Genotype-by-environment interactions and local adaptation shape selection in the US National Chip Processing Trial.

KEY MESSAGE: We find evidence of selection for local adaptation and extensive genotype-by-environment interaction in the potato National Chip Processing Trial (NCPT). We present a novel method for dissecting the interplay between selection, local adaptation and environmental response in plant breeding schemes. Balancing local adaptation and the desire for widely adapted cultivars is challenging for plant breeders and makes genotype-by-environment interactions (GxE) an important target of selection. Selecting for GxE requires plant breeders to evaluate plants across multiple environments. One way breeders have accomplished this is to test advanced materials across many locations. Public potato breeders test advanced breeding material in the National Chip Processing Trial (NCPT), a public-private partnership where breeders from ten institutions submit advanced chip lines to be evaluated in up to ten locations across the country. These clones are genotyped and phenotyped for important agronomic traits. We used these data to interrogate the NCPT for GxE. Further, because breeders submitting clones to the NCPT select in a relatively small geographic range for the first 3 years of selection, we examined these data for evidence of incidental selection for local adaptation, and the alleles underlying it, using an environmental genome-wide association study (envGWAS). We found genomic regions associated with continuous environmental variables and discrete breeding programs, as well as regions of the genome potentially underlying GxE for yield.

Epigenetic Modifications Related to Potato Skin Russeting.

Potato tuber skin is a protective corky tissue consisting of suberized phellem cells. Smooth-skinned varieties are characterized by a clean, shiny appearance compared to the darker hue of russeted potatoes. The rough skin of russeted cultivars is a desired, genetically inherited characteristic; however, unwanted russeting of smooth-skinned cultivars often occurs under suboptimal growth conditions. The involvement of epigenetic modifiers in regulating the smooth skin russeting disorder was tested. We used smooth-skin commercial cultivars with and without the russeting disorder and three lines from a breeding population segregating for russeting. Anatomically, the russet skin showed similar characteristics, whether the cause was environmentally triggered or genetically determined. The old outer layers of the corky phellem remain attached to the newly formed phellem layers instead of being sloughed off. Global DNA methylation analysis indicated a significant reduction in the percentage of 5-methylcytosine in mature vs. immature skin and russet vs. smooth skin. This was true for both the smooth-skin commercial cultivars and the russeted lines. The expression level of selected DNA methyltransferases was reduced in accordance. DNA demethylase expression did not change between the skin types and age. Hence, the reduced DNA methylation in mature and russet skin is more likely to be achieved through passive DNA demethylation and loss of methyltransferase activity.

Clonal diploid and autopolyploid breeding strategies to harness heterosis: insights from stochastic simulation.

KEY MESSAGE: Reciprocal recurrent selection sometimes increases genetic gain per unit cost in clonal diploids with heterosis due to dominance, but it typically does not benefit autopolyploids. Breeding can change the dominance as well as additive genetic value of populations, thus utilizing heterosis. A common hybrid breeding strategy is reciprocal recurrent selection (RRS), in which parents of hybrids are typically recycled within pools based on general combining ability. However, the relative performances of RRS and other breeding strategies have not been thoroughly compared. RRS can have relatively increased costs and longer cycle lengths, but these are sometimes outweighed by its ability to harness heterosis due to dominance. Here, we used stochastic simulation to compare genetic gain per unit cost of RRS, terminal crossing, recurrent selection on breeding value, and recurrent selection on cross performance considering different amounts of population heterosis due to dominance, relative cycle lengths, time horizons, estimation methods, selection intensities, and ploidy levels. In diploids with phenotypic selection at high intensity, whether RRS was the optimal breeding strategy depended on the initial population heterosis. However, in diploids with rapid-cycling genomic selection at high intensity, RRS was the optimal breeding strategy after 50 years over almost all amounts of initial population heterosis under the study assumptions. Diploid RRS required more population heterosis to outperform other strategies as its relative cycle length increased and as selection intensity and time horizon decreased. The optimal strategy depended on selection intensity, a proxy for inbreeding rate. Use of diploid fully inbred parents vs. outbred parents with RRS typically did not affect genetic gain. In autopolyploids, RRS typically did not outperform one-pool strategies regardless of the initial population heterosis.

