drcSeedGerm (version 1.0.1)

HTTLL: 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:

$$ P(t, T, \Psi) = \frac{1}{1 + \exp \left\{ - \frac{ \log \left[ \Psi - \left( \frac{\theta_{HT}}{t ( T - T_b )} \right) + \delta \right] - \log \left[ \Psi_b + K_t (T - T_b) + \delta \right] }{\sigma_{\Psi_b}} \right\} } $$

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)

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.

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

Author

Andrea Onofri

Details

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

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)
# \donttest{
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)
# }