Genome-enabled predictions for binomial traits in sugar beet populations
© Biscarini et al.; licensee BioMed Central Ltd. 2014
Received: 7 April 2014
Accepted: 4 July 2014
Published: 22 July 2014
Genomic information can be used to predict not only continuous but also categorical (e.g. binomial) traits. Several traits of interest in human medicine and agriculture present a discrete distribution of phenotypes (e.g. disease status). Root vigor in sugar beet (B. vulgaris) is an example of binomial trait of agronomic importance. In this paper, a panel of 192 SNPs (single nucleotide polymorphisms) was used to genotype 124 sugar beet individual plants from 18 lines, and to classify them as showing “high” or “low” root vigor.
A threshold model was used to fit the relationship between binomial root vigor and SNP genotypes, through the matrix of genomic relationships between individuals in a genomic BLUP (G-BLUP) approach. From a 5-fold cross-validation scheme, 500 testing subsets were generated. The estimated average cross-validation error rate was 0.000731 (0.073%). Only 9 out of 12326 test observations (500 replicates for an average test set size of 24.65) were misclassified.
The estimated prediction accuracy was quite high. Such accurate predictions may be related to the high estimated heritability for root vigor (0.783) and to the few genes with large effect underlying the trait. Despite the sparse SNP panel, there was sufficient within-scaffold LD where SNPs with large effect on root vigor were located to allow for genome-enabled predictions to work.
KeywordsGenomic predictions Binomial traits Root vigor Sugar beet
Most of current research and applications in genetics are driven by the large quantity of data on individual genomic polymorphisms produced by modern high-throughput genotyping and sequencing technologies . A thriving area is that of genomic predictions in animal and plant science and human medicine.
Genomic data are used to predict future or unobserved events (e.g. disease risk ), or the unknown genetic component of given phenotypes (e.g. GEBVs -genomic breeding values- in livestock, crops and trees [3–5]). Such predictions are based on the entire available genomic information, irrespective of the position along the genome or point effects on the response. This ingenious and highly effective “black box” approach was conceived and first described by Meuwissen et al. around the turn of the millennium  and has since then found several applications and started fruitful areas of research.
Genomic information can in principle be used to predict continuous or categorical (ordered or unordered) polygenic traits. Most works so far focussed on continuous traits, while fewer studies dealt with genomic predictions for categorical traits [7–11]. However, several traits of interest in human medicine and agriculture present a discrete distribution of phenotypes (e.g. litter size in mammals), often binomial (e.g. disease status). Statistical methods used for genomic predictions of continuous traits cannot be adequately applied for such traits: the relationship between predictors and binomial phenotypes is logistic rather than linear; the phenotypes follow a binomial rather than normal distribution; the variance is no longer constant but a function of the expectation . Root vigor in sugar beet (B. vulgaris) is an example of binomial trait of agronomic importance.
In this paper, SNP (single nucleotide polymorphisms) genotypes were used for the classification problem of predicting “high” or “low” root vigor inidividual plants in sugar beet.
Pioneering works on genomic predictions for continuous traits in sugar beet already exist [13, 14]. However, this is the first study to propose direct modeling of genomic predictions for binomial traits in sugar beet and, to our knowledge, among the few to address this problem in plants in general.
A population of 124 individual sugar beet (B. vulgaris) plants from 18 high- and low-root-vigor lines were available. These lines were characterised by different productivity and were provided by Lion Seeds Ltd. (UK). Root vigor is related to nutrient uptake from the soil and plant productivity , and is recorded as a binary trait (either high or low). The lines were phenotyped by measuring the root elongation rate of eleven-days-old seedlings grown under hydroponic conditions. There was no predetermined root elongation rate threshold to classify a sugar beet as having high or low root vigour, and the decision was subjectively made upon phenotypic inspection. The classification has nevertheless been shown to be robust: seedlings classified as “low” or “high” maintain the same class also at the adult plant stage . There were three low-root-vigor (24 individuals) and 15 high-root-vigor (100 individuals) lines. Root elongation rate was < 3 mm/day in the low-root-vigor lines and > 6 mm/day in the high-root-vigor lines.
Marker genotypes and imputation
All individual plants were genotyped for 192 SNP markers with the high-throughput marker array QuantStudio 12K Flex system coupled with Taqman OpenArray technology. Additional details on the genotyping procedure are described in Stevanato et al., 2013 .
