HTE2: Hydrotime model with log-logistic distribution of germination...

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

Hydrotime model with log-logistic distribution of germination time (Onofri et al., 2018)

Description

This model relates the time-course of the proportion of germinated seeds to the water potential in the substrate. It is based on a truncated log-logistic distribution of germination time:

P(t) = \frac{d}{1 + exp≤ft[ b (\log(x) - \log(e)\right]}

where two of the three usual parameters ('d' and 'e') are expressed as functions of water potential (Ψ). In this function, the two submodels are: (1) for the parameter 'd', we used a shifted exponential function:

d = G ≤ft[ 1 - \exp ≤ft( \frac{ Ψ - Ψ_b }{σ_{Ψ_b}} \right) \right]

while, (2) for the parameter 'e' we considered that its inverse corresponds to the median Germination Rate within the population (i.e. 1/e = GR_{50}) and modelled this latter parameter as:

GR_{50} = \frac{≤ft[Ψ - Ψ_b \right]^2}{θ_H}

The difference with the 'HTE1()' function is that, in this case, the relationship between GR50 and water potential is not linear, but curvilinear (convex down). The 'HTE2.fun()' is a generic function, which can be used for plotting or other applications, while the 'HTE2()' function is meant to be used for model fitting with the 'drmte()' function in the 'drcte()' package.

Usage

HTE2(fixed = c(NA, NA, NA, NA, NA),
                  names = c("G", "Psib", "sigmaPsib", "thetaH", "b"))
HTE2.fun(time, Psi, G, Psib, sigmaPsib, thetaH, b)

Arguments

These functions have the following arguments:

fixed	numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. At the moment, only the parameter G can be held fixed.
names	a vector of character strings giving the names of the parameters. The default is reasonable.
time	time
Psi	water potential in the substrate
G	maximum germination capability of the seed lot
Psib	base water potential
sigmaPsib	standard deviation for the base water potential within the seed lot
thetaH	hydro-time constant
b	shape parameter for the cumulative distribution function of germination time

Details

No more detail, at the moment.

Value

The 'HTE2.fun()' function returns the proportion of germinated seeds, for any given values of time and water potential in the substrate, depending on model parameters G, Psib, sigmaPsib, thetaH and b. The 'HTE2()' function returns a list containing the nonlinear function, the self starter function, the parameter names and other items which are internally used by the 'drmte()' function.

Author(s)

Andrea Onofri

References

Onofri, A., Benincasa, P., Mesgaran, M.B., Ritz, C., 2018. Hydrothermal-time-to-event models for seed germination. European Journal of Agronomy 101, 129–139. https://www.statforbiology.com/2020/stat_seedgermination_ht1step/

Examples

# Fitting model
data(rape)
modHTE2 <- drmte( nSeeds ~ timeBef + timeAf + Psi,
            data=rape, fct=HTE2())
summary(modHTE2)

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