Modelling spatial trends in sorghum breeding field trials using a two-dimensional P-spline mixed model

Abstract

Key message A flexible and user-friendly spatial method called SpATS performed comparably to more elaborate and trial-specific spatial models in a series of sorghum breeding trials.AbstractAdjustment for spatial trends in plant breeding field trials is essential for efficient evaluation and selection of genotypes. Current mixed model methods of spatial analysis are based on a multi-step modelling process where global and local trends are fitted after trying several candidate spatial models. This paper reports the application of a novel spatial method that accounts for all types of continuous field variation in a single modelling step by fitting a smooth surface. The method uses two-dimensional P-splines with anisotropic smoothing formulated in the mixed model framework, referred to as SpATS model. We applied this methodology to a series of large and partially replicated sorghum breeding trials. The new model was assessed in comparison with the more elaborate standard spatial models that use autoregressive correlation of residuals. The improvements in precision and the predictions of genotypic values produced by the SpATS model were equivalent to those obtained using the best fitting standard spatial models for each trial. One advantage of the approach with SpATS is that all patterns of spatial trend and genetic effects were modelled simultaneously by fitting a single model. Furthermore, we used a flexible model to adequately adjust for field trends. This strategy reduces potential parameter identification problems and simplifies the model selection process. Therefore, the new method should be considered as an efficient and easy-to-use alternative for routine analyses of plant breeding trials.

Modelling spatial variation in agricultural field trials with INLA

“…Through the analysis of simulated wheat data sets we showed that the estimates of genetic effects can be improved by accounting for spatial dependency in trials irrespective of the magnitude of the spatial variation. This is in line with the other studies (Elias et al, 2018;Rodríguez-Álvarez et al, 2018;Velazco et al, 2017;Piepho et al, 2008).…”

Mega‐Environmental Design: Using Genotype × Environment Interaction to Optimize Resources for Cultivar Testing

“…The S2D is probably being able to better compensate for some of the local control of more advanced experimental designs. The flexibility of this type of spatial adjustment has been positively assessed in other studies where spatial variability patterns were modeled (Stefanova et al, 2009: Velazco et al, 2017; van Eeuwijk et al, 2018). Finally, the ranking of the experimental designs was consistent across different levels of noise that generate different heritabilities (i.e., from 0.58 to 0.86; Supplemental Fig.…”

“…Therefore, modeling spatial correlations might be necessary to improve genotypic effect estimation even after a good experimental design is used (Federer, 1998; Qiao et al, 2000; Campbell and Bauer, 2007; Casler, 2015; Borges et al, 2019). Several approaches have been proposed to control spatial variability such as nearest‐neighbor adjustment (Katsileros et al, 2015), smoothing techniques including penalized splines analysis (Stefanova et al, 2009; Piepho and Williams, 2010; Velazco et al, 2017), modeling the variance–covariance matrix of spatial correlations using geostatistical components (Williams, 1986; Williams et al, 2006; Piepho and Williams, 2010), or using mixed models (Smith et al, 2005). In mixed models, one‐ or two‐dimensional models are used to control spatial heterogeneity with two‐dimensional models outperforming one‐dimensional models in terms of the genotypic effects estimation (Cullis and Gleeson, 1991, Kempton et al, 1994, Piepho and Williams, 2010).…”

When a phenotype is not the genotype: Implications of phenotype misclassification and pedigree errors in genomics-assisted breeding of sweetpotato [Ipomoea batatas(L.) Lam.]

“…Precise phenotypic data of the training population is a prerequisite for improving the accuracy of predicting untested genotypes in genomic selection models (Velazco et al, 2017). However, GE interactions are known to increase with increasing number of genotypes and environments.…”

“…The sheer large number of genotypes tested in early breeding stages means that experimental plots are large hence leading to local heterogeneity within experiments. To further improve prediction accuracies, different spatial adjustment models have been fronted to help deal with heterogeneity in experiments especially in these large early stage breeding trials (Lado et al, 2013; Bernal-Vasquez et al, 2014; Piepho et al, 2015; Velazco et al, 2017; Ward et al, 2019). Multidisciplinary teams are therefore continually working to improve the precision of measuring the phenotypes of the training populations to improve predictive ability of genomic selection in plant breeding, as summarized by Ward et al (2019).…”