Description of the experimental population and SNP marker genotypes
N. plant samples
N. sugar beet lines
N. of SNP call-rate ≤ 85%
N. SNPs MAF ≤ 2.5%
N. SNPs MAF ≥ 2.5%
Per-chromosome distribution of scaffolds and SNPs along the Beta vulgaris genome (“-” indicates scaffolds and SNPs not yet assigned to chromosomes)
Marker genotypes can be used for genome-enabled predictions either by directly estimating and summing their effects over all loci (Ridge Regression BLUP - RR-BLUP) or, indirectly, through the estimation of realized relationships between individuals (genomic BLUP - G-BLUP). These are two different parametrizations of the genomic selection model described in Meuwissen et al. . The two approaches have been shown to be equivalent [18, 19].
where G is the matrix of genomic relationships, Z is the matrix of centered SNP genotypes per individual (-1, 0 or 1 for the homozygous, heterozygous and other homozygous respectively), and p i is the allele frequency at SNP i. Genomic relationships were used to model covariances between observations and to evaluate the genetic structure of the population.
Low and high root vigor (coded as 0 and 1 respectively) phenotypes were the input of model 2, which returned a probability (for individuals with known or unknown phenotype) of belonging to either class. The probability of classifying each observation i into high- or low-root-vigor plant was obtained from the cumulative distribution function of the logistic distribution (i.e. the logistic function: ). Individuals were classified as high-/low-root vigour if p i >/≤ 0.5.
The programme Beagle was used to impute missing genotypes . The computer package for linear mixed models Asreml was used to fit the threshold model in (2) and estimate variance components . Genomic relationships between plants were estimated with “ad hoc” Python code. Data preparation and figures were produced with the open source statistical environment R.
Heritability and classification
Model fit was evaluated comparing the full (model (2)) and the reduced (null model: the intercept only) models through a likelihood ratio test. Deviance dropped significantly (p-value ≈0), showing good fit of the model. The estimated genetic variance was 11.856, on the liability scale. From Eq. 3 heritability was then estimated as h2 = 0.783, with a standard error of 0.086.
From cross-validation, 500 testing subsets were generated. In each of these, observations were classified according to the model fitted to the corresponding training subset, and the classification error calculated as in (4), then averaged over all subsets. The estimated cross-validation error rate from (5) was 0.000731 (0.073%). Only 9 out of 12326 test observations (500 replicates for an average test set size of 24.65) were wrongly classified. All 9 missclassified observations belonged to a single low-root vigor line (line “LOW1”).
In this paper, the problem of classifying binomial phenotypes using SNP markers in sugar beet (B. vulgaris) has been addressed. A very low cross-validation test error rate (<1%) was estimated for the genome-based classification of root vigor in sugar beet lines. Genomic predictions with different accuracies have been reported in literature: high (e.g. 0.89 for soluble solids content in apple trees ; 0.92 for fat and protein percentage in cattle ), moderate (e.g. ≈ 0.60 for egg weight in laying hens ) and low (e.g. 0.38 for stem height in loblolly pines ) accuracy of prediction. Wang et al. () reported accuracies ranging from 0.17 to 0.69 for a simulated categorical trait. In sugar beet, moderate to high prediction accuracies were estimated for a number of traits such as sugar content, molasses loss, root yield and mineral (Na, K) content [13, 14].
The few prediction errors were all observed in line “LOW1”. This line had the strongest off-diagonal genomic relationship with line “HIGH1”. “LOW1” and “HIGH1” differ for root vigor (and related genes) but share most of their genetic basis. The close relationship of “LOW1” to “HIGH1” (a high root vigor line) may well explain why all 9 misclassifications were observed in this line, considering that SNP genotypes -through the genomic relationship matrix- were used as predictors. The error rate in line “LOW1” was nonetheless very low (∼1.1%).
The accuracy of genomic predictions is known to depend on a number of factors related to the nature of the analysed trait (e.g. heritability ) and to the experimental population at hand (e.g. sample size, number of markers, relatedness between the training and validation sets [3, 27]).
Some relevant aspects are discussed below.