Using haplotype and QTL analysis to fix favorable alleles in diploid potato breeding.

At present, the potato (Solanum tuberosum L.) of international commerce is autotetraploid, and the complexity of this genetic system creates limitations for breeding. Diploid potato breeding has long been used for population improvement, and because of an improved understanding of the genetics of gametophytic self-incompatibility, there is now sustained interest in the development of uniform F1 hybrid varieties based on inbred parents. We report here on the use of haplotype and quantitative trait locus (QTL) analysis in a modified backcrossing (BC) scheme, using primary dihaploids of S. tuberosum as the recurrent parental background. In Cycle 1, we selected XD3-36, a self-fertile F2 individual homozygous for the self-compatibility gene Sli (S-locus inhibitor). Signatures of gametic and zygotic selection were observed at multiple loci in the F2 generation, including Sli. In the BC1 cycle, an F1 population derived from XD3-36 showed a bimodal response for vine maturity, which led to the identification of late versus early alleles in XD3-36 for the gene CDF1 (Cycling DOF Factor 1). Greenhouse phenotypes and haplotype analysis were used to select a vigorous and self-fertile F2 individual with 43% homozygosity, including for Sli and the early-maturing allele CDF1.3. Partially inbred lines from the BC1 and BC2 cycles have been used to initiate new cycles of selection, with the goal of reaching higher homozygosity while maintaining plant vigor, fertility, and yield.

Fully efficient, two-stage analysis of multi-environment trials with directional dominance and multi-trait genomic selection.

KEY MESSAGE: R/StageWise enables fully efficient, two-stage analysis of multi-environment, multi-trait datasets for genomic selection, including support for dominance heterosis and polyploidy. Plant breeders interested in genomic selection often face challenges to fully utilizing multi-trait, multi-environment datasets. R package StageWise was developed to go beyond the capabilities of most specialized software for genomic prediction, without requiring the programming skills needed for more general-purpose software for mixed models. As the name suggests, one of the core features is a fully efficient, two-stage analysis for multiple environments, in which the full variance-covariance matrix of the Stage 1 genotype means is used in Stage 2. Another feature is directional dominance, including for polyploids, to account for inbreeding depression in outbred crops. StageWise enables selection with multi-trait indices, including restricted indices with one or more traits constrained to have zero response. For a potato dataset with 943 genotypes evaluated over 6 years, including the Stage 1 errors in Stage 2 reduced the Akaike Information Criterion (AIC) by 29, 67, and 104 for maturity, yield, and fry color, respectively. The proportion of variation explained by heterosis was largest for yield but still only 0.03, likely because of limited variation for the genomic inbreeding coefficient. Due to the large additive genetic correlation (0.57) between yield and maturity, naïve selection on an index combining yield and fry color led to an undesirable response for later maturity. The restricted index coefficients to maximize genetic merit without delaying maturity were identified. The software and three vignettes are available at https://github.com/jendelman/StageWise .

Genomic selection and genome-wide association studies in tetraploid chipping potatoes.

Potato is a major food crop in the United States and around the world. Most potatoes grown in the United States are destined for processing. Genomic selection can speed up breeding progress for important traits, including those with complex inheritance by guiding the identification of the best parents and guiding selection to advance clones in the breeding program. However, the application of genomic selection in polyploid species has been challenging. In this study, we obtained breeding values of 384 chipping clones evaluated in Texas between 2017 and 2020. The mean reliability of the genomic-estimated breeding values obtained were 0.77, 0.41, 0.61, 0.71, and 0.24 for chip color, chip quality, specific gravity, vine maturity, and total yield, respectively. Potato clones with good chip quality, high yield, high specific gravity, and light-color chips were identified using a multi-trait selection index based on weighted standardized genomic-estimated breeding values. Genome-wide association studies identified quantitative trait loci on chromosome 5 for vine maturity and chromosomes 1, 3, and 7 for chip color. This research has laid the groundwork for implementing genomic selection in tetraploid potato breeding and understanding the genetic basis of chip processing traits in potatoes.

