Generating Improved Experimental Designs with Spatially and Genetically Correlated Observations Using Mixed Models

Abstract

The aim of this study was to generate and evaluate the efficiency of improved field experiments while simultaneously accounting for spatial correlations and different levels of genetic relatedness using a mixed models framework for orthogonal and non-orthogonal designs. Optimality criteria and a search algorithm were implemented to generate randomized complete block (RCB), incomplete block (IB), augmented block (AB) and unequally replicated (UR) designs. Several conditions were evaluated including size of the experiment, levels of heritability, and optimality criteria. For RCB designs with half-sib or full-sib families, the optimization procedure yielded important improvements under the presence of mild to strong spatial correlation levels and relatively low heritability values. Also, for these designs, improvements in terms of overall design efficiency (ODE%) reached values of up to 8.7%, but these gains varied depending on the evaluated conditions. In general, for all evaluated designs, higher ODE% values were achieved from genetically unrelated individuals compared to experiments with half-sib and full-sib families. As expected, accuracy of prediction of genetic values improved as levels of heritability and spatial correlations increased. This study has demonstrated that important improvements in design efficiency and prediction accuracies can be achieved by optimizing how the levels of a treatment are assigned to the experimental units.

Evaluating Algorithm Efficiency for Optimizing Experimental Designs with Correlated Data

“…A scenario, the amount of design improvement was, for some conditions, about four times larger than that realized under Ω (196) A scenario. This means that more iterations (>50,000) might be required for larger experiments than it would take for a smaller experiment to to reach an adequate optimal solution [10]. The number of successful swaps displayed in Figure 3 indicates that they decrease with increasing heritability for all families for experiments evaluated under Ω A scenarios for almost all algorithms.…”

“…from which the trace and determinant of the matrix M(Ω) are calculated based on Aand D-optimality criteria, respectively (For further details see [10]).…”

“…To generate experimental designs under the above framework an optimality criterion is used together with the implementation of an iterative search algorithm. Aand D-optimality information based criterion are the most widely used procedures in field experiments to generate optimal or near-optimal designs [7][8][9] and most recently were used by Butler et al [6] and Mramba et al [10] to design experiments with correlated observations. These procedures are very useful in the process of selecting an optimal design [11].…”

“…Some of the computer search algorithms available include pairwise swap procedure, and its variants where a single or multiple pairs of treatments are swapped at a time [3], and simulated annealing where a cooling strategy is employed [14]. Most of the applications of these algorithms focus on the analysis of data and little has been done on their applications to improve the designs of genetic experiments, yet, estimated parameters from improved designs can be obtained with increased precision if variability of treatment effects is minimized [10].…”

Long-term selection of biparental crosses: a comparison among genomic methods and phenotypic selection

“…The error effects usually are modeled using a normal distribution ε ∼ N (0, σ 2 e ), and the realizations of the distribution are added up with the genotypic values. Also, we can simulate the spatial dependency of these errors by using some correlation structure (e.g., autoregressive structure), sampling values from a multivariate normal distribution, as presented by Mramba et al (2018).…”