logistic.solution.Rd
Function describing exponential decline from a defined starting value, with an increasing rate constant, supposedly caused by microbial growth
logistic.solution(t, parent.0, kmax, k0, r)
t | Time. |
---|---|
parent.0 | Starting value for the response variable at time zero. |
kmax | Maximum rate constant. |
k0 | Minumum rate constant effective at time zero. |
r | Growth rate of the increase in the rate constant. |
The solution of the logistic model reduces to the
SFO.solution
if k0
is equal to
kmax
.
The value of the response variable at time t
.
FOCUS (2014) “Generic guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in EU Registration” Report of the FOCUS Work Group on Degradation Kinetics, Version 1.1, 18 December 2014 http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics
# Reproduce the plot on page 57 of FOCUS (2014) plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.2), from = 0, to = 100, ylim = c(0, 100), xlab = "Time", ylab = "Residue")plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.4), from = 0, to = 100, add = TRUE, lty = 2, col = 2)plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.8), from = 0, to = 100, add = TRUE, lty = 3, col = 3)plot(function(x) logistic.solution(x, 100, 0.08, 0.001, 0.2), from = 0, to = 100, add = TRUE, lty = 4, col = 4)plot(function(x) logistic.solution(x, 100, 0.08, 0.08, 0.2), from = 0, to = 100, add = TRUE, lty = 5, col = 5)legend("topright", inset = 0.05, legend = paste0("k0 = ", c(0.0001, 0.0001, 0.0001, 0.001, 0.08), ", r = ", c(0.2, 0.4, 0.8, 0.2, 0.2)), lty = 1:5, col = 1:5)# Fit with synthetic data logistic <- mkinmod(parent = mkinsub("logistic")) sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120) parms_logistic <- c(kmax = 0.08, k0 = 0.0001, r = 0.2) d_logistic <- mkinpredict(logistic, parms_logistic, c(parent = 100), sampling_times) d_2_1 <- add_err(d_logistic, sdfunc = function(x) sigma_twocomp(x, 0.5, 0.07), n = 1, reps = 2, digits = 5, LOD = 0.1, seed = 123456)[[1]] m <- mkinfit("logistic", d_2_1, quiet = TRUE) plot_sep(m)#> Estimate se_notrans t value Pr(>t) Lower #> parent_0 1.057896e+02 2.3743105248 44.5559374 6.656664e-16 1.006602e+02 #> kmax 6.398190e-02 0.0193490291 3.3067243 2.836921e-03 3.329058e-02 #> k0 1.612775e-04 0.0009640761 0.1672871 4.348592e-01 3.972250e-10 #> r 2.263946e-01 0.2822811886 0.8020181 2.184792e-01 1.531165e-02 #> Upper #> parent_0 110.9190170 #> kmax 0.1229682 #> k0 65.4803698 #> r 3.3474197