Design and analysis of unreplicated plant breeding trials
Final Report Abstract
This project was focussed on the experimental design of breeding trials. In particular, we looked at designs that can be used in the early stages where seed is limited and so full replication is not feasible. Thus, we looked at partially replicated (p-rep) and unreplicated designs. A key objective was to develop new p-rep designs that entail an efficient blocking structure, to devise methods for analysis (randomization-based and spatial), and to evaluate the design and analysis methods. In addition, we also considered some related design and analysis issues in the context replicated designs. We developed a general approach, based on α-arrays, to generate augmented partially replicated (p-rep) designs for variety trials. This design is for a multi-environment trial, and at each location only a fraction of the entries are replicated for local error control. Such designs have the advantage compared to classical augmented designs that replicated checks, which are not usually of interest in themselves, are replaced by replicated entries that are of direct interest. Thus, the p-rep design entails a more efficient use of resources. The method has been implemented in the user-friendly CycDesigN package (Version 5.1; http://www.vsni.co.uk/de/software/ CycDesigN) and so is now readily available for use in practice. The performance of p-rep designs in comparison to other designs was investigated by a simulation based on uniformity trial data. The extensive results show that the design does very well in terms of efficiency compared to fully replicated designs and classical augmented designs with replicated checks. It is only slightly outperformed by a completely unreplicated design. The main advantage of the p-rep design is that it can also be analysed for individual locations. We considered the recovery of inter-block information for p-rep designs. Recovery of information is implemented by fitting a random effect for blocks, whereas an intra-block analysis, which discards the inter-block information, is forthcoming by fitting block effects as fixed. In practice, one has to decide whether or not to recover this information. We investigated two competing decision rules for this problem, one based on the Kenward-Roger method for adjusting the empirical variance-covariance matrix of variety effects and a simulation-based method that assesses the mean squared error of both methods. The striking outcome is that almost invariably it is preferable to take block effects random throughout, except when the number of blocks is very small indeed (<5). We explored spatial designs comparing the linear variance model (LV) and the first-order autoregressive model (AR(1)). It turned out that the LV model often leads to very efficient estimates even for designs optimized with respect to AR(1), showing that the LV model is a good basis for both the spatial design and analysis of variety trials. The main advantage of the LV model is that for the design it is not necessary to specify parameter values of the model. By contrast, the AR(1) model requires specification of the autocorrelation parameter. Finally, we wrote a tutorial-type paper emphasizing the importance of proper randomization of field experiments, no matter whether or not spatial analysis is intended, and we demonstrated using a striking example that classical analysis of covariance can out-compete spatial analysis of a trial subject to environmental stress.
Publications
- (2011): Augmented p-rep designs. Biometrical Journal 53, 19-27
Williams, E.R., Piepho, H.P., Whitaker, D.
- (2013): A comparison of spatial designs for field variety trials. Australian and New Zealand Journal of Statistics 55, 253-258
Williams, E.R., Piepho, H.P.
- (2013): Visual scorings of drought stress intensity as covariates for improved variety trial analysis. Journal of Agronomy and Crop Science 199, 321-330
Mühleisen, J., Reif, J., Maurer, H.P., Möhring, J., Piepho, H.P.
(See online at https://doi.org/10.1111/jac.12025) - (2013): Why randomize agricultural experiments? Journal of Agronomy and Crop Science 199, 374-383
Piepho, H.P., Möhring, J., Williams, E.R.
- (2014): Efficiency of augmented p-rep designs in multi-environment trials. Theoretical and Applied Genetics 127, 1049-1060
Möhring, J., Williams, E.R., Piepho, H.P.
(See online at https://doi.org/10.1007/s00122-014-2278-y)
