# fitCF: Fit a model of Clutch Frequency for marine turtles. In phenology: Tools to Manage a Parametric Function that Describes Phenology and More

 fitCF R Documentation

## Fit a model of Clutch Frequency for marine turtles.

### Description

This function fits a model of clutch frequency.
This model is an enhanced version of the one published by Briane et al. (2007).
Parameters are `mu` and `sd` being the parameters of a distribution used to model the clutch frequency.
This distribution is used only as a guide but has not statistical meaning.
The parameter `p` is the -logit probability that a female is seen on the beach for a particular nesting event. It includes both the probability that it is captured but also the probability that it uses that specific beach.
Several categories of females can be included in the model using index after the name of the parameter, for example `mu1`, `sd1` and `mu2`, `sd2` indicates that two categories of females with different clutch frequencies distribution are present. Similarly `p1` and `p2` indicates that two categories of females with different capture probabilities are present.
If more than one category is used, then it is necessary to include the parameter `OTN` to indicate the relative frequencies of each category. If two categories are used, one `OTN` parameter named `ONT1` must be included. The `OTN2` is forced to be 1. Then the relative frequency for category 1 is `OTN1/(OTN1+1)` and for category 2 is `1/(OTN1+1)`. Same logic must be applied for 3 and more categories with always the last one being fixed to 1.

if p or a (logit of the capture probability) are equal to -Inf, the probability of capture is 0 and if they are equal to +Inf, the probability is 1.

The value of p out of the period of nesting must be set to +Inf (capture probability=1) to indicate that no turtle is nesting in this period.

p must be set to -Inf (capture probability=0) to indicate that no monitoring has been done during a specific period of the nesting season.

The best way to indicate capture probability for 3D model (OCF, ECF, Period) is to indicate p.period common for all categories and a1, a2, etc for each category. The capture probability for category 1 will be p.period * a1, and for category 2 will be p.period * a2, etc.

In this case, the parameters p.period should be indicated in fitted parameters as well as a1, but a2 must be fixed to +Inf in fixed.parameters. Then the capture probability for category 2 will be p.period and for category 1 a1 * p.period.

If itnmax is equal to 0, it will return the model using the parameters without fitting them.

### Usage

``````fitCF(
x = c(mu = 4, sd = 100, p = 0),
fixed.parameters = NULL,
data = stop("Data formated with TableECFOCF() must be provided"),
control = list(trace = 1, REPORT = 100, maxit = 500),
itnmax = c(500, 100),
hessian = TRUE,
parallel = TRUE,
verbose = FALSE
)
``````

### Arguments

 `x` Initial parameters to be fitted `fixed.parameters` Parameters that are fixed. `data` CMR data formated using TableECFOCF() `method` Method to be used by optimx() `control` List of controls for optimx() `itnmax` A vector with maximum iterations for each method. `hessian` Logical to estimate SE of parameters `parallel` If TRUE, will use parallel computing for ECFOCF_f() `verbose` If TRUE, print the parameters at each step

### Details

fitCF fit a model of Clutch Frequency for marine turtles.

### Value

Return a list of class ECFOCF with the fit information.
The list has the following items:

• `data`: The observations to be fitted

• `par`: The fitted parameters

• `SE`: The standard error of parameters if hessian is TRUE

• `value`: The -log likelihood of observations within the fitted model

• `AIC`: The AIC of fitted model

• `mu`: The vector of fitted mu values

• `sd`: The vector of fitted sd values

• `prob`: The vector of fitted capture probabilities

• `a`: The vector of fitted capture probabilities multiplier

• `OTN`: The vector of fitted relative probabilities of contribution

• `period_categories`: A list with the different period probabilities as named vectors for each category

• `period`: The combined period probabilities using OTN as named vector

• `CF_categories`: A list with the different CF probabilities as named vectors for each category

• `CF`: The combined CF probabilities using OTN as named vector

• `ECFOCF_categories`: A list with the different probability ECFOCF tables for each category

• `ECFOCF`: The combined table of ECFOCF using OTN probabilities tables

• `ECFOCF_0`: The combined table of ECFOCF probabilities tables using OTN without the OCF=0

• `SE_df`: A data.frame with SE and 95% confidence intervals for meanx and vx (mean and variance of clutch frequency for x category), OTNx (proportion for x category), and probx (capture probability for x category)

