New Genomic Method Blends Sequence and Array Data Without Imputation

A stubborn practical problem has persisted in genomic selection breeding programs: populations are genotyped with a patchwork of technologies. Some animals carry low-density SNP arrays, others sit on high-density chips, and a growing few are fully sequenced. Standard single step genomic evaluation, the workhorse method that blends pedigree with genotypes, can only handle one marker list at a time, forcing evaluators to impute everyone up to the densest platform before analysis. A new study published in Genetics Selection Evolution proposes a way around that bottleneck.

Miguel Pérez-Enciso, the author of the short communication, presents a generalized single step (GSS) theory that accommodates any number of hierarchical molecular datasets alongside pedigree information, eliminating the imputation step entirely. The key requirement is hierarchy: every marker on a lower-density array must also appear in every higher-density dataset. Under that condition, the method computes a combined relationship matrix recursively, starting from the individuals with the most complete molecular information and working backwards toward those known only through their pedigrees.

The mathematical core builds on classical single step theory. In the standard approach, the variance of breeding values is approximated by an H matrix that combines the pedigree-based numerator relationship matrix A for ungenotyped animals with the genomic relationship matrix G for genotyped ones. Its great computational appeal is that the inverse of H requires inverting a matrix only as large as the number of genotyped individuals, which is typically far smaller than the full pedigree. The new work proves that the same efficient inversion algorithm survives generalization: the inverse of the generalized H equals the inverse of A plus a correction block involving only individuals with molecular data.

The recursion works like this. Begin with the block of individuals sequenced or genotyped at the highest density, where their variance block is simply their genomic relationship matrix. Then, moving down one density level at a time, compute the variance and covariance blocks for individuals genotyped only at the current level, using the genomic relationship matrix of that level together with the already-computed higher-density blocks. Because each step depends only on previously computed blocks and the current marker set’s relationship matrix, the procedure extends naturally to any number of ordered marker lists, from sequence down through successive array densities to pedigree alone.

Pérez-Enciso illustrates the theory with a simulation built in AlphaSimR. A founder population of 1000 diploid individuals was simulated across 20 chromosomes carrying 1000 markers each, with a quantitative trait of heritability 0.5 controlled by 100 QTL. Three non-overlapping generations of random matings produced a pedigree of 4000 individuals.

Four strategies were compared: pedigree only; standard single step with low-density genotyping across generations one to three; generalized single step adding sequence data in generation three; and full sequencing of the entire population. As expected, prediction was worst with pedigree alone and best when everyone was sequenced. The generalized method increased predictive accuracy relative to standard single step, with an improvement the author describes as moderate in the scenario considered, noting that actual gains will depend on specific parameters and vary between replicates. Correlations between elements of the generalized H matrix and the sequence-based relationship matrix were higher than those between the sequence matrix and the standard single step H, reflecting the larger amount of molecular information incorporated.

The study also tested what happens when the hierarchy assumption breaks. In a scenario with two partially overlapping arrays, a 1000-SNP low-density chip and a 19,500-SNP high-density chip sharing 500 markers, GSS was applied while pretending the arrays were truly hierarchical, and its results were compared with the EM-Wishart consensus method of Akdemir and colleagues, which combines partially overlapping relationship matrices iteratively. Because that iterative method was more than 100 times slower, the comparison used a smaller population of 100 individuals per generation. The correlations between the two combined matrices and the sequence-based matrix were very similar, 0.88 versus 0.89, and their predictions were comparable, suggesting GSS offers a substantially faster route with little loss in this example.

Computational considerations shape where the method shines. Each recursion step requires inverting a submatrix whose order is the sum of individuals in all higher-density blocks, so many large blocks can become demanding. The method is most efficient when the largest block consists of ungenotyped individuals known only through pedigree, since the inverse of the numerator relationship matrix can be computed in linear time and is sparse. For the genomic matrices themselves, which lack such efficient inversion algorithms, the author points to Misztal’s APY algorithm or equivalents as a remedy, and notes that the inverse of the generalized H can itself be computed recursively.

Beyond breeding programs, the author highlights applications where pedigree is unavailable but molecular data of varying density exist, such as ecological field studies or human genetics, scenarios where standard single step cannot be applied at all. The method could also serve as a tool for optimizing how sequencing and genotyping budgets are allocated across a population, in combination with simulation software, by revealing how much predictive value additional marker density actually buys. The author expects sequence data to matter most when linkage disequilibrium is low, meaning large effective population sizes, or when a subset of causal mutations can be identified.

The note is deliberately a theoretical contribution rather than a systematic performance evaluation, and the author provides documented R code on GitHub so that researchers can test custom scenarios with simulated or real data. Future work flagged in the paper includes comparisons with genome-wide imputation pipelines and with related approaches for combining heterogeneous omics sources. Within its scope, the message is clear: single step theory, one of the most widely used frameworks in genomic evaluation, can be extended cleanly to any number of hierarchical genomic matrices, and the extension retains the computational elegance that made the original method the industry standard.

Subject of Research: A generalized single step genomic prediction theory for combining multiple hierarchical marker datasets with pedigree

Article Title: A note on a generalized single step theory for any number of hierarchical genomic matrices

Article References: Pérez-Enciso, M. (2026). A note on a generalized single step theory for any number of hierarchical genomic matrices. Genetics Selection Evolution, 58(1), Article 66. https://doi.org/10.1186/s12711-026-01084-3

Image Credits: AI Generated

DOI: 10.1186/s12711-026-01084-3

Keywords: genomic selection, single step method, genomic relationship matrices, animal breeding, SNP arrays, imputation, predictive accuracy, simulation, pedigree, quantitative genetics, note, generalized