TTE_models: Thermal-time models with log-logistic distribution of...

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

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

Description

These models relates the time-course of germinations to the environmental temperature and they are based on a truncated log-logistic distribution of germination time:

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

where the usual parameters ('b', 'd' and 'e') are expressed as functions of wtemperature (T). In the function 'TTEM()', we implemented the following submodels: (1) for the parameter 'd', we implemented the following submodels:

d = G \, ≤ft[ 1 - \exp ≤ft( - \frac{ T_c - T }{σ_{T_c}} \right) \right]

1/[e(T)] = GR_{50}(T) = \frac{T - T_b }{θ_T} ≤ft[1 - \frac{T - T_b}{T_c - T_b}\right]

while 'b' was regarded as constant and independent from temperature.

In the 'TTERF()' function, the last submodel was modified, according to Rowse and Finch-Savage (2003):

1/[e(T)] = GR_{50}(T) = ≤ft\{ {\begin{array}{ll} \frac{T - T_b}{θ_T} & \textrm{if} \,\,\, T_b < T < T_d \\ \frac{T - T_b}{θ_T} ≤ft[ 1 - \frac{T - T_d}{T_c - T_d} \right] & \textrm{if} \,\,\, T_d < T < T_c \\ 0 & \textrm{if} \,\,\, T ≤q T_b \,\,\, or \,\,\, T ≥q T_c \end{array}} \right.

In the In the 'TTERFc()' function a further submodel was introduced, to model the effect of temperature in the shape parameter 'b':

σ(T) = \frac{1}{b} = \frac{1}{b_0} + s (T - T_b)

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

Usage

TTEM()
TTEM.fun(time, Temp, G, Tc, sigmaTc, Tb, ThetaT, b)
TTERF()
TTERF.fun(time, Temp, G, Tc, sigmaTc, Td, Tb, ThetaT, b)
TTERFc()
TTERFc.fun(time, Temp, G, Tc, sigmaTc, Td, Tb, ThetaT, b0, s)

Arguments

The TTEM(), TTERF() and TTERFc() functions have no arguments. The TTEM.fun(), TTERF.fun() and TTERFc.fun() functions have the following arguments:

time	time
Temp	temperature
G	maximum germination capability of the seed lot
Tc	ceiling temperature
sigmaTc	standard deviation for the ceiling temperature within the seed lot
Tb	base temperature
Td	close to optimal temperature
ThetaT	Thermal-time parameter
b	shape parameter for the cumulative distribution function of germination time
b0	shape parameter for the cumulative distribution function of germination time at T = Tb
s	parameter for the effect of temperature on the scale parameter for the log-logistic distribution of germination times

Details

The detail of these functions are described in Onofri et al. (2018).

Value

The 'TTEM.fun()', 'TTERF.fun()' and 'TTERFc.fun()' functions return the proportion of germinated seeds, for given values of time and temperature. The 'TTEM()', 'TTERF()' and 'TTERFc()' 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.

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. Rowse, H.R., Finch-Savage, W.E., 2003. Hydrothermal threshold models can describe the germination response of carrot (Daucus carota) and onion (Allium cepa) seed populations across both sub- and supra-optimal temperatures. New Phytologist 158, 101–108. https://www.statforbiology.com/2020/stat_drcte_11_ExampleTTE

Examples

data(barley)
modTTE <- drmte(nSeeds ~ timeBef + timeAf + Temp, data = barley,
               fct = TTERF())
summary(modTTE)

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