# Bayesian inference in nonlinear growth models and hypothesis testing of sexual dimorphism in Black Utrerana chickens

## TL;DR

This study uses Bayesian methods to model the growth of Black Utrerana chickens and finds sexual dimorphism only in adult weight.

## Contribution

First application of Bayesian inference to growth modeling in Black Utrerana chickens and formal testing of sexual dimorphism.

## Key findings

- Gompertz and von Bertalanffy models best described chicken growth.
- Sexual dimorphism was found only in asymptotic weight, with males being heavier.
- Bayesian hypothesis testing confirmed significant differences in final weight between sexes.

## Abstract

Poultry growth is a dynamic process that can be influenced by several factors, such as sexual dimorphism, which in most studies is described without the use of formal statistical tests. Understanding animal growth is vital for proper management and breedin. Nonlinear models are often used to describe animal growth, as they allow biological interpretation of the parameters and capture the sigmoid nature of the growth curve. Despite the widespread use of nonlinear modeling in poultry growth, no studies have been found that apply Bayesian inference to the estimation and comparison of parameters in chickens. This approach incorporates prior knowledge on the topic and produces probability distributions for the parameters, providing a clearer view of uncertainty and more robust inference. Therefore, to fill these knowledge gaps, this study aims to select the most suitable nonlinear model to characterize the body weight growth of male and female Black Utrerana chickens among the Logistic, Gompertz, Brody and von Bertalanffy models using the Bayesian methodology, which has not previously been applied to growth modeling in this species, and to evaluate the existence of sexual dimorphism in this breed. The data are mean weights (g) measured over age in days of Black male and female Utrerana (Spanish breed) chickens raised in a free-range system. The nonlinear models were fitted using the “brms” package of the R software, which implements the Hamiltonian Monte Carlo algorithm with No-U-Turn (NUTS) sampler. The Gompertz and von Bertalanffy models performed best in describing bird growth, regardless of sex. For clarity and conciseness, only the von Bertalanffy results are presented. After model selection, a Bayesian hypothesis test was performed based on the Savage-Dickey method in order to investigate sexual dimorphism in the growth parameters. The results indicated sexual dimorphism only in the asymptotic weight, being significantly higher in males. In conclusion, the Bayesian approach proved effective for modeling poultry growth, and our findings highlight that sexual dimorphism in Black Utrerana chickens is limited to asymptotic weight.