Predicting complex traits using a diffusion kernel on genetic markers with an application to dairy cattle and wheat data

Abstract

BackgroundArguably, genotypes and phenotypes may be linked in functional forms that are not well addressed by the linear additive models that are standard in quantitative genetics. Therefore, developing statistical learning models for predicting phenotypic values from all available molecular information that are capable of capturing complex genetic network architectures is of great importance. Bayesian kernel ridge regression is a non-parametric prediction model proposed for this purpose. Its essence is to create a spatial distance-based relationship matrix called a kernel. Although the set of all single nucleotide polymorphism genotype configurations on which a model is built is finite, past research has mainly used a Gaussian kernel.ResultsWe sought to investigate the performance of a diffusion kernel, which was specifically developed to model discrete marker inputs, using Holstein cattle and wheat data. This kernel can be viewed as a discretization of the Gaussian kernel. The predictive ability of the diffusion kernel was similar to that of non-spatial distance-based additive genomic relationship kernels in the Holstein data, but outperformed the latter in the wheat data. However, the difference in performance between the diffusion and Gaussian kernels was negligible.ConclusionsIt is concluded that the ability of a diffusion kernel to capture the total genetic variance is not better than that of a Gaussian kernel, at least for these data. Although the diffusion kernel as a choice of basis function may have potential for use in whole-genome prediction, our results imply that embedding genetic markers into a non-Euclidean metric space has very small impact on prediction. Our results suggest that use of the black box Gaussian kernel is justified, given its connection to the diffusion kernel and its similar predictive performance.

Kernel-based whole-genome prediction of complex traits: a review

“…Since BLUP is linearly invariant, the BLUP of α is given by = A −1 * = A −1 ( A + λ I ) −1 y . This is equivalent to Equation (6) and is the Bayesian kernel ridge regression employed in de los Campos et al ( 2010 ) and Morota et al ( 2013 ). Thus, BLUP of additive effects can be viewed as a regression on pedigree or on additive genomic relationship kernels.…”

“…Characterizing the metric space governed by these SNP predictors prior to the analysis is of importance in a spatial prediction problem. Recently, Morota et al ( 2013 ) used SNP codes as coordinates of genotypes in m -dimensional spaces. Therein, an m -dimensional grid graph with vertices representing a vector of individual's genotypes was proposed as a spatial structure of genotypes.…”

“…The diffusion kernel, which is a discretized Gaussian kernel, can be viewed as functions on discrete spaces, such as a graph. Morota et al ( 2013 ) employed the SNP grid kernel, that is, the diffusion kernel specifically developed to model SNP data distributed on a grid graph, as described earlier. This measures how similar two vertices are in terms of Manhattan distance on an m -dimensional grid graph.…”

“…where d ( x , x ′) is the Hamming distance, that is, number of coordinates at which x and x ′ differ. Morota et al ( 2013 ) evaluated the performance of the diffusion and of the Gaussian kernels using dairy cattle and wheat line data. It turned out that differences in predictive ability were negligible, suggesting that the simple Gaussian kernel is very robust.…”

Applications of Population Genetics to Animal Breeding, from Wright, Fisher and Lush to Genomic Prediction

“…As a linear model is not fitted, such predictions also incorporate any epistatic interactions. Methods have been discussed by Gianola and colleagues, and in a study comparing linear and nonparametric approaches for dairy and wheat data, the nonparametric method gave more accurate predictions (Morota et al 2013). A weakness of this approach seems, however, to be that as a linear additive model is not used in the analysis, predicted breeding value of unselected offspring cannot be assumed to be simply half that of the parent.…”