Genomic Characterization of Local Croatian Sheep Breeds-Effective Population Size, Inbreeding & Signatures of Selection.

The Istrian (IS) and the Pag sheep (PS) are local Croatian breeds which provide significant income for the regional economy and have a cultural and traditional importance for the inhabitants. The aim of this study was to estimate some important population specific genetic parameters in IS (N = 1293) and PS (N = 2637) based on genome wide SNPs. Estimates of linkage disequilibrium effective population size (Ne) evidenced more genetic variability in PS (Ne = 838) compared to IS (Ne = 197), regardless of historical time (both recent and ancient genetic variability). The discrepancy in the recent genetic variability between these breeds was additionally confirmed by the estimates of genomic inbreeding (FROH), which was estimated to be notably higher in IS (FROH>2 = 0.062) than in PS (FROH>2 = 0.029). The average FROH2-4, FROH4-8, FROH8-16, and FROH>16 were 0.26, 1.65, 2.14, and 3.72 for IS and 0.22, 0.61, 0.75, and 1.58 for PS, thus evidencing a high contribution of recent inbreeding in the overall inbreeding. One ROH island with > 30% of SNP incidence in ROHs was detected in IS (OAR6; 34,253,440-38,238,124 bp) while there was no ROH islands detected in PS. Seven genes (CCSER1, HERC3, LCORL, NAP1L5, PKD2, PYURF, and SPP1) involved in growth, feed intake, milk production, immune responses, and resistance were associated with the found autozygosity. The results of this study represent the first comprehensive insight into genomic variability of these two Croatian local sheep breeds and will serve as a baseline for setting up the most promising strategy of genomic Optimum Contribution Selection.

SNP profile for quantitative trait nucleotide in populations with small effective size and its impact on mapping and genomic predictions.

Increasing SNP density by incorporating sequence information only marginally increases prediction accuracies of breeding values in livestock. To find out why, we used statistical models and simulations to investigate the shape of distribution of estimated SNP effects (a profile) around Quantitative Trait Nucleotides (QTN) in populations with a small effective population size (Ne). A QTN profile created by averaging SNP effects around each QTN was similar to the shape of expected pairwise linkage disequilibrium (PLD) based on Ne and genetic distance between SNP, with a distinct peak for the QTN. Populations with smaller Ne showed lower but wider QTN profiles. However, adding more genotyped individuals with phenotypes dragged the profile closer to the QTN. The QTN profile was higher and narrower for populations with larger compared to smaller Ne. Assuming the PLD curve for the QTN profile, 80% of the additive genetic variance explained by each QTN was contained in ± 1/Ne Morgan interval around the QTN, corresponding to 2 Mb in cattle, and 5 Mb in pigs and chickens. With such large intervals, identifying QTN is difficult even if all of them are in the data and the assumed genetic architecture is simplistic. Additional complexity in QTN detection arises from confounding of QTN profiles with signals due to relationships, overlapping profiles with closely-spaced QTN, and spurious signals. However, small Ne allows for accurate predictions with large data even without QTN identification because QTN are accounted for by QTN profiles if SNP density is sufficient to saturate the segments.

A method for partitioning trends in genetic mean and variance to understand breeding practices.

BACKGROUND: In breeding programmes, the observed genetic change is a sum of the contributions of different selection paths represented by groups of individuals. Quantifying these sources of genetic change is essential for identifying the key breeding actions and optimizing breeding programmes. However, it is difficult to disentangle the contribution of individual paths due to the inherent complexity of breeding programmes. Here we extend the previously developed method for partitioning genetic mean by paths of selection to work both with the mean and variance of breeding values. METHODS: First, we extended the partitioning method to quantify the contribution of different paths to genetic variance assuming that the breeding values are known. Second, we combined the partitioning method with the Markov Chain Monte Carlo approach to draw samples from the posterior distribution of breeding values and use these samples for computing the point and interval estimates of partitions for the genetic mean and variance. We implemented the method in the R package AlphaPart. We demonstrated the method with a simulated cattle breeding programme. RESULTS: We show how to quantify the contribution of different groups of individuals to genetic mean and variance and that the contributions of different selection paths to genetic variance are not necessarily independent. Finally, we observed that the partitioning method under the pedigree-based model has some limitations, which suggests the need for a genomic extension. CONCLUSIONS: We presented a partitioning method to quantify sources of change in genetic mean and variance in breeding programmes. The method can help breeders and researchers understand the dynamics in genetic mean and variance in a breeding programme. The developed method for partitioning genetic mean and variance is a powerful method for understanding how different selection paths interact within a breeding programme and how they can be optimised.

Assessment of long-term trends in genetic mean and variance after the introduction of genomic selection in layers: a simulation study.

