Estimate Size at Sexual Maturity.

Description

Estimate morphometric and gonadal size at sexual maturity for organisms, usually fish and invertebrates. It includes methods for classification based on relative growth (principal components analysis, hierarchical clustering, discriminant analysis), logistic regression (frequentist or Bayes), parameters estimation and some basic plots. The size at sexual maturity is defined as the length at which a randomly chosen specimen has a 50% chance of being mature.

Details

Package: sizeMat

Type: Package

The Size at Morphometric and Gonad maturity are estimating using different functions (process). 1) The estimation of the Size at Morphometric Maturity involves two processes:

1.1) A Principal Components Analysis is conducted with two allometric variables (x: independent variable, y: dependent variable) in log base, allowing to distinguish two groups that would represent juveniles and adult. The individuals are assigned to each group using a hierarchical classification procedure (hierarchical cluster). This method is based on establishing a predetermined number of groups (in this case, two) and assigning individuals to one of the groups according to their loads on the two axes of the PCA (Corgos and Freire, 2006). Using the results of the classification (PCA + cluster), a discriminant analysis (linear or quadratic) is carried out to obtain a discriminating function that permitted any individuals to be classified as a juvenile or an adult on the basis of the X and Y allometric variables.

1.2) After classification, the logistic approach is used. The size at 50% maturity (L_{50}) is estimated as the length at which a randomly chosen specimen has a 50% chance of being mature (Somerton 1980, Roa et al. 1999, Corgos & Freire 2006). In the regression analysis, X (i.e. carapace width) is considered the explanatory variable and the classification CL (juveniles: 0, adults: 1) is considered the response variable (binomial).

The variables are fitted to a logistic function with the form:

P_{CL} = \frac{1}{(1 + e^{-(beta_{0} + beta_{1}*X)})}

where:

P_{CL} is the probability of an individual of being mature at a determinate X length.

beta_{0} (intercept) and beta_{1} (slope) are parameters estimated.

The L_{50} is calculated as:

L_{50} = \frac{-beta_{0}}{beta_{1}}

Some basic plotting (classification, beta_{0}, beta_{1} and L_{50} histogram, and maturity ogive) are also provided.

2) The estimation of Size at Gonad Maturity use the logistic approach.

To estimate size at gonadal maturity, the database must contains the stage of sexual maturity and at least one allometric variable (i.e. total length, fork length, carapace width). The stage of sexual maturity is referred to the gonadal maturation stages (i.e. I, II, III, IV or 0, 1, etc).

So, in the regression analysis, the allometric variable (i.e. total length) is considered the explanatory variable and the stage of sexual maturity (immature: 0, mature: 1) is considered the response variable (binomial). The regression analysis is performed in the same way as the size at morphometric maturity.

Author(s)

Josymar Torrejon-Magallanes <ejosymart@gmail.com>

References

Agostinho, C. S. (2000). Use of otoliths to estimate size at sexual maturity in fish. Brazilian Archives of Biology and Technology, 43(4):437-440, doi:10.1590/s1516-89132000000400014.

Corgos, A. and Freire, J. (2006). Morphometric and gonad maturity in the spider crab Maja brachydactyla: a comparison of methods for estimating size at maturity in species with determinate growth. ICES Journal of Marine Science, 63(5): 851-859, doi:10.1016/j.icesjms.2006.03.003.

Roa, R., Ernst, B. and Tapia, F. (1999). Estimation of size at sexual maturity: an evaluation of analytical and resampling procedures. Fishery Bulletin, 97(3): 570-580.

Somerton, D. A. (1980). A computer technique for estimating the size of sexual maturity in crabs. Canadian Journal of Fisheries and Aquatic Sciences, 37(10): 1488-1494. doi:10.1139/f80-192.

Examples

#See examples for functions morph_mature() and gonad_mature().

Crab data

Description

A database containing allometric measures and other attributes of 223 crabs of the specie Chionectes tanneri. The variables carapace width and chela height were published in Somerton & Donaldson (1996).

Usage

data(crabdata)

Format

A data frame with different variables:

year

month

carapace_width (mm.)

carapace_length (mm.)

chela_height (mm.)

chela_width (mm.)

sex_category (m: male, f: female).

Source

Somerton, D. A., & Donaldson, W. (1996). Contribution of the biology of the grooved and triangle Tanner crabs, Chionectes tanneri and C. angulatus, in the eastern Bering Sea. Fishery Bulletin, 94(2), 348-357.

References

Watters, G., & Hobday, A. J. (1998). A new method for estimating the morphometric size at maturity of crabs. Canadian Journal of Fisheries and Aquatic Sciences, 55(3), 704-714.

Fish gonadal maturity data

Description

A data set containing the total length and the stages of sexual maturity of 1733 fishes.

Usage

data(matFish)

Format

A data frame with two variables:

total_length the total length in cm.

stage_mat the stages of sexual maturity (gonadal maturation stages, I: immature, II-III-IV: mature)

Classify mature

Description

Classify the individuals in two groups (0: juveniles, 1: adults) based on relative growth.

