Smoothing fertility trends in agricultural field experiments

Taye, Girma; Njuho, Peter Mungai

doi:10.1080/02331880701736580

Cited by 5 publications

(6 citation statements)

References 14 publications

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“…The structure of spatial variation found in our data set (Fig. 2 ) and in the previous studies of agricultural and forest field trials demonstrate that fitting only additive gradients in one dimension may result in insufficient modelling of global trend (Federer 1998 ; Fu et al 1999 ; Taye and Njuho 2008 ). It is in principle possible to extend the standard spatial model with additional fixed terms, like a linear x linear interaction term (Federer 1998 ), and random terms, like a smoothing spline interaction term, but these extensions were never used under the standard approach and are prone to cause problems (Gilmour 2000 ).…”

Section: Discussionmentioning

confidence: 47%

“…These studies considered a single smoothing parameter that controls the smoothness of the spatial effects in the direction of both rows and columns, imposing isotropic smoothing. In agricultural experiments, Taye and Njuho ( 2008 ) proposed using P-splines in two dimensions to adjust for global trend and to model local variation with Papadakis and kriged covariates. The authors compared P-spline models assuming additive trends or interaction between trends and emphasized the importance of choosing between both model settings.…”

Section: Introductionmentioning

confidence: 99%

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Modelling spatial trends in sorghum breeding field trials using a two-dimensional P-spline mixed model

et al. 2017

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Key message A flexible and user-friendly spatial method called SpATS performed comparably to more elaborate and trial-specific spatial models in a series of sorghum breeding trials.AbstractAdjustment for spatial trends in plant breeding field trials is essential for efficient evaluation and selection of genotypes. Current mixed model methods of spatial analysis are based on a multi-step modelling process where global and local trends are fitted after trying several candidate spatial models. This paper reports the application of a novel spatial method that accounts for all types of continuous field variation in a single modelling step by fitting a smooth surface. The method uses two-dimensional P-splines with anisotropic smoothing formulated in the mixed model framework, referred to as SpATS model. We applied this methodology to a series of large and partially replicated sorghum breeding trials. The new model was assessed in comparison with the more elaborate standard spatial models that use autoregressive correlation of residuals. The improvements in precision and the predictions of genotypic values produced by the SpATS model were equivalent to those obtained using the best fitting standard spatial models for each trial. One advantage of the approach with SpATS is that all patterns of spatial trend and genetic effects were modelled simultaneously by fitting a single model. Furthermore, we used a flexible model to adequately adjust for field trends. This strategy reduces potential parameter identification problems and simplifies the model selection process. Therefore, the new method should be considered as an efficient and easy-to-use alternative for routine analyses of plant breeding trials.

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Section: Discussionmentioning

confidence: 47%

Section: Introductionmentioning

confidence: 99%

Modelling spatial trends in sorghum breeding field trials using a two-dimensional P-spline mixed model

et al. 2017

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“…We should mention that our approach is not completely new in the agricultural literature. In Taye and Njuho (2008) and Robbins et al (2012) the authors discuss similar approaches in the context of field experiments, and in forest research the topic has been covered by Cappa and Cantet (2008). This paper goes one step further by proposing a fully anisotropic penalized approach framed within the mixed-effects model context.…”

Section: Introductionmentioning

confidence: 99%

Spatial Models for Field Trials

Rodríguez‐Álvarez¹,

Boer²,

Eeuwijk³

et al. 2016

Preprint

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An important aim of the analysis of agricultural field trials is to obtain good predictions for genotypic performance, by correcting for spatial effects. In practice these corrections turn out to be complicated, since there can be different types of spatial effects; those due to management interventions applied to the field plots and those due to various kinds of erratic spatial trends. This paper presents models for field trials in which the random spatial component consists of tensor product Penalized splines (P-splines). A special ANOVA-type reformulation leads to five smooth additive spatial components, which form the basis of a mixed model with five unknown variance components. On top of this spatial field, effects of genotypes, blocks, replicates, and/or other sources of spatial variation are described by a mixed model in a standard way. We show the relation between several definitions of heritability and the effective dimension or the effective degrees of freedom associated to the genetic component. The approach is illustrated with large-scale field trial experiments. An R-package is provided.

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“…However, more complex two-dimensional gradients that do not align well with row and column directions are expected to affect field trials as well. The structure of spatial variation found in our dataset (Figure 2) and in previous studies of agricultural and forest field trials demonstrate that fitting only additive gradients in one dimension may result in insufficient modelling of global trend (Federer 1998;Fu et al 1999;Taye and Njuho 2008). It is in principle possible to extend the standard spatial model with additional fixed terms, like a linear-by-linear interaction term (Federer 1998), and random terms, like a smoothing spline interaction term, but these extensions were never used under the standard approach and are prone to cause problems (Gilmour 2000).…”

Section: Comparison Of Spats and The Standard Method: Parametrizationmentioning

confidence: 50%

“…These studies considered a single smoothing parameter that controls the smoothness of the spatial effects in the direction of both rows and columns, imposing isotropic smoothing. In agricultural experiments, Taye and Njuho (2008) proposed using P-splines in two dimensions to adjust for global trend and to model local variation with Papadakis and kriged covariates. The authors compared P-spline models assuming additive trends or interaction between trends and emphasized the importance of choosing between both model settings.…”

Section: Introductionmentioning

confidence: 99%

Statistical modeling of phenotypic, pedigree and genomic information for improved genetic evaluation in modern plant breeding: a case study with sorghum

Velazco

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Adjustment for spatial trends in plant breeding field trials is essential for efficient evaluation and selection of genotypes. Current mixed model methods of spatial analysis are based on a multi-step modelling process where global and local trends are fitted after trying several candidate spatial models. This paper reports the application of a novel spatial method that accounts for all types of continuous field variation in a single modelling step by fitting a smooth surface. The method uses twodimensional P-splines with anisotropic smoothing formulated in the mixed model framework, referred to as SpATS model. We applied this methodology to a series of large and partially replicated sorghum breeding trials. The new model was assessed in comparison with the more elaborate standard spatial models that use autoregressive correlation of residuals. The improvements in precision and the predictions of genotypic values produced by the SpATS model were equivalent to those obtained using the best fitting standard spatial models for each trial. One advantage of the approach with SpATS is that all patterns of spatial trend and genetic effects were modelled simultaneously by fitting a single model. Furthermore, we used the same flexible model to adequately adjust for field trends in every site and for different traits. This strategy reduces potential parameter identification problems and simplifies the model selection process. Therefore, the new method should be considered as an efficient and easy-to-use alternative for routine analyses of plant breeding trials.

show abstract

Smoothing fertility trends in agricultural field experiments

Cited by 5 publications

References 14 publications

Modelling spatial trends in sorghum breeding field trials using a two-dimensional P-spline mixed model

Modelling spatial trends in sorghum breeding field trials using a two-dimensional P-spline mixed model

Spatial Models for Field Trials

Statistical modeling of phenotypic, pedigree and genomic information for improved genetic evaluation in modern plant breeding: a case study with sorghum

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