# Estimate the parameters that best describe LD50 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+d**S)) 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 : [REMOVE_ME]$$ if dose < P then (1 + (2^K1 - 1) * exp(4 * S1 * (P - x)))^(-1/K1)if dose < P then (1 + (2^K1 - 1) * exp(4 * S1 * (P - x)))^(-1/K1) [REMOVE_ME_2]$$ [REMOVE_ME]$$ if dose > P then 1-((1 + (2^K2 - 1) * exp(4 * S2 * (x - P)))^(-1/K2)if dose > P then 1-((1 + (2^K2 - 1) * exp(4 * S2 * (x - P)))^(-1/K2) [REMOVE_ME_2]$$ with: [REMOVE_ME]$$ S1 = S/((4/K1)*(2^(-K1))^(1/K1+1)*(2^K1-1))S1 = S/((4/K1)*(2^(-K1))^(1/K1+1)*(2^K1-1)) [REMOVE_ME_2]$$ [REMOVE_ME]$$ S2 = S/((4/K2)*(2^(-K2))^(1/K2+1)*(2^K2-1))S2 = S/((4/K2)*(2^(-K2))^(1/K2+1)*(2^K2-1)) [REMOVE_ME_2]$$ ```r 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 ## Returns A list with the LD50, Transitional Range of Doses and their SE ## 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+d**S)) 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 : $$ if dose < P then (1 + (2^K1 - 1) * exp(4 * S1 * (P - x)))^(-1/K1)if dose < P then (1 + (2^K1 - 1) * exp(4 * S1 * (P - x)))^(-1/K1) $$ $$ if dose > P then 1-((1 + (2^K2 - 1) * exp(4 * S2 * (x - P)))^(-1/K2)if dose > P then 1-((1 + (2^K2 - 1) * exp(4 * S2 * (x - P)))^(-1/K2) $$ with: $$ S1 = S/((4/K1)*(2^(-K1))^(1/K1+1)*(2^K1-1))S1 = S/((4/K1)*(2^(-K1))^(1/K1+1)*(2^K1-1)) $$ $$ S2 = S/((4/K2)*(2^(-K2))^(1/K2+1)*(2^K2-1))S2 = S/((4/K2)*(2^(-K2))^(1/K2+1)*(2^K2-1)) $$ ## Details LD50 estimates the parameters that best describe LD50 ## Examples ```r ## 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) ``` ## See Also Other LD50 functions: `LD50_MHmcmc()`, `LD50_MHmcmc_p()`, `logLik.LD50()`, `plot.LD50()`, `predict.LD50()` ## Author(s) Marc Girondot marc.girondot@gmail.com