Lin Xing, Patricio Munoz, Luis Inostroza, Hernan Acuna

Abstract
The randomized complete block design (RCBD) is widely used in agricultural and horticultural experiments to control environmental variation because of its simplicity. However, in plant breeding experiments can have large number of genotypes, which will create large replicates with heterogeneous environmental conditions. In such cases, the use of alpha-lattice or row-column design may offer a better alternative to control the environmental variation. The objective of this study is to compare the accuracy of genetic parameters estimated by RCBD, Alpha-lattice and row-column models.
Three white clover (Trifolium repens L.) experiments were established in Chillan, Chile at different altitudes (100, 500 and 1000 m.a.m.s.).  Each experiment was designed with two repetitions and 192 genotypes in each rep (single plant-plot) in an alpha-lattice design. Several growth, morphological, and physiological traits were measured and its heritability estimated. Three traits with high (leaf area), medium (dry matter) and low (stolon growth rate) heritability were chosen to investigate the effect of modeling on the accuracy of heritability, genotype-by-environment interaction and trait-trait genetic correlations. Linear mixed models in the software ASReml were used to estimate such parameters using a RCBD, Alpha-lattice and row-col models.
Our results indicate that Alpha-lattice and row-col design yield slighltly better accuracy on estimating these genetic parameters than RCBD. Minor differences were found between alpha-lattice and row-column accuracy. Although, easy to design and implement, these experimental designs are still not widely used in agronomy or horticulture. Even when differences are small, it is expected that the genetic parameters accuracy of these two methods increase respect to RCBD as the field heterogeneity and/or as the number of genotypes (treatments) increase.