Modeling Spatial Correlation Structure in Sugarcane (Saccharum spp.) Multi-Environment Trials

Abstract

Comparative multi-environment trials (METs) of sugarcane genotypes are frequently conducted using a randomized complete-block design (RCBD) within environments. However, blocking does not always ensure spatial variation control because of differential competition for resources among neighboring genotypes. Heterogeneity within trials may also cause between-trial heterocedasticity. This work aims to evaluate different linear mixed models (LMMs) that enable the analysis of spatial correlation and residual heterogeneity among trials for both tons of cane per hectare (TCH) and sucrose content (SC%) in three series of multi-environmental trials conducted to evaluate advanced sugarcane clones. A total of 16 sugarcane trials conducted at different sites and in different crop cycles (age) were analyzed. Individual (age×site combination) and multi-environment analyses were performed. For SC%, the classic RCBD analysis within trial was adequate. For TCH, the anisotropic autoregressive model of order 1 (AR1×AR1) was the best to compare genotype means in most trials, allowing gain in information equivalent, on average, to the addition of 1.6 replicates to the original design. In the case of multi-environment analysis, the AR1×AR1 within-trial with among-trial heteroscedasticity was the best model to compare variety means, both for TCH and SC%. The results showed how a more appropriate mixed model would help avoid commission of judgment errors in sugarcane variety recommendations.

KEYWORDS:

• anisotropic-autoregressive spatial models
• efficiency
• experimental design
• linear mixed model
• yield trials