Usage

classify_mature(
  data,
  varNames = c("x", "y"),
  varSex = "sex",
  selectSex = NULL,
  method = "ld"
)

Arguments

Details

Classify the individuals in two groups (juveniles = 0 and adult = 1).

A Principal Components Analysis was conducted with two allometric variables (x: independent variable, y: dependent variable) in log base, allowing to distinguish two groups that would represent juveniles and adult. The individuals are assigned to each group using a hierarchical classification procedure (hierarchical cluster with agglomeration method: "Ward.D" and the distance measure: "euclidean"). This method is based on establishing a predetermined number of groups (in this case, two) and assigning individuals to one of the groups according to their loads on the two axes of the PCA (Corgos and Freire, 2006).

Using the results of the classification (PCA + cluster), a discriminant analysis (linear or quadratic) is conducted to obtain a discriminating function that permitted any individuals to be classified as a juvenile or an adult on the basis of the X and Y allometric variables.

Value

A data.frame of class 'classify', with x (independent), y (dependent) and classification of maturity (juveniles = 0, adult = 1) variables.

Examples

data(crabdata)

classify_data = classify_mature(crabdata, varNames = c("carapace_width", "chela_height"),
varSex = "sex_category", selectSex = NULL, method = "ld")

classify_data

Estimate gonadal maturity

Description

Estimate size at gonad maturity.

Usage

gonad_mature(
  data,
  varNames = c("allometric", "stage"),
  inmName = "inm",
  matName = "mad",
  method = "fq",
  niter = 999,
  seed = 70388
)

Arguments

Details

Estimate the size at gonad maturity using a logistic regression with X variable and stages of sexual maturity (two categories: immature and mature).

The function requires a data.frame with the X (allometric variable) and the stage of sexual maturity (gonad maturation stage).

The argument varNames requires a character string indicating the name of one allometric and the stage of sexual maturity variable to be used for analysis (i.e. varNames = c("total_length", "stage_mat")). So the argument varNames must contain two character strings only, the first is the allometric variable and the second is the stage of sexual maturity.

The arguments inmName and matName require a character string indicating the name of the stages of sexual maturity in the data.frame. The argument could contain one character string or should be a vector (i.e. inmName = "I", matName = c("II", "III", "IV")).

The argument method requires a character string indicating which regression will be used for the test. If method = "fq" the logistic regression is based on GLM (frequentist), if method = "bayes" a sample from the posterior distribution of a logistic regression model using a random walk Metropolis algorithm is generated (see MCMClogit function).

The argument niter requires a number. For the GLM regression (method = "fq"), a non-parametric bootstrap method consists in generate B bootstrap samples, by resampling with replacement the original data. Then all statistics for each parameter can be calculated from each bootstrap sample (median and confidence intervals). For the method = "bayes", the argument niter is related to the number of Metropolis iterations for the sampler.

Value

An object of class 'gonadMat'.

model the summary statistics of the model.

A_boot the 'n iter' values of parameter A.

B_boot the 'n iter' values of parameter B.

L50 the 'n iter' values of parameter L50 (size at gonad maturity).

out a dataframe with the allometric variable "X", stage of sexual maturity, the fitted values for logistic regression and confidence intervals (95%). Also the summary statistics of the model is provided.

Examples

data(matFish)

gonad_mat = gonad_mature(matFish, varNames = c("total_length", "stage_mat"), inmName = "I", 
matName = c("II", "III", "IV"), method = "fq", niter = 50)

# 'niter' parameters:
gonad_mat$A_boot
gonad_mat$B_boot
gonad_mat$L50_boot
gonad_mat$out

Estimate morphometric mature

Description

Estimate size at morphometric maturity.

Usage

morph_mature(data, method = "fq", niter = 999, seed = 70388)

Arguments

Details

Estimate the size at morphometric maturity using a logistic regression with X variable and maturity classification (two categories: juveniles and adults).

The function requires an object of class "classify" with the X, Y (allometric variables) and classification of maturity (juveniles = 0, adults = 1).

The argument method requires a character string indicating which regression will be used for the test. If method = "fq" the logistic regression is based on GLM (frequentist) and if method = "bayes" a sample from the posterior distribution of a logistic regression model using a random walk Metropolis algorithm is generated (see MCMClogit function).

The argument niter requires a number. For the GLM regression (method = "fq"), a non-parametric bootstrap method consists in generate B bootstrap samples, by resampling with replacement the original data. Then all statistics for each parameter can be calculated from each bootstrap sample (median and confidence intervals). For the method = "bayes", the argument 'niter' is related to the number of Metropolis iterations for the sampler.

Value

An object of class 'morphMat'.

model the summary statistics of the model.

A_boot the 'n iter' values of parameter A.

B_boot the 'n iter' values of parameter B.

L50 the 'n iter' values of parameter L50 (size at morphometric maturity).

out a dataframe with the allometric variables "X" and "Y", classification of maturity, the fitted values for logistic regression and confidence intervals (95%). Also the summary statistics of the model is provided.

