Spatial Corrections of Single Replication Field Trials Using Autoregressive and Two-Dimensional Spline Models.

Simultaneous spatial correction of multiple fields is not always feasible for large scale trials. In such cases methods are needed for single field spatial analyses that avoid confounding of spatial and genetic effects for single replication trials. To identify methods best suited for this purpose, the performances of autoregressive models of the first (AR1), second (AR2), and third order (AR3), as well as, two-dimensional spline interpolation (2DS) and randomized complete block (RCB) models were evaluated using simulated (SD) and real maize yield data (YD). Both SD and YD were arranged in RCB with no replication of tested lines within field. Simulated spatial effects were sampled from a multivariate normal distribution (MVN) using several spatial correlation structures. Genotype effects were simulated as MVN using maize pedigrees, and residuals were sampled as iid normal. For SD, model performance was evaluated using correlations between true and estimated spatial effects (Rs), as well as, correlations between estimated spatial effects and the true genotype effects (Rg). For YD performance was measured using error variance estimates. For SD, Rs ranged from .73-.84 for AR1, .73-.83 for AR2, .74-.84 for AR3, .45-.71 for 2DS, and .3-.54 for RCB models. Although the AR models consistently provided the best estimates of spatial effects, the Rg values were greater than those of 2DS (.16-.31, versus .04-.06), indicating AR models should be restricted to repeated records. Implementing AR models using only repeated check records (ARC) reduced Rg, but at the cost of substantial decreases in Rs (.35-.6). Due to the high Rg associated with the AR models, they were excluded from analysis of YD. As with SD, 2DS again showed superior performance over ARC for YD. Overall, 2DS performed consistently well across all data sets, making it a good choice for nested implementation in single replication field trials.