Analysis of edge type for validation in studies of age of sharks: applying circular models

Abstract

Validation analysis is important in aging studies of fishes. In the last decades, researches in this field were often based on marginal increments of vertebrae, and the results have been interpreted based on visual inspection of graphs. Subjective interpretations can result in misleading conclusions. Recently, statistical models with Bernoulli probability distribution and with mixture of circular distributions were proposed as an objective solution in validation studies based on the analysis of the edge type. In this work, several of those models were used to analyze data of mako (Isurus oxyrinchus) and crocodile (Pseudocarcharias kamoharai). In some circumstances, results are not conclusive. Parameter estimations are imprecise when the sample size is small. However, there is not guarantee that large samples will result in successful estimation of parameters and validation analysis. Adequate models as well as accurate data are necessary in order to obtain conclusive evidences in the analysis of the edge type. The use of Akaike Information Criterion can result in the selection of over-parametrized mixture models, while simple models are selected when using Bayesian Information Criterion. The use of the circular statistical models stand for an advance with respect to the subjective approach, but further studies are necessary concerning asymmetric probability distributions, and procedures to assess over-parametrizations when using mixture models.