Examples

data(crabdata)

classify_data = classify_mature(crabdata, varNames = c("carapace_width", "chela_height"),
varSex = "sex_category", selectSex = NULL, method = "ld")

my_mature = morph_mature(classify_data, method = "fq", niter = 50)

# 'niter' parameters:
my_mature$A_boot
my_mature$B_boot
my_mature$L50_boot
my_mature$out

Nagelkerme method R-square

Description

Estimate Nagelkerke's R squared from the result of glm(). Evaluate the goodness of fit for logistic regression.

Usage

nagelkerkeR2(x)

Arguments

Value

Rsquare Nagelkerke's R squared.

Examples

set.seed(7388)
n <- 300
x <- rnorm(n)
a <- 1
b <- -2
p <- 1/(1+exp(a+b*x))
y <- factor(ifelse(runif(n) < p, 1, 0), levels = 0:1)
mod1 <- glm(y ~ x, family=binomial)
nagelkerkeR2(mod1)

Plot method for classify class

Description

Plot method for classify class

Usage

## S3 method for class 'classify'
plot(
  x,
  xlab = "X",
  ylab = "Y",
  col = c(1, 2),
  pch = c(4, 5),
  cex = c(1, 1),
  lty_lines = c(1, 1),
  lwd_lines = c(1, 1),
  legendPlot = TRUE,
  cex_label = 0.8,
  ...
)

Arguments

Examples

data(crabdata)

classify_data = classify_mature(crabdata, varNames = c("carapace_width", "chela_height"),
varSex = "sex_category", selectSex = NULL, method = "ld")

## Showing different plots
plot(classify_data, xlab = "X")

plot(classify_data, xlab = "X", ylab = "Y", col = c(1, 2), pch = c(4, 5), cex = c(1, 3))

plot(classify_data, xlab = "Carapace width (mm.)", ylab = "Y", col = c(1, 2),
pch = c(4, 5), cex = c(1, 3), lwd_lines = c(1, 3))

plot(classify_data, xlab = "Carapace width (mm.)", ylab = "Y", col = c(1, 2),
pch = c(4, 5), cex = c(1, 3), lwd_lines = c(1, 3), main = "Classification")

Plot method for gonadMat class (size at gonad maturity)

Description

Plot method for gonadMat class (size at gonad maturity)

Usage

## S3 method for class 'gonadMat'
plot(
  x,
  xlab = "X",
  ylab = "Proportion mature",
  col = c("blue", "red"),
  lwd = 2,
  lty = 2,
  vline_hist = "black",
  lwd_hist = 2,
  lty_hist = 2,
  onlyOgive = FALSE,
  ...
)

Arguments

Examples

data(matFish)

gonad_mat = gonad_mature(matFish, varNames = c("total_length", "stage_mat"), inmName = "I", 
matName = c("II", "III", "IV"), method = "fq", niter = 50)

plot(gonad_mat, xlab = "Total length (cm.)", ylab = "Proportion mature", col = c("blue", "red"))

Plot method for morphMat class (size at morphometric maturity)

Description

Plot method for morphMat class (size at morphometric maturity)

Usage

## S3 method for class 'morphMat'
plot(
  x,
  xlab = "X",
  ylab = "Proportion mature",
  col = c("blue", "red"),
  lwd = 2,
  lty = 2,
  vline_hist = "black",
  lwd_hist = 2,
  lty_hist = 2,
  onlyOgive = FALSE,
  ...
)

Arguments

Examples

data(crabdata)

classify_data = classify_mature(crabdata, varNames = c("carapace_width", "chela_height"),
varSex = "sex_category", selectSex = NULL, method = "ld")

my_mature = morph_mature(classify_data, method = "fq", niter = 50)

plot(my_mature, xlab = "Carapace width (mm.)", ylab = "Proportion mature", col = c("blue", "red"))

Print method for classify class

Description

Print method for classify class

Usage

## S3 method for class 'classify'
print(x, ...)

Arguments

Value

The number of juveniles and adults. Also shows the regression analysis for juveniles and adults and an ANCOVA analysis to compare slopes.

Examples

data(crabdata)

classify_data = classify_mature(crabdata, varNames = c("carapace_width", "chela_height"),
varSex = "sex_category", selectSex = NULL, method = "ld")

print(classify_data)

Print method for gonadMat class (size at gonad maturity)

Description

Print method for gonadMat class (size at gonad maturity)

Usage

## S3 method for class 'gonadMat'
print(x, ...)

Arguments

Value

The median of the size at gonad maturity estimation, parameters and the Nagelkerke's R squared.

Examples

data(matFish)

gonad_mat = gonad_mature(matFish, varNames = c("total_length", "stage_mat"), inmName = "I", 
matName = c("II", "III", "IV"), method = "fq", niter = 50)

print(gonad_mat)

Print method for morphMat class (size at morphometric maturity)

Description

Print method for morphMat class (size at morphometric maturity)

Usage

## S3 method for class 'morphMat'
print(x, ...)

Arguments

Value

The median of the size at morphometric maturity estimation, parameters and the Nagelkerke's R square.

Examples

data(crabdata)

classify_data = classify_mature(crabdata, varNames = c("carapace_width", "chela_height"),
varSex = "sex_category", selectSex = NULL, method = "ld")

my_mature = morph_mature(classify_data, method = "fq", niter = 50)

print(my_mature)