Best linear unbiased prediction: A mixed model approach in multi-environment trials (Chapter 12)

BALZARINI M.; MILLIGAN S.B.; KANG M.S.

Crop Improvement: Challenges in the 21st Century

Food Products Press Inc.

Lugar: Binghamton NY; Año: 2001; p. 102 - 113

The best linear unbiased predictor (BLUP) approach has been extensively used for evaluating and predicting the genetic merit in animals (Henderson, 1975). The BLUP is a traditional estimation procedure under the mixed linear model approach (Searle et al., 1992). It has relatively recently been introduced to and used in plant breeding for predicting cross performance and choosing parental lines elite progeny with a relatively high probability  (Bernardo, 1994,1995,1996a, 1996b; Panter and Allen, 1995; Balzarini, 2000). The BLUP procedure is not only being routinely used by maize breeders for selecting single crosses but also for choosing F2 populations for inbred development (Bernardo, 1999). As the BLUP procedures become more common and better understood, additional applications are expected to evolve. For example, this paper illustrates a new application of BLUP, viz., it can be used to improve genotype performance prediction in multi-environment trials (METs). Multi-environment, replicated yield trials are often conducted in advanced stages of breeding programs to select genotypes based on yield and other economically important traits. The METs are also common in agricultural research to evaluate cropping systems and other selected treatments. A usual feature of all METs is the representation of a relatively large number of elements (Littell et al., 1996).  In METs, environments might be reasonably assumed to be random effects. However, the genotype effects might be treated as fixed since only a few highly selected genotypes are usually involved in the late breeding stages.  Therefore, the mixed-model approach, with environmental effects and genotype-by-environment effects as random, and genotype effects as fixed is most appropriate. The main aim of METs in plant breeding is to compare genotype performance of new cultivars. In addition to comparing mean genotypic performance, there is an interest in analyzing genotype-by-environment interaction (GEI) (Kang, 1990; Kang and Gauch, 1996) and quantifying stability of genotype performance across diverse environments (Lin et al., 1986; Becker and Leon, 1988; Crossa, 1990; Lin and Binns, 1994; Kang and Gauch, 1996). The mixed model approach allows an analysis of METs relative to mean performance, GEI, and genotype stability in a unique framework.     Two types of inference about mean genotype performance are of interest in METs:  (1) broad inference, i.e., general performance of a genotype across environments, and (2) environment-specific or narrow inference, i.e., performance of a genotype in a specific environment. The traditional analytical approach relates to multiple pairwise comparisons of genotype means.  The narrow inference from METs relies on comparisons of genotypic means in specific environments. Unfortunately, this procedure does not use all the available information.  It is only possible to make inferences about performance of genotypes that have been tested in a specific environment.  Mixed model prediction uses information from an entire data set to obtain environment-specific inferences, allowing prediction of genotype performance even in environments where the genotype was not tested. Most of the analytical procedures to quantify a genotype?s contribution to the overall GEI are based on the fixed-effects model approach.  Such fixed models are applicable only to balanced data, i.e., a complete set of GEI data.   However, a common feature of most yield trials is that test entries vary from year to year because new entries are included as they become available and those with poor performance may be deleted from further consideration (Hill and Rosenberg, 1985).  The deletion and substitution results in incomplete or unbalanced data.  Even within a year, a complete data set may not be available because, for one reason or another, one or more genotypes could not be included in some replications and/or locations. Mixed model and restricted maximum likelihood-based estimation procedures relative to parameters in the models provide a more flexible analytical approach for the analysis of METs because balanced data are not required (Hill and Rosenberg, 1985; Stroup and Mulitze, 1991; Piepho, 1994, 1997, 1998a). Magari and Kang (1997) used the restricted maximum likelihood (REML) method under a mixed model to estimate stability variances in unbalanced data sets when analyzing GEI for ear moisture loss rate in corn (Zea mays L.).  The REML variance components, assigned to each genotype, estimate the same statistics as Shukla?s stability variance (Shukla, 1972).  The mixed model with heterogeneous GEI terms is a priori more tenable than the traditional mixed analysis of variance because it allows different stability statistics for each genotype while still assuming independence among the GEI effects. By further modeling the variance-covariance structure of environment and interaction random effects, well-known stability measures can be expressed as parameters of closely related mixed models (Piepho, 1998a).  The common regression approaches for studying genotype sensitivities to environmental changes with multiplicative models for GEI (Yates and Cochran, 1938; Finlay and Wilkinson, 1963; Eberhart and Russell, 1966), including AMMI models (Gauch, 1988; Zobel et al., 1988), can be handled by integrating a factor-analytic variance-covariance structure into a mixed model (Oman, 1991; Piepho, 1997; Piepho, 1998b).