TSE | R Documentation |
TSE
is used to calculate y
values at given x
values using
the Todd and Smart's re-expression of Preston's universal egg shape.
TSE(P, x, simpver = NULL)
P |
the parameters of the original Todd-Smart equation or one of its simplified versions. |
x |
the given |
simpver |
an optional argument to use the simplified version of the original Todd-Smart equation. |
When simpver = NULL
, the original Preston equation is selected:
y = d_{0}z_{0} + d_{1}z_{1} + d_{2}z_{2} + d_{3}z_{3},
where
z_{0}=\sqrt{1-x^2},
z_{1}=x\sqrt{1-x^2},
z_{2}=x^{2}\sqrt{1-x^2},
z_{3}=x^{3}\sqrt{1-x^2}.
Here, x
and y
represent the abscissa and ordinate of an arbitrary point on the Todd-Smart curve;
d_{0}
, d_{1}
, d_{2}
, and d_{3}
are parameters to be estimated.
\quad
When simpver = 1
, the simplified version 1 is selected:
y = d_{0}z_{0} + d_{1}z_{1} + d_{2}z_{2},
where x
and y
represent the abscissa and ordinate of an arbitrary point on the Todd-Smart curve;
d_{0}
, d_{1}
, and d_{2}
are parameters to be estimated.
\quad
When simpver = 2
, the simplified version 2 is selected:
y = d_{0}z_{0} + d_{1}z_{1},
where x
and y
represent the abscissa and ordinate of an arbitrary point on the Todd-Smart curve;
d_{0}
, and d_{1}
are parameters to be estimated.
\quad
When simpver = 3
, the simplified version 3 is selected:
y = d_{0}z_{0} + d_{2}z_{2},
where x
and y
represent the abscissa and ordinate of an arbitrary point on the Todd-Smart curve;
d_{0}
, and d_{2}
are parameters to be estimated.
The y
values predicted by the Todd-Smart equation.
Here, x
and y
in the Todd-Smart equation are actually equal to y/a
and x/a
, respectively, in the Preston equation (See PE
for details).
Since a
represents half the egg length, this means that the egg length is fixed to be 2,
and the maximum egg width is correspondingly adjusted to keep the same scale.
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")}
Nelder, J.A., Mead, R. (1965). A simplex method for function minimization.
Computer Journal 7, 308-
313. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/comjnl/7.4.308")}
Preston, F.W. (1953) The shapes of birds' eggs. The Auk 70, 160-
182.
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")}
Todd, P.H., Smart, I.H.M. (1984) The shape of birds' eggs. Journal of Theoretical Biology
106, 239-
243. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/0022-5193(84)90021-3")}
lmPE
, PE
Par <- c(0.695320398, -0.210538656, -0.070373518, 0.116839895)
xb1 <- seq(-1, 1, len=20000)
yb1 <- TSE(P=Par, x=xb1)
xb2 <- seq(1, -1, len=20000)
yb2 <- -TSE(P=Par, x=xb2)
dev.new()
plot(xb1, yb1, asp=1, type="l", col=2, ylim=c(-1, 1), cex.lab=1.5, cex.axis=1.5,
xlab=expression(italic(x)), ylab=expression(italic(y)))
lines(xb2, yb2, col=4)
graphics.off()
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