Bayesian Estimation of Age and Length at 50% Maturity

Abstract

Fish age and length at 50% maturity are used extensively in the management of exploited fish populations. These parameters are historically estimated using logistic regression models (e.g., frequentist inference) for individual yearclasses and often fail to converge or result in insignificant results when a small sample size is used. The sample-size problem motivated us to evaluate whether a hierarchical logistic regression model fit using frequentist inference or Bayesian inference, could improve our ability to fit these models. Our objective was to compare Bayesian and frequentist inference for estimating age and length at 50% maturity to determine whether the models produced similar values. To make this evaluation, we used a long-term data set of Yellow Perch Perca flavescens from southern Lake Michigan. Frequentist inference of the year-class-specific models resulted in significant results when sample size was sufficiently large, a result that occurred in 76% of the models. The hierarchical model produces estimates of age (or length) at 50% maturity for all year-classes using both frequentist and Bayesian inference. However, Bayesian inference of the hierarchical model resulted in more precise parameter estimates and provided the complete posterior distribution in one seamless and easy approach, and the computation time was 78% to 83% faster. We suggest that a hierarchical model fit using Bayesian inference of age (or length) at 50% maturity is an improvement over frequentist interference methods by providing more information about the population of interest, particularly when sample sizes are limited.

De novo transcriptome sequencing and analysis of male, pseudo-male and female yellow perch, Perca flavescens

“…The results might indicate that: 1) female and pseudo-male yellow perch had much the same genomic resource including sex-related genes; 2) female and pseudo-male were in much the same special stage and had much the same trascriptomic profile; 3) there exists but cannot be identified based on the present databases. Yellow perch have sexual size dimorphism that females were significantly larger than males starting from at least one-year-old fish [ 31 ], since lower growth rate was observed in mature males [ 32 , 33 ], and estimates of female age and length at 50% maturity ranged from 1.0 to 5.8 years and from 15.7 to 20.1 cm, respectively, while male age and length at 50% maturity ranged from 1.2 to 2.1 years and from 9.4 to 12 cm [ 34 ]. To some extent, the results from pathway analysis also showed that the sexual size dimorphism among female, male, and pseudo-male did not yet occur significantly in yellow perch when sampling was performed.…”

Biological characteristics of inland Lake Whitefish populations in Ontario

“…The probability of individual Lake Whitefish being mature was assumed to follow a Bernoulli distribution. Non‐informative priors (N[0, 1000]) were used for α (intercept) and β (log odds parameter), whereas the inflection point (50% maturity at length or age) of the logistic curve was determined from −α/β (Doll and Lauer 2013). Variation in length or age at 50% maturity between females and males was assessed by determining the difference between the posterior distributions of the parameters; differences were considered significant if zero was not included in their 95% CRIs.…”

“…Length and age at 50% maturity for female and male Lake Whitefish were estimated using a (1) Bayesian binomial logistic regression model (Doll and Lauer 2013). Stage of sexual maturity was not assessed during the BsM Program; therefore, Lake Whitefish samples collected from other standardized projects across Ontario and stored in the OMNRF application FISHNET were used.…”

Reproduction Aspects of Cobia Caught in Pernambuco Coast, Northeastern Brazil

“…Size at first maturity (L 50 ) for females and males was defined as the FL at which 50% of the population is mature (Doll and Lauer, 2013) and was estimated using Bayesian inference, assuming binomial distribution. For such, the runjags package (Denwood, 2016) was implemented in R version 3.5.1 (R Core Team, 2018).…”