### Author(s)

Marc Girondot marc.girondot@gmail.com

Briane J-P, Rivalan P, Girondot M (2007) The inverse problem applied to the Observed Clutch Frequency of Leatherbacks from Yalimapo beach, French Guiana. Chelonian Conservation and Biology 6:63-69

Fossette S, Kelle L, Girondot M, Goverse E, Hilterman ML, Verhage B, Thoisy B, de, Georges J-Y (2008) The world's largest leatherback rookeries: A review of conservation-oriented research in French Guiana/Suriname and Gabon. Journal of Experimental Marine Biology and Ecology 356:69-82

Other Model of Clutch Frequency: `ECFOCF_full()`, `ECFOCF_f()`, `TableECFOCF()`, `fitCF_MHmcmc_p()`, `fitCF_MHmcmc()`, `generateCF()`, `lnLCF()`, `logLik.ECFOCF()`, `plot.ECFOCF()`, `plot.TableECFOCF()`

### Examples

``````## Not run:
library(phenology)
# Example
data(MarineTurtles_2002)
ECFOCF_2002 <- TableECFOCF(MarineTurtles_2002)

# Parametric model for clutch frequency
o_mu1p1_CFp <- fitCF(x = c(mu = 2.1653229641404539,
sd = 1.1465246643327098,
p = 0.25785366120357966),
fixed.parameters=NULL,
data=ECFOCF_2002, hessian = TRUE)

# Non parametric model for clutch frequency
o_mu1p1_CFnp <- fitCF(x = c(mu.1 = 18.246619595610383,
mu.2 = 4.2702163522832892,
mu.3 = 2.6289986859556458,
mu.4 = 3.2496360919228611,
mu.5 = 2.1602522716550943,
mu.6 = 0.68617023351032846,
mu.7 = 4.2623607001877026,
mu.8 = 1.1805600042630455,
mu.9 = 2.2786176350939731,
mu.10 = 0.47676265496204945,
mu.11 = 5.8988238539197062e-08,
mu.12 = 1.4003187851424953e-07,
mu.13 = 2.4128444894899776e-07,
mu.14 = 2.4223748020049825e-07,
p = 0.32094401970037578),
fixed.parameters=c(mu.15 = 1E-10),
data=ECFOCF_2002, hessian = TRUE)

o_mu2p1 <- fitCF(x = c(mu1 = 1.2190766766978423,
sd1 = 0.80646454821956925,
mu2 = 7.1886819592223246,
sd2 = 0.18152887523015518,
p = 0.29347220802963259,
OTN = 2.9137627675219533),
fixed.parameters=NULL,
data=ECFOCF_2002, hessian = TRUE)

o_mu1p2 <- fitCF(x = c(mu = 5.3628701816871462,
sd = 0.39390555498088764,
p1 = 0.61159637544418755,
p2 = -2.4212753004659189,
OTN = 0.31898004668901009),
data=ECFOCF_2002, hessian = TRUE)

o_mu2p2 <- fitCF(x = c(mu1 = 0.043692606004492131,
sd1 = 1.9446036983033428,
mu2 = 7.3007868915644751,
sd2 = 0.16109296152913491,
p1 = 1.6860260469536992,
p2 = -0.096816113083788985,
OTN = 2.2604431232973501),
data=ECFOCF_2002, hessian = TRUE)

compare_AIC(mu1p1=o_mu1p1_CFp,
mu2p1=o_mu2p1,
mu1p2=o_mu1p2,
mu2p2=o_mu2p2)

o_mu3p3 <- fitCF(x = c(mu1 = 0.24286312214288761,
sd1 = 0.34542255091729313,
mu2 = 5.0817174343025551,
sd2 = 1.87435099405695,
mu3 = 5.2009265101740683,
sd3 = 1.79700447678357,
p1 = 8.8961708614726156,
p2 = 0.94790116453886453,
p3 = -0.76572930634505421,
OTN1 = 1.2936848663276974,
OTN2 = 0.81164278235645926),
data=ECFOCF_2002, hessian = TRUE)

o_mu3p1 <- fitCF(x = structure(c(0.24387978183477,
1.2639261745506,
4.94288464711349,
1.945082889758,
4.9431672350811,
1.287663104591,
0.323636536050397,
1.37072039291397,
9.28055412564559e-06),
.Names = c("mu1", "sd1", "mu2",
"sd2", "mu3", "sd3",
"p", "OTN1", "OTN2")),
data=ECFOCF_2002, hessian = TRUE)

o_mu1p3 <- fitCF(x = structure(c(4.65792402108387,
1.58445909785,
-2.35414198317177,
