VolumeAM: Calculation of the Volume of an Apical meristem.

In biogeom: Biological Geometries

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.

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.

Note

The argument P in the VolumeAM function has three parameters for model = "Hybrid", and two parameters for model = "Superparabola".

Author(s)

Peijian Shi [e-mail], Johan Gielis [e-mail], Brady K. Quinn [e-mail].

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/nyas.14862")}

See Also

fitAM, PlanCoor, SurfaceAreaAM, SAMs

Examples

  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)

biogeom documentation built on Aug. 24, 2025, 5:08 p.m.