VolumeAM: Calculation of the Volume of an Apical meristem.

Description

VolumeAM is used to calculate the volume of an apical meristem that follows the the hybrid catenary-parabolic equation or the superparabolic equation.

Usage

VolumeAM(model = "Hybrid", P, upper = Inf, subdivisions = 100L,
         rel.tol = .Machine$double.eps^0.25, abs.tol = rel.tol,
         stop.on.error = TRUE, keep.xy = FALSE, aux = NULL)

Arguments

model: an optional argument to select a model to calculate the volume.
P: the parameters of the hybrid catenary-parabolic equation or the superparabolic equation.
upper: the upper limit of integration in $x$.
subdivisions: please see the arguments for the integrate function in package stats.
rel.tol: please see the arguments for the integrate function in package stats.
abs.tol: please see the arguments for the integrate function in package stats.
stop.on.error: please see the arguments for the integrate function in package stats.
keep.xy: please see the arguments for the integrate function in package stats.
aux: please see the arguments for the integrate function in package stats.

Author

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

Details

The formula of the volume ($V$) of an apical meristem based on the hybrid catenary-parabolic equation or the superparabolic equation have two cases.

$\quad$ Case (i): if the AM's profile is a downward-opening curve, $V$ takes the form $$V(x) = 2\, \pi \int_{0}^{a} x\, \left|y\left(x\right) \right| dx,$$ where $a$ is the upper limit of integration in $x$. The lower limit of integration in $x$ is 0.

$\quad$ Case (ii): if the AM's profile is an upward-opening curve, $V$ takes the form $$V(x) = \pi a^2 \left|y\left(a\right)\right| - 2\, \pi \int_{0}^{a} x\, \left|y\left(x\right) \right| dx,$$ where $a$ is the upper limit of integration in $x$. The lower limit of integration in $x$ is 0.

$\quad$ If model = "Hybrid", $y$ denotes the hybrid catenary-parabolic equation, which equals $y\left(x\right) = \alpha\,\mbox{cosh}(\beta x) + \gamma x^{2}-\alpha$. Here, $\alpha$, $\beta$ and $\gamma$ are model parameters provided by the argument P.

$\quad$ If model = "Superparabola", $y$ denotes the superparabolic equation, which equals $y\left(x\right) = \beta_{1}\, {\left|x\right|}^{\beta_{2}}$. Here, $\beta_{1}$ and $\beta_{2}$ are model parameters provided by the argument P.

References

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")

Examples

Run this code

  par3 <- c(-20, 0.9695, 11.40)
  VolumeAM(model = "Hybrid", P = par3, upper=1)
  
  par5 <- c(1.3807, 1.3173)
  VolumeAM(model = "Superparabola", P = par5, upper=1)

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