The genetic architectures of vine and skin maturity in tetraploid potato.

KEY MESSAGE: The genetic architectures of potato vine and skin maturity, as well as the correlation between the traits, were investigated using multiple techniques from quantitative genetics and genomics. Potato vine and skin maturity, which refer to foliar senescence and adherence of the tuber periderm, respectively, are both important to production and therefore breeding. Our objective was to investigate the genetic architectures of these traits in a genome-wide association panel of 586 genotypes, and through joint linkage mapping in a half-diallel subset (N = 397). Skin maturity was measured by image analysis after mechanized harvest 120 days after planting. To correct for the influence of vine maturity on skin maturity under these conditions, the former was used as a covariate in the analysis. The genomic heritability based on a 10 K SNP array was 0.33 for skin maturity vs. 0.46 for vine maturity. Only minor QTLs were detected for skin maturity, the largest being on chromosome 9 and explaining 8% of the variation. As in many previous studies, S. tuberosum Cycling DOF Factor 1 (CDF1) had a large influence on vine maturity, explaining 33% of the variation in the panel as a bi-allelic SNP and 44% in the half-diallel as a multi-allelic QTL. From the estimated effects of the parental haplotypes in the half-diallel and prior knowledge of the allelic series for CDF1, the CDF1 allele for each haplotype was predicted and ultimately confirmed through whole-genome sequencing. The ability to connect statistical alleles from QTL models with biological alleles based on DNA sequencing represents a new milestone in genomics-assisted breeding for tetraploid species.

Phased, chromosome-scale genome assemblies of tetraploid potato reveal a complex genome, transcriptome, and predicted proteome landscape underpinning genetic diversity.

Cultivated potato is a clonally propagated autotetraploid species with a highly heterogeneous genome. Phased assemblies of six cultivars including two chromosome-scale phased genome assemblies revealed extensive allelic diversity, including altered coding and transcript sequences, preferential allele expression, and structural variation that collectively result in a highly complex transcriptome and predicted proteome, which are distributed across the homologous chromosomes. Wild species contribute to the extensive allelic diversity in tetraploid cultivars, demonstrating ancestral introgressions predating modern breeding efforts. As a clonally propagated autotetraploid that undergoes limited meiosis, dysfunctional and deleterious alleles are not purged in tetraploid potato. Nearly a quarter of the loci bore mutations are predicted to have a high negative impact on protein function, complicating breeder's efforts to reduce genetic load. The StCDF1 locus controls maturity, and analysis of six tetraploid genomes revealed that 12 allelic variants of StCDF1 are correlated with maturity in a dosage-dependent manner. Knowledge of the complexity of the tetraploid potato genome with its rampant structural variation and embedded deleterious and dysfunctional alleles will be key not only to implementing precision breeding of tetraploid cultivars but also to the construction of homozygous, diploid potato germplasm containing favorable alleles to capitalize on heterosis in F1 hybrids.

Haplotype reconstruction in connected tetraploid F1 populations.

