t‐Latinized Designs

Abstract

A variety trial sometimes requires a resolvable block design in which the replicates are set out next to each other. The long blocks running through the replicates are then of interest. A t-latinized design is one in which groups of these t long blocks are binary. In this paper examples of such designs are given. It is shown that the algorithm described by John & Whitaker (1993) can be used to construct designs with high average efficiency factors. Upper bounds on these efficiency factors are also derived.

Impact of reconstructed pedigrees on progeny-test breeding values in red spruce

“…Although forward, within-family selection is necessary for recurrent population improvement, there is some controversy whether forward selected progenies should be used directly in the production population because of their lower breeding value accuracy (Ruotsalainen and Lindgren 1998;Burdon and Kumar 2004). Accuracy can be increased by increasing the number of tested sibs per family, clonal testing (Shaw and Hood 1985;Kumar 2006) or using more efficient statistical test designs (John and Williams 1998), but these must be applied prior to implementing tests. Alternatively, retrospective analysis of quantitative data using mixed model methodology can make more efficient use of limited resources allocated to breeding programs by adjusting records for microsite spatial variation (Joyce et al 2002), identifying causal sources of genotype by environment interaction variation (Frensham et al 1998) or better modeling of the true underlying pedigree structure.…”

Neighbor balance and evenness of distribution of treatment replications in row‐column designs

“…The grouping of rows and columns into rowgroups and columngroups, respectively, is used to achieve ED across the field. We will henceforth refer to the grouping of rows or columns as t ‐Latinization (John & Williams, ). The following description is for columngroups, but the same types of structure can be imposed for the rows, and we do so in the model‐based approach described later.…”

Genetic Variability Evaluation and Selection in Ancient Grapevine Varieties

“…The most relevant experimental designs for working with a high number of treatments (greater than 100 genotypes) are the alpha designs (Patterson & Williams, 1976), the rowcolumn designs (Williams & John, 1989), the t-latinised designs (John & Williams, 1998) and the resolvable spatial row-column designs (Williams et al, 2006). The use of these designs in initial trials of grapevines was studied by Gonçalves et al (2010).…”