embryogrowth (version 7.1)

tsd: Estimate the parameters that best describe temperature-dependent sex determination

Description

Estimate the parameters that best describe the thermal reaction norm for sex ratio when temperature-dependent sex determination occurs. It can be used also to evaluate the relationship between incubation duration and sex ratio. The parameter l was defined in Girondot (1999). The TRT is defined from the difference between the two boundary temperatures giving sex ratios of \(l\) and \(1 - l\), respectively: $$TRT_{l}=abs\left ( S\: K_{l} \right )$$ where \(K_{l}\) is a constant equal to \(2\: log\left ( \frac{l}{1-l} \right )\). In Girondot (1999), l was 0.05 and then the TRT was defined as being the range of temperatures producing from 5% to 95% of each sex. Models Richards, Double-Richards and Hulin are particularly sensitive for K parameters. If you want estimate confidence interval for TRT using these models, it is better to use mcmc.

Usage

tsd(df = NULL, males = NULL, females = NULL, N = NULL,
  temperatures = NULL, durations = NULL, l = 0.05,
  parameters.initial = c(P = NA, S = -2, K = 0, K1 = 1, K2 = 0),
  males.freq = TRUE, fixed.parameters = NULL, equation = "logistic",
  replicate.CI = 10000, range.CI = 0.95, print = TRUE)

Arguments

df

A dataframe with at least two columns named males, females or N and temperatures, Incubation.temperature or durations column

males

A vector with male numbers

females

A vector with female numbers

N

A vector with total numbers

temperatures

The constant incubation temperatures used to fit sex ratio

durations

The duration of incubation or TSP used to fit sex ratio

l

Sex ratio limits to define TRT are l and 1-l (see Girondot, 1999)

parameters.initial

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

males.freq

If TRUE data are shown as males frequency

fixed.parameters

Parameters that will not be changed

equation

Could be "logistic", "Hill", "Richards", "Hulin", "Double-Richards" or "GSD"

replicate.CI

Number of replicates to estimate confidence intervals

range.CI

The range of confidence interval for estimation, default=0.95

print

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

Value

A list the pivotal temperature, transitional range of temperatures and their SE

Details

tsd estimates the parameters that best describe temperature-dependent sex determination

References

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.

See Also

Other Functions for temperature-dependent sex determination: DatabaseTSD, P_TRT, TSP.list, predict.tsd, stages, tsd_MHmcmc_p, tsd_MHmcmc

Examples

# NOT RUN {
library(embryogrowth)
CC_AtlanticSW <- subset(DatabaseTSD, RMU=="Atlantic, SW" & 
                          Species=="Caretta caretta" & (!is.na(Sexed) & Sexed!=0))
tsdL <- with (CC_AtlanticSW, tsd(males=Males, females=Females, 
                                 temperatures=Incubation.temperature-Correction.factor, 
                                 equation="logistic", replicate.CI=NULL))
tsdH <- with (CC_AtlanticSW, tsd(males=Males, females=Females, 
                                 temperatures=Incubation.temperature-Correction.factor, 
                                 equation="Hill", replicate.CI=NULL))
tsdR <- with (CC_AtlanticSW, tsd(males=Males, females=Females, 
                                 temperatures=Incubation.temperature-Correction.factor, 
                                 equation="Richards", replicate.CI=NULL))
tsdDR <- with (CC_AtlanticSW, tsd(males=Males, females=Females, 
                                 temperatures=Incubation.temperature-Correction.factor, 
                                 equation="Double-Richards", replicate.CI=NULL))
gsd <- with (CC_AtlanticSW, tsd(males=Males, females=Females, 
                                 temperatures=Incubation.temperature-Correction.factor, 
                                 equation="GSD", replicate.CI=NULL))
compare_AIC(Logistic_Model=tsdL, Hill_model=tsdH, Richards_model=tsdR, 
               DoubleRichards_model=tsdDR, GSD_model=gsd)
compare_AICc(Logistic_Model=tsdL, Hill_model=tsdH, Richards_model=tsdR, 
               DoubleRichards_model=tsdDR, GSD_model=gsd, factor.value = -1)
compare_BIC(Logistic_Model=tsdL, Hill_model=tsdH, Richards_model=tsdR, 
               DoubleRichards_model=tsdDR, GSD_model=gsd, factor.value = -1)
##############
eo <- subset(DatabaseTSD, Species=="Emys orbicularis", c("Males", "Females", 
                                       "Incubation.temperature"))
                                       
eo_Hill <- with(eo, tsd(males=Males, females=Females, 
                                       temperatures=Incubation.temperature,
                                       equation="Hill"))
eo_Hill <- tsd(df=eo, equation="Hill", replicate.CI=NULL)
eo_logistic <- tsd(eo, replicate.CI=NULL)
eo_Richards <- with(eo, tsd(males=Males, females=Females, 
                                 temperatures=Incubation.temperature, 
                                 equation="Richards", replicate.CI=NULL))
### The Hulin model is a modification of Richards (See Hulin et al. 2009)
par <- eo_Richards$par
names(par)[which(names(par)=="K")] <- "K2"
par <- c(par, K1=0)
eo_Hulin <- with(eo, tsd(males=Males, females=Females, 
                                 parameters.initial=par, 
                                 temperatures=Incubation.temperature, 
                                 equation="Hulin", replicate.CI=NULL))
### The Double-Richards model is a Richards model with K1 and K2 using the two values
### below and above P
par <- eo_Richards$par
names(par)[which(names(par)=="K")] <- "K2"
par <- c(par, K1=as.numeric(par["K2"])-0.1)
par["K1"] <- par["K1"]-0.1
eo_Double_Richards <- with(eo, tsd(males=Males, females=Females,
                                 parameters.initial=par,
                                 temperatures=Incubation.temperature,
                                 equation="Double-Richards", replicate.CI=NULL))
compare_AIC(Logistic=eo_logistic, Hill=eo_Hill, Richards=eo_Richards, 
             Hulin=eo_Hulin, Double_Richards=eo_Double_Richards)
### Note the asymmetry of the Double-Richards model
predict(eo_Double_Richards, 
       temperatures=c(eo_Double_Richards$par["P"]-0.2, eo_Double_Richards$par["P"]+0.2))
predict(eo_Double_Richards)
### It can be used also for incubation duration
CC_AtlanticSW <- subset(DatabaseTSD, RMU=="Atlantic, SW" & 
                          Species=="Caretta caretta" & Sexed!=0)
tsdL_IP <- with (CC_AtlanticSW, tsd(males=Males, females=Females, 
                                 durations=IP.mean, 
                                 equation="logistic", replicate.CI=NULL))
plot(tsdL_IP, xlab="Incubation durations in days")
# }