In diploid species, many multiparental populations have been developed to increase genetic diversity and quantitative trait loci (QTL) mapping resolution. In these populations, haplotype reconstruction has been used as a standard practice to increase the power of QTL detection in comparison with the marker-based association analysis. However, such software tools for polyploid species are few and limited to a single biparental F1 population. In this study, a statistical framework for haplotype reconstruction has been developed and implemented in the software PolyOrigin for connected tetraploid F1 populations with shared parents, regardless of the number of parents or mating design. Given a genetic or physical map of markers, PolyOrigin first phases parental genotypes, then refines the input marker map, and finally reconstructs offspring haplotypes. PolyOrigin can utilize single nucleotide polymorphism (SNP) data coming from arrays or from sequence-based genotyping; in the latter case, bi-allelic read counts can be used (and are preferred) as input data to minimize the influence of genotype calling errors at low depth. With extensive simulation we show that PolyOrigin is robust to the errors in the input genotypic data and marker map. It works well for various population designs with ≥30 offspring per parent and for sequences with read depth as low as 10x. PolyOrigin was further evaluated using an autotetraploid potato dataset with a 3 × 3 half-diallel mating design. In conclusion, PolyOrigin opens up exciting new possibilities for haplotype analysis in tetraploid breeding populations.

QTL mapping in outbred tetraploid (and diploid) diallel populations.

Over the last decade, multiparental populations have become a mainstay of genetics research in diploid species. Our goal was to extend this paradigm to autotetraploids by developing software for quantitative trait locus (QTL) mapping in connected F1 populations derived from a set of shared parents. For QTL discovery, phenotypes are regressed on the dosage of parental haplotypes to estimate additive effects. Statistical properties of the model were explored by simulating half-diallel diploid and tetraploid populations with different population sizes and numbers of parents. Across scenarios, the number of progeny per parental haplotype (pph) largely determined the statistical power for QTL detection and accuracy of the estimated haplotype effects. Multiallelic QTL with heritability 0.2 were detected with 90% probability at 25 pph and genome-wide significance level 0.05, and the additive haplotype effects were estimated with over 90% accuracy. Following QTL discovery, the software enables a comparison of models with multiple QTL and nonadditive effects. To illustrate, we analyzed potato tuber shape in a half-diallel population with three tetraploid parents. A well-known QTL on chromosome 10 was detected, for which the inclusion of digenic dominance lowered the Deviance Information Criterion (DIC) by 17 points compared to the additive model. The final model also contained a minor QTL on chromosome 1, but higher-order dominance and epistatic effects were excluded based on the DIC. In terms of practical impacts, the software is already being used to select offspring based on the effect and dosage of particular haplotypes in breeding programs.

Genomic Prediction of Autotetraploids; Influence of Relationship Matrices, Allele Dosage, and Continuous Genotyping Calls in Phenotype Prediction.

Estimation of allele dosage, using genomic data, in autopolyploids is challenging and current methods often result in the misclassification of genotypes. Some progress has been made when using SNP arrays, but the major challenge is when using next generation sequencing data. Here we compare the use of read depth as continuous parameterization with ploidy parameterizations in the context of genomic selection (GS). Additionally, different sources of information to build relationship matrices were compared. A real breeding population of the autotetraploid species blueberry (Vaccinium corybosum), composed of 1,847 individuals was phenotyped for eight yield and fruit quality traits over two years. Continuous genotypic based models performed as well as the best models. This approach also reduces the computational time and avoids problems associated with misclassification of genotypic classes when assigning dosage in polyploid species. This approach could be very valuable for species with higher ploidy levels or for emerging crops where ploidy is not well understood. To our knowledge, this work constitutes the first study of genomic selection in blueberry. Accuracies are encouraging for application of GS for blueberry breeding. GS could reduce the time for cultivar release by three years, increasing the genetic gain per cycle by 86% on average when compared to phenotypic selection, and 32% when compared with pedigree-based selection. Finally, the genotypic and phenotypic data used in this study are made available for comparative analysis of dosage calling and genomic selection prediction models in the context of autopolyploids.

Expected Genotype Quality and Diploidized Marker Data from Genotyping-by-Sequencing of Urochloa spp. Tetraploids.

