HTTLL: Hydro-thermal-time model with log-logistic distribution of...

In OnofriAndreaPG/drcSeedGerm: Utilities for data analyses in seed germination/emergence assays

Hydro-thermal-time model with log-logistic distribution of base water potential (Mesgaran et al., 2017)

Description

This model relates the time-course of the proportion of germinated seeds to the water potential and temperature in the substrate and it is based on a log-logistic distribution of base water potential within the seed lot. Two similar functions are available within the 'drcSeedGerm' package: the first one is 'HTTLL.M()' that assumes that the base water potential decreases with temperature for any T > T_b. The equation is:

P(t, T, Ψ) = \frac{1}{1 + \exp ≤ft\{ - \frac{ \log ≤ft[ Ψ - ≤ft( \frac{θ_{HT}}{t ( T - T_b )} \right) + δ \right] - \log ≤ft[ Ψ_b + K_t (T - T_b) + δ \right] }{σ_{Ψ_b}} \right\} }

The second function is 'HTTLL.BS()' and it assumes that the base water potential decreases with temperature only for any T > T_o, where T_o is the optimal temperature level. For this case, the element K_t(T - T_b) is modified as K_t[\max(T,T_o) - T_o] and the optimal temperature T_o is included as an explicit parameter.

The 'HTTLL.M.fun()' and 'HTTLL.BS.fun()' are two generic functions, which can be used for plotting or other applications, while the 'HTTLL.M()' and 'HTTLL.BS()' functions are meant to be used for model fitting with the 'drmte()' function in the 'drcte()' package.

Usage

HTTLL.M()
HTTLL.BS()
HTTLL.M.fun(time, Psi, Temp, thetaHT, Tb, Psib50, Kt, delta, sigmaPsib)
HTTLL.BS.fun(time, Psi, Temp, thetaHT, Tb, To, Psib50, Kt, delta, sigmaPsib)

Arguments

The 'HTTLL.M()' and 'HTTLL.BS()' functions have no arguments. The 'HTTLL.M.fun()' and the 'HTTLL.BS.fun()' functions have the following arguments:

time	time
Psi	water potential in the substrate
Temp	temperature
thetaHT	hydro-time parameter
Tb	base temperature
To	optimal temperature
Psib50	median base water potential
Kt	parameter measuring the effect of temperature on base water potential
delta	shifting parameter to allow for a log-logistic distribution of negative values for base water potential
sigmaPsib	scale parameter for log-logistic distribution

Details

The detail of this time-to-event model and the meaning of parameters are described in Mesgaran et al. (2017).

Value

The 'HTTLL.M.fun()' and 'HTTLL.BS.fun()' functions return the proportion of germinated seeds, for any given values of time, water potential and temperature in the substrate. The 'HTTLL.M()' and 'HTTLL.BS()' functions return a list containing the nonlinear function, the self-starter function, the parameter names and other items which are internally used by the 'drmte()' function.

Note

This function is for use with the function 'drmte()'

Author(s)

Andrea Onofri

References

Bradford, K.J., 2002. Applications of hydrothermal time to quantifying and modeling seed germination and dormancy. Weed Science 50, 248–260.

Examples

data(hordeum)
modHTTLL.M <- drmte(nSeeds ~ timeBef + timeAf + water + temp,
                 data=hordeum,
                 fct = HTTLL.M(),
  start=c(832,-2.5, -3, 0.07, 3, 0.5))
summary(modHTTLL.M)

modHTTLL.BS <- drmte(nSeeds ~ timeBef + timeAf + water + temp,
                 data=hordeum,
                 fct = HTTLL.BS(),
  start=c(932,-2.5, 15, -3, 0.07, 3, 0.5))
summary(modHTTLL.BS)

OnofriAndreaPG/drcSeedGerm documentation built on March 14, 2023, 5:45 p.m.