LD50 {HelpersMG}

Estimate the parameters that best describe LD50

Description

Estimate the parameters that best describe LD50
Logistic and logit models are the same but with different parametrization:
logistic = 1/(1+exp((1/S)(P-d)))
logit = 1/(1+exp(P+dS))
See these publications for the description of equations:
Girondot, M. 1999. Statistical description of temperature-dependent sex determination using maximum likelihood. Evolutionary Ecology Research, 1, 479-486.
Godfrey, M.H., Delmas, V., Girondot, M., 2003. Assessment of patterns of temperature-dependent sex determination using maximum likelihood model selection. Ecoscience 10, 265-272.
Hulin, V., Delmas, V., Girondot, M., Godfrey, M.H., Guillon, J.-M., 2009. Temperature-dependent sex determination and global change: are some species at greater risk? Oecologia 160, 493-506.
The flexit equation is not still published :

if dose < P then (1 + (2^K1 - 1) * exp(4 * S1 * (P - x)))^(-1/K1)

if dose > P then 1-((1 + (2^K2 - 1) * exp(4 * S2 * (x - P)))^(-1/K2)

with:

S1 = S/((4/K1)*(2^(-K1))^(1/K1+1)*(2^K1-1))

S2 = S/((4/K2)*(2^(-K2))^(1/K2+1)*(2^K2-1))

Usage

LD50(
  df = NULL,
  alive = NULL,
  dead = NULL,
  N = NULL,
  doses = NULL,
  l = 0.05,
  parameters.initial = NULL,
  fixed.parameters = NULL,
  SE = NULL,
  equation = "logistic",
  replicates = 1000,
  range.CI = 0.95,
  limit.low.TRD.minimum = 5,
  limit.high.TRD.maximum = 1000,
  print = TRUE,
  doses.plot = seq(from = 0, to = 1000, by = 0.1)
)

Arguments

df

A dataframe with at least two columns named alive, dead or N and doses columns

alive

A vector with alive individuals at the end of experiment

dead

A vector with dead individuals at the end of experiment

N

A vector with total numbers of tested individuals

doses

The doses

l

The limit to define TRD (see Girondot, 1999)

parameters.initial

Initial values for P, S or K search as a vector, ex. c(P=29, S=-0.3)

fixed.parameters

Parameters that will not be changed during fit

SE

Standard errors for parameters

equation

Could be "logistic", "logit", "probit", Hill", "Richards", "Hulin", "flexit" or "Double-Richards"

replicates

Number of replicates to estimate confidence intervals

range.CI

The range of confidence interval for estimation, default=0.95

limit.low.TRD.minimum

Minimum lower limit for TRD

limit.high.TRD.maximum

Maximum higher limit for TRD

print

Do the results must be printed at screen? TRUE (default) or FALSE

doses.plot

Sequences of doses that will be used for plotting. If NULL, does not estimate them

Details

LD50 estimates the parameters that best describe LD50

Value

A list with the LD50, Transitional Range of Doses and their SE

Author(s)

Marc Girondot [e-mail]

See Also

Other LD50 functions: LD50_MHmcmc(), LD50_MHmcmc_p(), logLik.LD50(), plot.LD50(), predict.LD50()

Examples

## Not run: 
library("HelpersMG")
data <- data.frame(Doses=c(80, 120, 150, 150, 180, 200),
Alive=c(10, 12, 8, 6, 2, 1),
Dead=c(0, 1, 5, 6, 9, 15))
LD50_logistic <- LD50(data, equation="logistic")
predict(LD50_logistic, doses=c(140, 170))
plot(LD50_logistic, xlim=c(0, 300), at=seq(from=0, to=300, by=50))
LD50_probit <- LD50(data, equation="probit")
predict(LD50_probit, doses=c(140, 170))
plot(LD50_probit)
LD50_logit <- LD50(data, equation="logit")
predict(LD50_logit, doses=c(140, 170))
plot(LD50_logit)
LD50_hill <- LD50(data, equation="hill")
predict(LD50_hill, doses=c(140, 170))
plot(LD50_hill)
LD50_Richards <- LD50(data, equation="Richards")
predict(LD50_Richards, doses=c(140, 170))
plot(LD50_Richards)
LD50_Hulin <- LD50(data, equation="Hulin")
predict(LD50_Hulin, doses=c(140, 170))
plot(LD50_Hulin)
LD50_DoubleRichards <- LD50(data, equation="Double-Richards")
predict(LD50_DoubleRichards, doses=c(140, 170))
plot(LD50_DoubleRichards)
LD50_flexit <- LD50(data, equation="flexit")
predict(LD50_flexit, doses=c(140, 170))
plot(LD50_flexit)

## End(Not run)