0.623757854800649,
-3.62623634029326,
11.6950204755787,
4.05273728846523),
.Names = c("mu", "sd",
"p1", "p2", "p3",
"OTN1", "OTN2")),
data=ECFOCF_2002, hessian = TRUE)

compare_AIC(mu1p1=o_mu1p1,
mu2p1=o_mu2p1,
mu1p2=o_mu1p2,
mu2p2=o_mu2p2,
mu3p3=o_mu3p3,
mu1p3=o_mu1p3,
mu3p1=o_mu3p1)

# 3D model for (ECF, OCF, period)

ECFOCF_2002 <- TableECFOCF(MarineTurtles_2002,
date0=as.Date("2002-01-01"))

fp <- rep(0, dim(ECFOCF_2002)[3])
names(fp) <- paste0("p.", formatC(1:(dim(ECFOCF_2002)[3]), width=2, flag="0"))
par <- c(mu = 2.6404831115214353,
sd = 0.69362774786433479,
mu_season = 12.6404831115214353,
sd_season = 1.69362774786433479)
par <- c(par, fp[attributes(ECFOCF_2002)\$table["begin"]:
attributes(ECFOCF_2002)\$table["final"]])

# The value of p (logit of the capture probability) out of the period
# of nesting must be set to +Inf (capture probability=1)
# to indicate that no turtle is nesting in this period

# p must be set to -Inf (capture probability=0) to indicate that no
# monitoring has been done during a specific period of the nesting season.

fixed.parameters <- c(p=+Inf)
# The fitted values are:
par <- c(mu = 2.4911638591178051,
sd = 0.96855483039640977,
mu_season = 13.836059118657793,
sd_season = 0.17440085345943984,
p.10 = 1.3348233607728222,
p.11 = 1.1960387774393837,
p.12 = 0.63025680979544774,
p.13 = 0.38648155002707452,
p.14 = 0.31547864054366048,
p.15 = 0.19720001827017075,
p.16 = 0.083199496372073328,
p.17 = 0.32969130595897905,
p.18 = 0.36582777525265819,
p.19 = 0.30301248314170637,
p.20 = 0.69993987591518514,
p.21 = 0.13642423871641118,
p.22 = -1.3949268190534629)

o_mu1p1season1 <- fitCF(x=par, data=ECFOCF_2002,
fixed.parameters=fixed.parameters)

# Same model but with two different models of capture probabilities

fp <- rep(0, dim(ECFOCF_2002)[3])
names(fp) <- paste0("p1.", formatC(1:(dim(ECFOCF_2002)[3]), width=2, flag="0"))
par <- c(mu = 2.6404831115214353,
sd = 0.69362774786433479,
mu_season = 12.6404831115214353,
sd_season = 1.69362774786433479)
par <- c(par, fp[attributes(ECFOCF_2002)\$table["begin"]:
attributes(ECFOCF_2002)\$table["final"]])
names(fp) <- paste0("p2.", formatC(1:(dim(ECFOCF_2002)[3]), width=2, flag="0"))
par <- c(par, fp[attributes(ECFOCF_2002)\$table["begin"]:
attributes(ECFOCF_2002)\$table["final"]])
fixed.parameters <- c(p1=+Inf, p2=+Inf)

o_mu1p2season1 <- fitCF(x=par, data=ECFOCF_2002,
fixed.parameters=fixed.parameters)

# Here the two different capture probabilities are different
# by a constant:
# p1=invlogit(-p)     [Note that invlogit(-a1) = 1]
# p2=invlogit(-p)*invlogit(-a2)

fp <- rep(0, dim(ECFOCF_2002)[3])
names(fp) <- paste0("p.", formatC(1:(dim(ECFOCF_2002)[3]), width=2, flag="0"))
par <- c(mu = 2.6404831115214353,
sd = 0.69362774786433479,
mu_season = 12.6404831115214353,
sd_season = 1.69362774786433479,
a2=0)
par <- c(par, fp[attributes(ECFOCF_2002)\$table["begin"]:
attributes(ECFOCF_2002)\$table["final"]])
fixed.parameters <- c(a1=+Inf, p=+Inf)

o_mu1p1aseason1 <- fitCF(x=par, data=ECFOCF_2002,
fixed.parameters=fixed.parameters)
data=ECFOCF_2002)

## End(Not run)
``````

phenology documentation built on Oct. 16, 2023, 9:06 a.m.