CORE IDEAS: Introduced concept of expected genotype quality (EGQ) and software to calculate it Provided read depth guidelines for GBS in tetraploids Developed software to generate diploidized genotype calls from VCF files Demonstrated value of aligning GBS reads to a mock reference genome for SNP discovery Recommend filtering based on GQ and read depth to prevent genotype bias Although genotyping-by-sequencing (GBS) is a well-established marker technology in diploids, the development of best practices for tetraploid species is a topic of current research. We determined the theoretical relationship between read depth and the phred-scaled probability of genotype misclassification conditioned on the true genotype, which we call expected genotype quality (EGQ). If the GBS method has 0.5% allelic error, then 17 reads are needed to classify simplex tetraploids as heterozygous with 95% accuracy (EGQ = 13) vs. 61 reads to determine allele dosage. We developed an R script to convert tetraploid GBS data in variant call format (VCF) into diploidized genotype calls and applied it to 267 interspecific hybrids of the tetraploid forage grass Urochloa. When reads were aligned to a mock reference genome created from GBS data of the Urochloa brizantha (Hochst. ex A. Rich.) R. D. Webster cultivar Marandu, 25,678 biallelic single nucleotide polymorphism (SNPs) were discovered, compared with ∼3000 SNPs when aligning to the closest true reference genomes, Setaria viridis (L.) P. Beauv. and S. italica (L.) P. Beauv. Cross-validation revealed that missing genotypes were imputed by the random forest method with a median accuracy of 0.85 regardless of heterozygote frequency. Using the Urochloa spp. hybrids, we illustrated how filtering samples based only on genotype quality (GQ) creates genotype bias; a depth threshold based on EGQ is also needed regardless of whether genotypes are called using a diploidized or allele dosage model.

Genetic Variance Partitioning and Genome-Wide Prediction with Allele Dosage Information in Autotetraploid Potato.

As one of the world's most important food crops, the potato (Solanum tuberosum L.) has spurred innovation in autotetraploid genetics, including in the use of SNP arrays to determine allele dosage at thousands of markers. By combining genotype and pedigree information with phenotype data for economically important traits, the objectives of this study were to (1) partition the genetic variance into additive vs. nonadditive components, and (2) determine the accuracy of genome-wide prediction. Between 2012 and 2017, a training population of 571 clones was evaluated for total yield, specific gravity, and chip fry color. Genomic covariance matrices for additive (G), digenic dominant (D), and additive × additive epistatic (G#G) effects were calculated using 3895 markers, and the numerator relationship matrix (A) was calculated from a 13-generation pedigree. Based on model fit and prediction accuracy, mixed model analysis with G was superior to A for yield and fry color but not specific gravity. The amount of additive genetic variance captured by markers was 20% of the total genetic variance for specific gravity, compared to 45% for yield and fry color. Within the training population, including nonadditive effects improved accuracy and/or bias for all three traits when predicting total genotypic value. When six F1 populations were used for validation, prediction accuracy ranged from 0.06 to 0.63 and was consistently lower (0.13 on average) without allele dosage information. We conclude that genome-wide prediction is feasible in potato and that it will improve selection for breeding value given the substantial amount of nonadditive genetic variance in elite germplasm.

Automated tetraploid genotype calling by hierarchical clustering.

KEY MESSAGE: New software to make tetraploid genotype calls from SNP array data was developed, which uses hierarchical clustering and multiple F1 populations to calibrate the relationship between signal intensity and allele dosage. SNP arrays are transforming breeding and genetics research for autotetraploids. To fully utilize these arrays, the relationship between signal intensity and allele dosage must be calibrated for each marker. We developed an improved computational method to automate this process, which is provided as the R package ClusterCall. In the training phase of the algorithm, hierarchical clustering within an F1 population is used to group samples with similar intensity values, and allele dosages are assigned to clusters based on expected segregation ratios. In the prediction phase, multiple F1 populations and the prediction set are clustered together, and the genotype for each cluster is the mode of the training set samples. A concordance metric, defined as the proportion of training set samples equal to the mode, can be used to eliminate unreliable markers and compare different algorithms. Across three potato families genotyped with an 8K SNP array, ClusterCall scored 5729 markers with at least 0.95 concordance (94.6% of its total), compared to 5325 with the software fitTetra (82.5% of its total). The three families were used to predict genotypes for 5218 SNPs in the SolCAP diversity panel, compared with 3521 SNPs in a previous study in which genotypes were called manually. One of the additional markers produced a significant association for vine maturity near a well-known causal locus on chromosome 5. In conclusion, when multiple F1 populations are available, ClusterCall is an efficient method for accurate, autotetraploid genotype calling that enables the use of SNP data for research and plant breeding.

