Selection of sweet potato genotypes for industrial root shape via Bayesian Mixed Threshold Models

The evaluation of root shape in sweet potato (Ipomoea batatas L.) breeding programs aimed at industrial use is routinely based on visual rating scales. These classification scores are considered discrete and ordinal variables. Unlike other traits of agronomic interest, the classification fails to meet the assumptions of studies based on Linear Models. Although variable transformation is an alternative for using Linear Models in such cases, it can introduce bias into the evaluations and adds a layer of complexity that hinders the interpretation of results. Alternatively, Bayesian Generalized Linear Mixed Models (BGLMM) allow for modeling ordinal data so that the statistical approach faithfully captures the nature of the data. Therefore, the aim of this study was to characterize 15 sweet potato genotypes across three harvest times (90, 120, and 150 days after planting) focusing on root shape. The experiment was conducted in a randomized complete block design with three replications at the Experimental Field of the Center for Development and Technology Transfer (CDTT/UFLA), located in Ijaci-MG, Brazil, evaluating root shape on a rating scale from 1 (fusiform/excellent) to 5 (deformed). Data fitting was performed via BGLMM, adopting a threshold model with a multinomial distribution and probit link function, implemented in the R environment using the MCMCglmm package. The model was fitted via a Markov Chain Monte Carlo (MCMC) algorithm with a total of 500000 iterations, a burn-in of 100000, and a thinning interval of 200.  The non-informative prior inverse-gamma was assumed for the variance components of the random effects, with the residual variance fixed at 1 on the latent scale. Subsequently, posterior parameter distributions, latent genotypic values, and High Posterior Density (HPD) intervals were estimated. Chain convergence was successfully verified using Geweke and Heidelberger & Welch diagnostics. The analysis revealed high heritability on the latent scale of h² = 0.73 (95% HPD: 0.56 - 0.91) and a selective accuracy of r_ĝg = 0.85 (95% HPD: 0.75 - 0.96), indicating strong genetic control over root shape and high reliability in the selection process.  The analysis of posterior probabilities on the latent scale allowed the accurate identification of genotypes with superior genetic merit. The clones UFLA 1377, UFLA 1074, UFLA 527, and UFLA 1476 demonstrated superior genetic merit across the harvest times, with an extremely high posterior probability (>99%) of producing commercial fusiform roots at 90, 120, and 150 days. It is concluded that the Bayesian threshold mixed model approach enables precise genetic evaluation while respecting the categorical nature of the variable, and the selection and continuation of UFLA 1377, UFLA 1074, UFLA 527, and UFLA 1476 in the breeding program is recommended.