MBriereE is used to calculate \(y\) values at given \(x\) values using
the modified Brière equation or one of its simplified versions.
MBriereE(P, x, simpver = 1)The \(y\) values predicted by the modified Brière equation or one of its simplified versions.
the parameters of the modified Brière equation or one of its simplified versions.
the given \(x\) values.
an optional argument to use the simplified version of the modified Brière equation.
Peijian Shi pjshi@njfu.edu.cn, Johan Gielis johan.gielis@uantwerpen.be, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.
When simpver = NULL, the modified Brière equation is selected:
$$\mbox{if } x \in{\left(x_{\mathrm{min}}, \ x_{\mathrm{max}}\right)},$$
$$y = a\left|x(x-x_{\mathrm{min}})(x_{\mathrm{max}}-x)^{1/m}\right|^{\delta};$$
$$\mbox{if } x \notin{\left(x_{\mathrm{min}}, \ x_{\mathrm{max}}\right)},$$
$$y = 0.$$
Here, \(x\) and \(y\) represent the independent and dependent variables, respectively;
and \(a\), \(m\), \(x_{\mathrm{min}}\), \(x_{\mathrm{max}}\), and \(\delta\) are constants to be estimated,
where \(x_{\mathrm{min}}\) and \(x_{\mathrm{max}}\) represents the
lower and upper intersections between the curve and the \(x\)-axis. \(y\) is defined as 0
when \(x < x_{\mathrm{min}}\) or \(x > x_{\mathrm{max}}\). There are five elements in P, representing
the values of \(a\), \(m\), \(x_{\mathrm{min}}\), \(x_{\mathrm{max}}\), and \(\delta\), respectively.
\(\quad\) When simpver = 1, the simplified version 1 is selected:
$$\mbox{if } x \in{\left(0, \ x_{\mathrm{max}}\right)},$$
$$y = a\left|x^{2}(x_{\mathrm{max}}-x)^{1/m}\right|^{\delta};$$
$$\mbox{if } x \notin{\left(0, \ x_{\mathrm{max}}\right)},$$
$$y = 0.$$
There are four elements in P, representing
the values of \(a\), \(m\), \(x_{\mathrm{max}}\), and \(\delta\), respectively.
\(\quad\) When simpver = 2, the simplified version 2 is selected:
$$\mbox{if } x \in{\left(x_{\mathrm{min}}, \ x_{\mathrm{max}}\right)},$$
$$y = ax(x-x_{\mathrm{min}})(x_{\mathrm{max}}-x)^{1/m};$$
$$\mbox{if } x \notin{\left(x_{\mathrm{min}}, \ x_{\mathrm{max}}\right)},$$
$$y = 0.$$
There are four elements in P representing
the values of \(a\), \(m\), \(x_{\mathrm{min}}\), and \(x_{\mathrm{max}}\), respectively.
\(\quad\) When simpver = 3, the simplified version 3 is selected:
$$\mbox{if } x \in{\left(0, \ x_{\mathrm{max}}\right)},$$
$$y = ax^{2}(x_{\mathrm{max}}-x)^{1/m};$$
$$\mbox{if } x \notin{\left(0, \ x_{\mathrm{max}}\right)},$$
$$y = 0.$$
There are three elements in P representing
the values of \(a\), \(m\), and \(x_{\mathrm{max}}\), respectively.
Brière, J.-F., Pracros, P, Le Roux, A.-Y., Pierre, J.-S. (1999) A novel rate model of temperature-dependent development for arthropods. Environmental Entomology 28, 22\(-\)29. tools:::Rd_expr_doi("10.1093/ee/28.1.22")
Cao, L., Shi, P., Li, L., Chen, G. (2019) A new flexible sigmoidal growth model. Symmetry 11, 204. tools:::Rd_expr_doi("10.3390/sym11020204")
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")
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")
areaovate, curveovate, fitovate, fitsigmoid,
MbetaE, MLRFE, MPerformanceE, sigmoid
x2 <- seq(-5, 15, len=2000)
Par2 <- c(0.01, 3, 0, 10, 1)
y2 <- MBriereE(P=Par2, x=x2, simpver=NULL)
dev.new()
plot( x2, y2, cex.lab=1.5, cex.axis=1.5, type="l",
xlab=expression(italic(x)), ylab=expression(italic(y)) )
graphics.off()
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