Genetic architecture of the trait
The high predictive ability for root vigor estimated in this study (>99% of correct classifications) may be related to the heritability of the trait and to the number of segregating QTL underlying its expression: this is sometimes referred to as the “genetic architecture” of the trait .
The extent of linkage disequilibrium (LD) in the experimental population is a parameter relevant to the success of genomic predictions. The basic assumption underlying genome-wide predictions is indeed that observed genetic markers and unobserved QTLs are in LD . LD between adjacent markers of around 0.2 -measured as r2- is deemed to be required for reliable genomic predictions . Dense marker panels ensure that there is sufficient LD between markers. With sparser panels this may not be the case. The available release of the B. vulgaris genome was not assembled in chromosomes, but organised in 82305 scaffolds (and contigs). The sugar beet genome sequence comprises 567 Mbps of which 85% could be assigned to chromosomes . Most scaffolds -but not all- could therefore be mapped to chromosomes; however, the relative position of the scaffolds along the chromosomes was not known. Therefore, pairwise LD between adjacent SNPs could be estimated only within scaffold.
Imputing missing genotypes is usually a preliminary step to the analysis of genomic data. After markers and individuals with low call-rate are edited out, there is usually still a small proportion of uncalled genotypes (e.g. < 5%) randomly distributed along the genome. Such missing genotypes are imputed using pedigree-based or pedigree-free methods. Imputation accuracy is typically very high; for instance, >95% correctly imputed genotypes were reported in maize  and cattle . This usually applies to scenarios in which moderate to high density marker panels are available. With fewer markers genotype imputation may be less accurate, as a consequence of lower LD. This may be especially true for pedigree-free imputation methods, which rely heavily on between marker LD.
Imputation accuracy with increasing proportions of missing genotypes
Comparison with another classification method
The threshold model used in this study for genome-enabled prediction of the binary trait root vigor in sugar beet was compared with Support Vector Machine (SVM), another widely adopted method for classification of categorical observations [20, 33].
The kernel function and tuning parameter C to be used in SVM were chosen so to minimize the classification error through 5-fold cross-validation. A linear kernel (, for individual plant i and p parameters) and C=0.01 were chosen and used to classify sugar beet individual plants with SVM in the same cross-validation procedure adopted for the threshold model (5-fold, 100 repetitions). The estimated error rate was close to zero (0.025%), in line with what was obtained with the threshold model (0.073%). The two classifiers were compared also by looking at the ROC curves : the two curves overlapped almost completely, having both an area under the curve (AUC) close to 1 (∼0.98). This shows that with both classifiers the total error rate and the number of false positives and false negatives were very low.
Applications to sugar beet breeding
Root vigor, expressed as high root elongation rate, is essential for the efficient acquisition of mobile soil nutrients ; this is especially true in presence of water-nutritional stress . The increased root elongation rate in response to low water availability or nutrient deprivation allow plants to circumvent water or nutrients limitations . Of all sugar beet morphological root traits, root elongation rate shows the largest variation between high- and low-yielding genotypes and was shown to be significantly correlated with sugar beet yield .
Root traits are difficult to be measured accurately and this is an obstacle to reliable and effective selection. Genomic data can be used for early and accurate prediction of root vigor in sugar beet seeds, thereby enhancing the efficiency of breeding for rhizospheric stress tolerance and yield in sugar beet. Improvements are likely to come from shortened breeding cycles and more accurate and less expensive phenotypic evaluation.
In this paper, the use of genomic information to predict a binomially distributed phenotype (root vigor) in sugar beet populations was presented. Prediction accuracy proved to be quite high, with an estimated cross-validation error rate close to zero (0.073%). Such excellent prediction performance may be related to properties of the analysed trait and available population. Root vigor was estimated to have high heritability (0.783) and to be determined by few genes with large effect. Despite the sparse SNP panel, there was sufficient within-scaffold LD where SNPs with large effect on root vigor were located. For an oligogenic highly heritable trait with a favorable distribution of markers on the genome, even with relatively few SNPs very accurate predictions can be achieved. The results described in this paper constitute an interesting application of genomic predictions to binomial (and more generally categorical/multinomial) traits, and may lead to promising applications of genomic selection in sugar beet breeding programmes.
This research was financially supported by the Marie Curie European Reintegration Grant “NEUTRADAPT”.
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