MBriereE {biogeom}R Documentation

Modified Briere Equation

Description

MBriereE is used to calculate yy values at given xx values using the modified Brière equation or one of its simplified versions.

Usage

MBriereE(P, x, simpver = 1)

Arguments

P

the parameters of the modified Brière equation or one of its simplified versions.

x

the given xx values.

simpver

an optional argument to use the simplified version of the modified Brière equation.

Details

When simpver = NULL, the modified Brière equation is selected:

\mboxifx(xmin, xmax),\mbox{if } x \in{\left(x_{\mathrm{min}}, \ x_{\mathrm{max}}\right)},

y=ax(xxmin)(xmaxx)1/mδ;y = a\left|x(x-x_{\mathrm{min}})(x_{\mathrm{max}}-x)^{1/m}\right|^{\delta};

\mboxifx(xmin, xmax),\mbox{if } x \notin{\left(x_{\mathrm{min}}, \ x_{\mathrm{max}}\right)},

y=0.y = 0.

Here, xx and yy represent the independent and dependent variables, respectively; and aa, mm, xminx_{\mathrm{min}}, xmaxx_{\mathrm{max}}, and δ\delta are constants to be estimated, where xminx_{\mathrm{min}} and xmaxx_{\mathrm{max}} represents the lower and upper intersections between the curve and the xx-axis. yy is defined as 0 when x<xminx < x_{\mathrm{min}} or x>xmaxx > x_{\mathrm{max}}. There are five elements in P, representing the values of aa, mm, xminx_{\mathrm{min}}, xmaxx_{\mathrm{max}}, and δ\delta, respectively.

\quad When simpver = 1, the simplified version 1 is selected:

\mboxifx(0, xmax),\mbox{if } x \in{\left(0, \ x_{\mathrm{max}}\right)},

y=ax2(xmaxx)1/mδ;y = a\left|x^{2}(x_{\mathrm{max}}-x)^{1/m}\right|^{\delta};

\mboxifx(0, xmax),\mbox{if } x \notin{\left(0, \ x_{\mathrm{max}}\right)},

y=0.y = 0.

There are four elements in P, representing the values of aa, mm, xmaxx_{\mathrm{max}}, and δ\delta, respectively.

\quad When simpver = 2, the simplified version 2 is selected:

\mboxifx(xmin, xmax),\mbox{if } x \in{\left(x_{\mathrm{min}}, \ x_{\mathrm{max}}\right)},

y=ax(xxmin)(xmaxx)1/m;y = ax(x-x_{\mathrm{min}})(x_{\mathrm{max}}-x)^{1/m};

\mboxifx(xmin, xmax),\mbox{if } x \notin{\left(x_{\mathrm{min}}, \ x_{\mathrm{max}}\right)},

y=0.y = 0.

There are four elements in P representing the values of aa, mm, xminx_{\mathrm{min}}, and xmaxx_{\mathrm{max}}, respectively.

\quad When simpver = 3, the simplified version 3 is selected:

\mboxifx(0, xmax),\mbox{if } x \in{\left(0, \ x_{\mathrm{max}}\right)},

y=ax2(xmaxx)1/m;y = ax^{2}(x_{\mathrm{max}}-x)^{1/m};

\mboxifx(0, xmax),\mbox{if } x \notin{\left(0, \ x_{\mathrm{max}}\right)},

y=0.y = 0.

There are three elements in P representing the values of aa, mm, and xmaxx_{\mathrm{max}}, respectively.

Value

The yy values predicted by the modified Brière equation or one of its simplified versions.

Note

We have added a parameter δ\delta in the original Brière equation (i.e., simpver = 2) to increase the flexibility for data fitting.

Author(s)

Peijian Shi pjshi@njfu.edu.cn, Johan Gielis johan.gielis@uantwerpen.be, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.

References

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. 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. doi:10.3390/sym11020204

Jin, J., Quinn, B.K., Shi, P. (2022) The modified Brière equation and its applications. Plants 11, 1769. 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. doi:10.1111/nyas.14862

See Also

areaovate, curveovate, fitovate, fitsigmoid, MbetaE, MLRFE, MPerformanceE, sigmoid

Examples

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()

[Package biogeom version 1.4.3 Index]