETE
Par5 <- c(2.25, -0.38, -0.29, -0.16)
xx2 <- seq(-2.25, 2.25, len=2000)
yy3 <- ETE(P=Par5, x=xx2)
yy4 <- -ETE(P=Par5, x=xx2)
dev.new()
plot(xx2, yy3, asp=1, type="l", col=4, cex.lab=1.5, cex.axis=1.5,
xlim=c(-3, 3), ylim=c(-3, 3),
xlab=expression(italic(x)), ylab=expression(italic(y)))
lines(xx2, yy4, col=2)
graphics.off()
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.