Genomic selection using random regressions on known and latent environmental covariates.

KEY MESSAGE: The integration of known and latent environmental covariates within a single-stage genomic selection approach provides breeders with an informative and practical framework to utilise genotype by environment interaction for prediction into current and future environments. This paper develops a single-stage genomic selection approach which integrates known and latent environmental covariates within a special factor analytic framework. The factor analytic linear mixed model of Smith et al. (2001) is an effective method for analysing multi-environment trial (MET) datasets, but has limited practicality since the underlying factors are latent so the modelled genotype by environment interaction (GEI) is observable, rather than predictable. The advantage of using random regressions on known environmental covariates, such as soil moisture and daily temperature, is that the modelled GEI becomes predictable. The integrated factor analytic linear mixed model (IFA-LMM) developed in this paper includes a model for predictable and observable GEI in terms of a joint set of known and latent environmental covariates. The IFA-LMM is demonstrated on a late-stage cotton breeding MET dataset from Bayer CropScience. The results show that the known covariates predominately capture crossover GEI and explain 34.4% of the overall genetic variance. The most notable covariates are maximum downward solar radiation (10.1%), average cloud cover (4.5%) and maximum temperature (4.0%). The latent covariates predominately capture non-crossover GEI and explain 40.5% of the overall genetic variance. The results also show that the average prediction accuracy of the IFA-LMM is [Formula: see text] higher than conventional random regression models for current environments and [Formula: see text] higher for future environments. The IFA-LMM is therefore an effective method for analysing MET datasets which also utilises crossover and non-crossover GEI for genomic prediction into current and future environments. This is becoming increasingly important with the emergence of rapidly changing environments and climate change.

Optimisation of the core subset for the APY approximation of genomic relationships.

BACKGROUND: By entering the era of mega-scale genomics, we are facing many computational issues with standard genomic evaluation models due to their dense data structure and cubic computational complexity. Several scalable approaches have been proposed to address this challenge, such as the Algorithm for Proven and Young (APY). In APY, genotyped animals are partitioned into core and non-core subsets, which induces a sparser inverse of the genomic relationship matrix. This partitioning is often done at random. While APY is a good approximation of the full model, random partitioning can make results unstable, possibly affecting accuracy or even reranking animals. Here we present a stable optimisation of the core subset by choosing animals with the most informative genotype data. METHODS: We derived a novel algorithm for optimising the core subset based on a conditional genomic relationship matrix or a conditional single nucleotide polymorphism (SNP) genotype matrix. We compared the accuracy of genomic predictions with different core subsets for simulated and real pig data sets. The core subsets were constructed (1) at random, (2) based on the diagonal of the genomic relationship matrix, (3) at random with weights from (2), or (4) based on the novel conditional algorithm. To understand the different core subset constructions, we visualise the population structure of the genotyped animals with linear Principal Component Analysis and non-linear Uniform Manifold Approximation and Projection. RESULTS: All core subset constructions performed equally well when the number of core animals captured most of the variation in the genomic relationships, both in simulated and real data sets. When the number of core animals was not sufficiently large, there was substantial variability in the results with the random construction but no variability with the conditional construction. Visualisation of the population structure and chosen core animals showed that the conditional construction spreads core animals across the whole domain of genotyped animals in a repeatable manner. CONCLUSIONS: Our results confirm that the size of the core subset in APY is critical. Furthermore, the results show that the core subset can be optimised with the conditional algorithm that achieves an optimal and repeatable spread of core animals across the domain of genotyped animals.

Genomic selection in multi-environment plant breeding trials using a factor analytic linear mixed model.

Genomic selection (GS) is a statistical and breeding methodology designed to improve genetic gain. It has proven to be successful in animal breeding; however, key points of difference have not been fully considered in the transfer of GS from animal to plant breeding. In plant breeding, individuals (varieties) are typically evaluated across a number of locations in multiple years (environments) in formally designed comparative experiments, called multi-environment trials (METs). The design structure of individual trials can be complex and needs to be modelled appropriately. Another key feature of MET data sets is the presence of variety by environment interaction (VEI), that is the differential response of varieties to a change in environment. In this paper, a single-step factor analytic linear mixed model is developed for plant breeding MET data sets that incorporates molecular marker data, appropriately accommodates non-genetic sources of variation within trials and models VEI. A recently developed set of selection tools, which are natural derivatives of factor analytic models, are used to facilitate GS for a motivating data set from an Australian plant breeding company. The power and versatility of these tools is demonstrated for the variety by environment and marker by environment effects.

FieldSimR: an R package for simulating plot data in multi-environment field trials.

This paper presents a general framework for simulating plot data in multi-environment field trials with one or more traits. The framework is embedded within the R package FieldSimR, whose core function generates plot errors that capture global field trend, local plot variation, and extraneous variation at a user-defined ratio. FieldSimR's capacity to simulate realistic plot data makes it a flexible and powerful tool for a wide range of improvement processes in plant breeding, such as the optimisation of experimental designs and statistical analyses of multi-environment field trials. FieldSimR provides crucial functionality that is currently missing in other software for simulating plant breeding programmes and is available on CRAN. The paper includes an example simulation of field trials that evaluate 100 maize hybrids for two traits in three environments. To demonstrate FieldSimR's value as an optimisation tool, the simulated data set is then used to compare several popular spatial models for their ability to accurately predict the hybrids' genetic values and reliably estimate the variance parameters of interest. FieldSimR has broader applications to simulating data in other agricultural trials, such as glasshouse experiments.