logistic.solution {mkin} | R Documentation |
Logistic kinetics
Description
Function describing exponential decline from a defined starting value, with an increasing rate constant, supposedly caused by microbial growth
Usage
logistic.solution(t, parent_0, kmax, k0, r)
Arguments
t |
Time. |
parent_0 |
Starting value for the response variable at time zero. |
kmax |
Maximum rate constant. |
k0 |
Minimum rate constant effective at time zero. |
r |
Growth rate of the increase in the rate constant. |
Value
The value of the response variable at time t
.
Note
The solution of the logistic model reduces to the
SFO.solution
if k0
is equal to kmax
.
References
FOCUS (2006) “Guidance Document on Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in EU Registration” Report of the FOCUS Work Group on Degradation Kinetics, EC Document Reference Sanco/10058/2005 version 2.0, 434 pp, http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics 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
See Also
Other parent solutions:
DFOP.solution()
,
FOMC.solution()
,
HS.solution()
,
IORE.solution()
,
SFO.solution()
,
SFORB.solution()
Examples
# 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)
summary(m)$bpar
endpoints(m)$distimes