Quantitative Trait Loci for Resistance to Common Scab and Cold-Induced Sweetening in Diploid Potato.

The development of germplasm with resistance to common scab and cold-induced sweetening is a high priority for the potato ( L.) industry. A mapping population was developed from mating two individuals of a diploid family generated by crossing the susceptible cultivated potato clone US-W4 to the highly resistant wild relative ( Bitter) clone '524-8'. Progeny were evaluated in replicated field trials. Tubers were scored for percentage of surface area with scab lesions, scab lesion type, cold-induced sweetening, average tuber weight, and dry matter. Plants were evaluated for vine maturity. A genetic map was constructed, quantitative trait loci (QTLs) were identified, and the gene action of significant QTLs was characterized using 1606 single nucleotide polymorphisms (SNPs). Significant QTLs for common scab percentage of surface area covered with lesions and lesion type were identified in overlapping regions on chromosome 11 ( = 21.0 and 18.2%, respectively). Quantitative trait loci were identified on chromosomes 4 ( = 17.1%) and 6 ( = 19.4%) for cold-induced sweetening, chromosome 5 for maturity ( = 29.8%), and chromosome 1 ( = 26.3 and 22.0%) for average tuber weight. Identification of QTLs is the first step toward developing molecular markers for breeders to efficiently integrate these desirable traits into cultivars.

Software for Genome-Wide Association Studies in Autopolyploids and Its Application to Potato.

Genome-wide association studies (GWAS) are widely used in diploid species to study complex traits in diversity and breeding populations, but GWAS software tailored to autopolyploids is lacking. The objectives of this research were to (i) develop an R package for autopolyploids based on the + mixed model, (ii) validate the software with simulated data, and (iii) analyze a diversity panel of tetraploid potatoes. A unique feature of the R package, called GWASpoly, is its ability to model different types of polyploid gene action, including additive, simplex dominant, and duplex dominant. Using a simulated tetraploid population, we confirmed our hypothesis that statistical power is higher when the assumed gene action in the GWAS model matches the gene action at unobserved quantitative trait loci (QTL). Thirteen traits were analyzed in the Solanaceae Coordinated Agricultural Project (SolCAP) potato diversity panel and, consistent with previous studies, significant QTL for tuber shape and eye depth co-localized on chromosome 10. For the other traits, only marginally significant QTL were detected, most likely due to insufficient statistical power: for simulated traits with a heritability () of 0.3, the median genome-wide power was only 0.01. Our results indicate that both marker density and population size were limiting factors for GWAS with the SolCAP panel.

Genetic mapping with an inbred line-derived F2 population in potato.

KEY MESSAGE: This is the first report of the production and use of a diploid inbred line-based F2 population for genetic mapping in potato. Potato (Solanum tuberosum L.) is an important global food crop, for which tetrasomic inheritance and self-incompatibility have limited both genetic discovery and breeding gains. We report here on the creation of the first diploid inbred line-derived F2 population in potato, and demonstrate its utility for genetic mapping. To create the population, the doubled monoploid potato DM1-3 was crossed as a female to M6, an S7 inbred line derived from the wild relative S. chacoense, and a single F1 plant was then self-pollinated. A genetic linkage map with 2264 single nucleotide polymorphisms was constructed and used to improve the physical anchoring of superscaffolds in the potato reference genome, which is based on DM1-3. Segregation was observed for skin and flesh color, skin and flesh pigment intensity, tuber shape, anther development, jelly end, and the presence of eye tubers instead of normal sprouts. Using the R/qtl software, we detected 10 genes, 7 of which have been previously mapped and 3 for which this is the first publication. The latter category includes tightly linked genes for the jelly end and eye tuber traits on chromosome 5. The development of recombinant inbred lines from this F2 population by single-seed descent is underway and should facilitate even better resolution of these and other loci.

