Hierarchical Bayesian modeling for comparing nonlinear functions and estimating heritability of growth curve parameters in llamas

Abstract

Genetic modeling of growth curve parameters in llamas is fundamental for breeding programs; however, previous studies have relied predominantly on two-stage frequentist approaches or conventional MCMC algorithms (Gibbs/Metropolis-Hastings), which present limitations regarding computational efficiency and simultaneous incorporation of multiple information sources. The objective of this study was to compare nonlinear functions (Brody, Gompertz, and von Bertalanffy) and jointly estimate growth curve parameters (asymptotic weight, A; scaling parameter, B; and maturation rate, k), variance components, and heritabilities in young llamas through hierarchical Bayesian modeling implemented with the No-U-Turn Sampler (NUTS) algorithm via Stan/brms. We analyzed 11,409 monthly weight records from birth to 365 days of age from 1000 llamas (456 males and 544 females) of K'ara and Ch'accu breeds from the Quimsachata Experimental Station (Peru). A three-stage hierarchical Bayesian model was adopted: (i) normal likelihood for weights conditioned on individual curves; (ii) multivariate animal model for parameters A, B, and k, including systematic effects (sex and breed) and additive genetic effects; and (iii) normal prior distributions for standard deviations. Posterior sampling (4000 post-warmup iterations) showed adequate convergence according to the Gelman-Rubin, Geweke, and Effective sample size diagnostics. The von Bertalanffy model was selected as the most parsimonious (Watanabe-Akaike Information Criterion (WAIC) = 20104.8; Leave-One-Out Information Criterion (LOOIC) = 27588). Estimated heritabilities for A were high (0.79 - 0.87), while those associated with parameters B and k were close to zero (0.007 – 0.075). We conclude that the hierarchical Bayesian approach with NUTS/brms is computationally efficient and statistically robust for analyzing growth curves in llamas, evidencing high genetic potential for adult weight selection, in contrast to the low heritability of curve shape parameters. This study represents the first application of the NUTS algorithm in hierarchical growth models for South American camelids.