biogeom (version 1.4.3)

MBriereE: Modified Briere Equation

Description

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

Usage

MBriereE(P, x, simpver = 1)

Value

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

Arguments

P

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

x

the given $x$ values.

simpver

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

Author

Peijian Shi , Johan Gielis , Brady K. Quinn .

Details

When simpver = NULL, the modified Brière equation is selected: $$\text{if }x\in (x_{\min },x_{\max }),$$ $$y=a{|x(x-x_{\min })(x_{\max }-x{)}^{1/m}|}^{\delta };$$ $$\text{if }x\notin (x_{\min },x_{\max }),$$ $$y=0.$$ Here, $x$ and $y$ represent the independent and dependent variables, respectively; and $a$, $m$, $x_{\min }$, $x_{\max }$, and $\delta$ are constants to be estimated, where $x_{\min }$ and $x_{\max }$ represents the lower and upper intersections between the curve and the $x$-axis. $y$ is defined as 0 when $x<x_{\min }$ or $x>x_{\max }$. There are five elements in P, representing the values of $a$, $m$, $x_{\min }$, $x_{\max }$, and $\delta$, respectively.

$$ When simpver = 1, the simplified version 1 is selected: $$\text{if }x\in (0,x_{\max }),$$ $$y=a{|x^2(x_{\max }-x{)}^{1/m}|}^{\delta };$$ $$\text{if }x\notin (0,x_{\max }),$$ $$y=0.$$ There are four elements in P, representing the values of $a$, $m$, $x_{\max }$, and $\delta$, respectively.

$$ When simpver = 2, the simplified version 2 is selected: $$\text{if }x\in (x_{\min },x_{\max }),$$ $$y=ax(x-x_{\min })(x_{\max }-x{)}^{1/m};$$ $$\text{if }x\notin (x_{\min },x_{\max }),$$ $$y=0.$$ There are four elements in P representing the values of $a$, $m$, $x_{\min }$, and $x_{\max }$, respectively.

$$ When simpver = 3, the simplified version 3 is selected: $$\text{if }x\in (0,x_{\max }),$$ $$y=a{x}^2(x_{\max }-x{)}^{1/m};$$ $$\text{if }x\notin (0,x_{\max }),$$ $$y=0.$$ There are three elements in P representing the values of $a$, $m$, and $x_{\max }$, respectively.

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. 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")

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()