growthmodels: Compute model output given time and parameters.

In npjc/growr: High level functions to help summarise growth curve fits.

Description

Compute model output given time and parameters.

Usage

gm_blumberg(t, alpha, w0, m, t0 = 0)

gm_brody(t, alpha, w0, k)

gm_chapmanRichards(t, alpha, beta, k, m)

gm_gompertz(t, alpha, beta, k)

gm_janoschek(t, alpha, beta, b, c)

gm_logistic(t, alpha, beta, k)

gm_loglogistic(t, alpha, beta, k)

gm_mitcherlich(t, alpha, beta, k)

gm_mmf(t, alpha, w0, gamma, m)

gm_monomolecular(t, alpha, beta, k)

gm_negativeExponential(t, alpha, k)

gm_richard(t, alpha, beta, k, m)

gm_schnute(t, r0, beta, k, m)

gm_stannard(t, alpha, beta, k, m)

gm_vonBertalanffy(t, alpha, beta, k, m)

Arguments

t	time
alpha	upper asymptote
w0	a reference value at t = t0, the value at t = 0
m	slope of growth
t0	time shift (default 0)
k	growth rate
beta	growth range
b	growth parameter
c	shape parameter
gamma	parameter that controls the point of inflection
r0	reference value
beta	growth displacement
m	growth rate

Details

Blumberg growth model:

y(t) = ...

Brody growth model:

y(t) = α - (α - w_0) * exp(- k * t)

Chapman-Richards growth model:

y(t) = α * (1 - β * exp(-k * t)^{1/(1-m)})

Gompertz growth model:

y(t) = α * exp(-β * exp(-k^t))

Janoschek growth model:

y(t) = α *(α - β) \exp(-b * t^c))

Logistic growth model:

y(t) = α/(1 + β * exp(-k * t))

Log-logistic growth model:

y(t) = α/(1 + β * exp(-k * log(t))

Mitcherlich growth model:

y(t) = α - β * k^t

Morgan-Mercer-Flodin growth model:

y(t) = (w_0 * γ + α * t^m) / (γ + t^m)

Monomolecular growth model:

y(t) = α * ( 1 - β * exp(-k * t))

Negative exponential growth model:

y(t) = α * ( 1 - exp(-k * t))

Richard growth model:

y(t) = α/((1 + β * exp(-k * t))^(1 / m))

Schnute growth model:

y(t) = (r_0 + β * exp(k * t))^m

Stannard growth model:

y(t) = α *( 1 + exp(-(beta + k * t)/m))^(-m)

von Bertalanffy growth model:

y(t) = (α^(1-m) - β * exp(-k * t))^(1/(1-m))

Value

y-values of the specified model for given time points.

Author(s)

Daniel Rodriguez

References

M. M. Kaps, W. O. W. Herring, and W. R. W. Lamberson, "Genetic and environmental parameters for traits derived from the Brody growth curve and their relationships with weaning weight in Angus cattle.," Journal of Animal Science, vol. 78, no. 6, pp. 1436-1442, May 2000.

D. Fekedulegn, M. Mac Siurtain, and J. Colbert, "Parameter estimation of nonlinear growth models in forestry," Silva Fennica, vol. 33, no. 4, pp. 327-336, 1999.

Michael J. Panik, "Growth Curve Modeling: Theory and Applications", John Wiley & Sons, December 2013.

A. Khamiz, Z. Ismail, and A. T. Muhammad, "Nonlinear growth models for modeling oil palm yield growth," Journal of Mathematics and Statistics, vol. 1, no. 3, p. 225, 2005.

Examples

gm_blumberg(0:10, 10, 2, 0.5)

gm_brody(0:10, 10, 5, 0.3)

gm_chapmanRichards(0:10, 10, 0.5, 0.3, 0.5)

gm_gompertz(0:10, 10, 0.5, 0.3)

gm_janoschek(0:10, 10, 2, 0.5, 2)

gm_logistic(0:10, 10, 0.5, 0.3)

gm_loglogistic(0:10, 10, 0.5, 0.3)

gm_mitcherlich(0:10, 10, 0.5, 0.3)

gm_mmf(0:10, 10, 0.5, 4, 1)

gm_monomolecular(0:10, 10, 0.5, 0.3)

gm_negativeExponential(0:10, 1, 0.3)

gm_schnute(0:10, 10, 5, .5, .5)

gm_stannard(0:10, 1, .2, .1, .5)

gm_vonBertalanffy(0:10, 10, 0.5, 0.3, 0.5)

npjc/growr documentation built on Nov. 9, 2019, 7:29 a.m.