growthrates (version 0.8.4)

grow_richards: Growth Model According to Richards

Description

Richards growth model written as analytical solution of the differential equation.

Usage

grow_richards(time, parms)

Value

vector of dependent variable (y).

Arguments

time

vector of time steps (independent variable).

parms

named parameter vector of the Richards growth model with:

• y0 initial value of abundance,

• mumax maximum growth rate (note different interpretation compared to exponential growth),

• K carrying capacity (max. total concentration of cells),

• beta shape parameter determining the curvature.

Details

The equation used is:

$$y = K*(1-exp(-beta * mumax * time)*(1-(y0/K)^-beta))^(-1/beta)$$

The naming of parameters used here follows the convention of Tsoularis (2001), but uses mumax for growthrate and y for abundance to make them consistent to other growth functions.

References

Richards, F. J. (1959) A Flexible Growth Function for Empirical Use. Journal of Experimental Botany 10 (2): 290--300.

Tsoularis, A. (2001) Analysis of Logistic Growth Models. Res. Lett. Inf. Math. Sci, (2001) 2, 23--46.

See Also

Other growth models: grow_baranyi(), grow_exponential(), grow_gompertz2(), grow_gompertz(), grow_huang(), grow_logistic(), growthmodel, ode_genlogistic(), ode_twostep()

Examples

time <- seq(0, 30, length=200)
y    <- grow_richards(time, c(y0=1, mumax=.5, K=10, beta=2))[,"y"]
plot(time, y, type="l")
y    <- grow_richards(time, c(y0=1, mumax=.5, K=10, beta=100))[,"y"]
lines(time, y, col="red")
y    <- grow_richards(time, c(y0=1, mumax=.5, K=10, beta=.2))[,"y"]
lines(time, y, col="blue")