Joint Modeling of Genetics and Field Variation in Plant Breeding Trials Using Relationship and Different Spatial Methods: A Simulation Study of Accuracy and Bias

Modelling field spatial patterns is standard practice for the analysis of plant breeding. Jointly fitting the genetic relationship among individuals and spatial information enables better separability between the variance due to genetics and field variation. This study aims to quantify the accuracy and bias of estimative parameters using different approaches. We contrasted three settings for the genetic term: no relationship (I), pedigree relationship (A), and genomic relationship (G); and a set of approaches for the spatial variation: no-spatial (NS), moving average covariate (MA), row-column adjustment (RC), autoregressive AR1 × AR1 (AR), spatial stochastic partial differential equations, or SPDE (SD), nearest neighbor graph (NG), and Gaussian kernel (GK). Simulations were set to represent soybean field trials at F2:4 generation. Heritability was sampled from a uniform distribution U(0,1). The simulated residual-to-spatial ratio between residual variance and spatial variance (Ve:Vs) ranged from 9:1 to 1:9. Experimental settings were conducted under an augmented block design with the systematic distribution of checks accounting for 10% of the plots. Relationship information had a substantial impact on the accuracy of the genetic values (G > A > I) and contributed to the accuracy of spatial effects (30.63–42.27% improvement). Spatial models were ranked based on an improvement to the accuracy of estimative of genetic effects as SD ≥ GK ≥ AR ≥ NG ≥ MA > RC ≥ NS, and to the accuracy of estimative of spatial effects as GK ≥ SD ≥ NG > AR ≥ MA > RC. Estimates of genetic and spatial variance were generally biased downwards, whereas residual variances were biased upwards. The advent of relationship information reduced the bias of all variance components. Spatial methods SD, AR, and GK provided the least biased estimates of spatial and residual variance.