The USDA barley core collection: genetic diversity, population structure, and potential for genome-wide association studies.

New sources of genetic diversity must be incorporated into plant breeding programs if they are to continue increasing grain yield and quality, and tolerance to abiotic and biotic stresses. Germplasm collections provide a source of genetic and phenotypic diversity, but characterization of these resources is required to increase their utility for breeding programs. We used a barley SNP iSelect platform with 7,842 SNPs to genotype 2,417 barley accessions sampled from the USDA National Small Grains Collection of 33,176 accessions. Most of the accessions in this core collection are categorized as landraces or cultivars/breeding lines and were obtained from more than 100 countries. Both STRUCTURE and principal component analysis identified five major subpopulations within the core collection, mainly differentiated by geographical origin and spike row number (an inflorescence architecture trait). Different patterns of linkage disequilibrium (LD) were found across the barley genome and many regions of high LD contained traits involved in domestication and breeding selection. The genotype data were used to define 'mini-core' sets of accessions capturing the majority of the allelic diversity present in the core collection. These 'mini-core' sets can be used for evaluating traits that are difficult or expensive to score. Genome-wide association studies (GWAS) of 'hull cover', 'spike row number', and 'heading date' demonstrate the utility of the core collection for locating genetic factors determining important phenotypes. The GWAS results were referenced to a new barley consensus map containing 5,665 SNPs. Our results demonstrate that GWAS and high-density SNP genotyping are effective tools for plant breeders interested in accessing genetic diversity in large germplasm collections.

LPmerge: an R package for merging genetic maps by linear programming.

UNLABELLED: Consensus genetic maps constructed from multiple populations are an important resource for both basic and applied research, including genome-wide association analysis, genome sequence assembly and studies of evolution. The LPmerge software uses linear programming to efficiently minimize the mean absolute error between the consensus map and the linkage maps from each population. This minimization is performed subject to linear inequality constraints that ensure the ordering of the markers in the linkage maps is preserved. When marker order is inconsistent between linkage maps, a minimum set of ordinal constraints is deleted to resolve the conflicts. AVAILABILITY AND IMPLEMENTATION: LPmerge is on CRAN at http://cran.r-project.org/web/packages/LPmerge.

Genomic predictability of interconnected biparental maize populations.

Intense structuring of plant breeding populations challenges the design of the training set (TS) in genomic selection (GS). An important open question is how the TS should be constructed from multiple related or unrelated small biparental families to predict progeny from individual crosses. Here, we used a set of five interconnected maize (Zea mays L.) populations of doubled-haploid (DH) lines derived from four parents to systematically investigate how the composition of the TS affects the prediction accuracy for lines from individual crosses. A total of 635 DH lines genotyped with 16,741 polymorphic SNPs were evaluated for five traits including Gibberella ear rot severity and three kernel yield component traits. The populations showed a genomic similarity pattern, which reflects the crossing scheme with a clear separation of full sibs, half sibs, and unrelated groups. Prediction accuracies within full-sib families of DH lines followed closely theoretical expectations, accounting for the influence of sample size and heritability of the trait. Prediction accuracies declined by 42% if full-sib DH lines were replaced by half-sib DH lines, but statistically significantly better results could be achieved if half-sib DH lines were available from both instead of only one parent of the validation population. Once both parents of the validation population were represented in the TS, including more crosses with a constant TS size did not increase accuracies. Unrelated crosses showing opposite linkage phases with the validation population resulted in negative or reduced prediction accuracies, if used alone or in combination with related families, respectively. We suggest identifying and excluding such crosses from the TS. Moreover, the observed variability among populations and traits suggests that these uncertainties must be taken into account in models optimizing the allocation of resources in GS.