# sizeMat-package: Estimate Size at Sexual Maturity. In sizeMat: 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 differents functions (process). 1) The estimation of the Size at Morphometric Maturity involves two processes:

1.1) A Principal Components Analisys 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 & 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 CS (juveniles: 0, adults: 1) is considered the response variable (binomial).

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

P_{CS} = 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} = -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 refered to the gonadal maturarion 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 (inmature: 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 <[email protected]>

## 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. & 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. & 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

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

### Example output

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sizeMat documentation built on Aug. 1, 2019, 1:05 a.m.