Key message Established spatial models improve the analysis of agricultural field trials with or without genomic data and can be fitted with the open-source R package INLA. AbstractThe objective of this paper was to fit different established spatial models for analysing agricultural field trials using the open-source R package INLA. Spatial variation is common in field trials, and accounting for it increases the accuracy of estimated genetic effects. However, this is still hindered by the lack of available software implementations. We compare some established spatial models and show possibilities for flexible modelling with respect to field trial design and joint modelling over multiple years and locations. We use a Bayesian framework and for statistical inference the integrated nested Laplace approximations (INLA) implemented in the R package INLA. The spatial models we use are the well-known independent row and column effects, separable first-order autoregressive () models and a Gaussian random field (Matérn) model that is approximated via the stochastic partial differential equation approach. The Matérn model can accommodate flexible field trial designs and yields interpretable parameters. We test the models in a simulation study imitating a wheat breeding programme with different levels of spatial variation, with and without genome-wide markers and with combining data over two locations, modelling spatial and genetic effects jointly. The results show comparable predictive performance for both the and the Matérn models. We also present an example of fitting the models to a real wheat breeding data and simulated tree breeding data with the Nelder wheel design to show the flexibility of the Matérn model and the R package INLA.Electronic supplementary materialThe online version of this article (10.1007/s00122-019-03424-y) contains supplementary material, which is available to authorized users.
Background Breeders and geneticists use statistical models to separate genetic and environmental effects on phenotype. A common way to separate these effects is to model a descriptor of an environment, a contemporary group or herd, and account for genetic relationship between animals across environments. However, separating the genetic and environmental effects in smallholder systems is challenging due to small herd sizes and weak genetic connectedness across herds. We hypothesised that accounting for spatial relationships between nearby herds can improve genetic evaluation in smallholder systems. Furthermore, geographically referenced environmental covariates are increasingly available and could model underlying sources of spatial relationships. The objective of this study was therefore, to evaluate the potential of spatial modelling to improve genetic evaluation in dairy cattle smallholder systems. Methods We performed simulations and real dairy cattle data analysis to test our hypothesis. We modelled environmental variation by estimating herd and spatial effects. Herd effects were considered independent, whereas spatial effects had distance-based covariance between herds. We compared these models using pedigree or genomic data. Results The results show that in smallholder systems (i) standard models do not separate genetic and environmental effects accurately, (ii) spatial modelling increases the accuracy of genetic evaluation for phenotyped and non-phenotyped animals, (iii) environmental covariates do not substantially improve the accuracy of genetic evaluation beyond simple distance-based relationships between herds, (iv) the benefit of spatial modelling was largest when separating the genetic and environmental effects was challenging, and (v) spatial modelling was beneficial when using either pedigree or genomic data. Conclusions We have demonstrated the potential of spatial modelling to improve genetic evaluation in smallholder systems. This improvement is driven by establishing environmental connectedness between herds, which enhances separation of genetic and environmental effects. We suggest routine spatial modelling in genetic evaluations, particularly for smallholder systems. Spatial modelling could also have a major impact in studies of human and wild populations.
We propose a novel Bayesian approach that robustifies genomic modelling by leveraging expert knowledge through prior distributions. The central component is the hierarchical decomposition of phenotypic variation into additive and non-additive genetic variation, which leads to an intuitive model parameterization that can be visualised as a tree. The edges of the tree represent ratios of variances, for example broad-sense heritability, which are quantities for which expert knowledge is natural to exist. Penalized complexity priors are defined for all edges of the tree in a bottom-up procedure that respects the model structure and incorporates expert knowledge through all levels. We investigate models with different sources of variation and compare the performance of different priors implementing varying amounts of expert knowledge in the context of plant breeding. A simulation study shows that the proposed priors implementing expert knowledge improve the robustness of genomic modelling and the selection of the genetically best individuals in a breeding program. We observe this improvement in both variety selection on genetic values and parent selection on additive values; the variety selection benefited the most. In a real case study expert knowledge increases phenotype prediction accuracy for cases in which the standard maximum likelihood approach did not find optimal estimates for the variance components. Finally, we discuss the importance of expert knowledge priors for genomic modelling and breeding, and point to future research areas of easy-to-use and parsimonious priors in genomic modelling.
This paper introduces a hierarchical model to estimate haplotype effects based on phylogenetic relationships between haplotypes and their association with observed phenotypes. In a population there are usually many, but not all possible, distinct haplotypes and few observations per haplotype. Further, haplotype frequencies tend to vary substantially -few haplotypes have high frequency and many haplotypes have low frequency. Such data structure challenge estimation of haplotype effects. However, haplotypes often differ only due to few mutations and leveraging these similarities can improve the estimation of haplotype effects. There is extensive literature on this topic. Here we build on these observations and develop an autoregressive model of order one that hierarchically models haplotype effects by leveraging phylogenetic relationships between the haplotypes described with a directed acyclic graph. The phylogenetic relationships can be either in a form of a tree or a network and we therefore refer to the model as the haplotype network model. The haplotype network model can be included as a component in a phenotype model to estimate associations between haplotypes and phenotypes. The key contribution of this work is that by leveraging the haplotype network structure we obtain a sparse model and by using hierarchical autoregression the flow of information between similar haplotypes is estimated from the data. We show with a simulation study that the hierarchical model can improve estimates of haplotype effects compared to an independent haplotype model, especially when there are few observations for a specific haplotype.We also compared it to a mutation model and observed comparable performance, though the haplotype model has the potential to capture background specific effects. We demonstrate the model with a case study of modeling the effect of mitochondrial haplotypes on milk yield in cattle.
A major challenge with modelling non-additive genetic variation is that it is hard to separate nonadditive variation from additive and environmental variation. In this paper, we describe how to alleviate this issue, and improve genomic modelling of additive and non-additive variation, by leveraging the ample expert knowledge available about the relative magnitude of the sources of phenotypic variation. The method is Bayesian and uses the recently introduced penalized complexity and hierarchical decomposition prior frameworks, where priors can be specified and visualized in an intuitive way, and be used to induce parsimonious modelling. We evaluate the potential impact for plant breeding through a simulated case study of a wheat breeding program. We compare different models and different priors with varying amounts of expert knowledge. The results show that the proposed priors and expert knowledge improved the robustness of the genomic modelling and the selection of the genetically best individuals in the breeding program. We observed this improvement in both variety selection on genetic values and parent selection on additive values, but the variety selection benefited the most. An improvement was not observed in the overall accuracy of estimating genetic values for all individuals and variance components. Finally, we discuss the importance of expert-knowledge priors for genomic modelling and breeding, and point to future research areas of easy-to-use and parsimonious priors in genomic modelling.
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