Nucleus-based breeding programs are characterized by intense selection that results in high genetic gain, which inevitably means reduction of genetic variation in the breeding population. Therefore, genetic variation in such breeding systems is typically managed systematically, for example, by avoiding mating the closest relatives to limit progeny inbreeding. However, intense selection requires maximum effort to make such breeding programs sustainable in the long-term. The objective of this study was to use simulation to evaluate the long-term impact of genomic selection on genetic mean and variance in an intense layer chicken breeding program. We developed a large-scale stochastic simulation of an intense layer chicken breeding program to compare conventional truncation selection to genomic truncation selection optimized with either minimization of progeny inbreeding or full-scale optimal contribution selection. We compared the programs in terms of genetic mean, genic variance, conversion efficiency, rate of inbreeding, effective population size, and accuracy of selection. Our results confirmed that genomic truncation selection has immediate benefits compared to conventional truncation selection in all specified metrics. A simple minimization of progeny inbreeding after genomic truncation selection did not provide any significant improvements. Optimal contribution selection was successful in having better conversion efficiency and effective population size compared to genomic truncation selection, but it must be fine-tuned for balance between loss of genetic variance and genetic gain. In our simulation, we measured this balance using trigonometric penalty degrees between truncation selection and a balanced solution and concluded that the best results were between 45° and 65°. This balance is specific to the breeding program and depends on how much immediate genetic gain a breeding program may risk vs. save for the future. Furthermore, our results show that the persistence of accuracy is better with optimal contribution selection compared to truncation selection. In general, our results show that optimal contribution selection can ensure long-term success in intensive breeding programs using genomic selection.

Optimisation of the core subset for the APY approximation of genomic relationships.

BACKGROUND: By entering the era of mega-scale genomics, we are facing many computational issues with standard genomic evaluation models due to their dense data structure and cubic computational complexity. Several scalable approaches have been proposed to address this challenge, such as the Algorithm for Proven and Young (APY). In APY, genotyped animals are partitioned into core and non-core subsets, which induces a sparser inverse of the genomic relationship matrix. This partitioning is often done at random. While APY is a good approximation of the full model, random partitioning can make results unstable, possibly affecting accuracy or even reranking animals. Here we present a stable optimisation of the core subset by choosing animals with the most informative genotype data. METHODS: We derived a novel algorithm for optimising the core subset based on a conditional genomic relationship matrix or a conditional single nucleotide polymorphism (SNP) genotype matrix. We compared the accuracy of genomic predictions with different core subsets for simulated and real pig data sets. The core subsets were constructed (1) at random, (2) based on the diagonal of the genomic relationship matrix, (3) at random with weights from (2), or (4) based on the novel conditional algorithm. To understand the different core subset constructions, we visualise the population structure of the genotyped animals with linear Principal Component Analysis and non-linear Uniform Manifold Approximation and Projection. RESULTS: All core subset constructions performed equally well when the number of core animals captured most of the variation in the genomic relationships, both in simulated and real data sets. When the number of core animals was not sufficiently large, there was substantial variability in the results with the random construction but no variability with the conditional construction. Visualisation of the population structure and chosen core animals showed that the conditional construction spreads core animals across the whole domain of genotyped animals in a repeatable manner. CONCLUSIONS: Our results confirm that the size of the core subset in APY is critical. Furthermore, the results show that the core subset can be optimised with the conditional algorithm that achieves an optimal and repeatable spread of core animals across the domain of genotyped animals.

Temporal and genomic analysis of additive genetic variance in breeding programmes.

Genetic variance is a central parameter in quantitative genetics and breeding. Assessing changes in genetic variance over time as well as the genome is therefore of high interest. Here, we extend a previously proposed framework for temporal analysis of genetic variance using the pedigree-based model, to a new framework for temporal and genomic analysis of genetic variance using marker-based models. To this end, we describe the theory of partitioning genetic variance into genic variance and within-chromosome and between-chromosome linkage-disequilibrium, and how to estimate these variance components from a marker-based model fitted to observed phenotype and marker data. The new framework involves three steps: (i) fitting a marker-based model to data, (ii) sampling realisations of marker effects from the fitted model and for each sample calculating realisations of genetic values and (iii) calculating the variance of sampled genetic values by time and genome partitions. Analysing time partitions indicates breeding programme sustainability, while analysing genome partitions indicates contributions from chromosomes and chromosome pairs and linkage-disequilibrium. We demonstrate the framework with a simulated breeding programme involving a complex trait. Results show good concordance between simulated and estimated variances, provided that the fitted model is capturing genetic complexity of a trait. We observe a reduction of genetic variance due to selection and drift changing allele frequencies, and due to selection inducing negative linkage-disequilibrium.

Novel combination of CRISPR-based gene drives eliminates resistance and localises spread.

Invasive species are among the major driving forces behind biodiversity loss. Gene drive technology may offer a humane, efficient and cost-effective method of control. For safe and effective deployment it is vital that a gene drive is both self-limiting and can overcome evolutionary resistance. We present HD-ClvR in this modelling study, a novel combination of CRISPR-based gene drives that eliminates resistance and localises spread. As a case study, we model HD-ClvR in the grey squirrel (Sciurus carolinensis), which is an invasive pest in the UK and responsible for both biodiversity and economic losses. HD-ClvR combats resistance allele formation by combining a homing gene drive with a cleave-and-rescue gene drive. The inclusion of a self-limiting daisyfield gene drive allows for controllable localisation based on animal supplementation. We use both randomly mating and spatial models to simulate this strategy. Our findings show that HD-ClvR could effectively control a targeted grey squirrel population, with little risk to other populations. HD-ClvR offers an efficient, self-limiting and controllable gene drive for managing invasive pests.

Core-dependent changes in genomic predictions using the Algorithm for Proven and Young in single-step genomic best linear unbiased prediction.

Single-step genomic best linear unbiased prediction with the Algorithm for Proven and Young (APY) is a popular method for large-scale genomic evaluations. With the APY algorithm, animals are designated as core or noncore, and the computing resources to create the inverse of the genomic relationship matrix (GRM) are reduced by inverting only a portion of that matrix for core animals. However, using different core sets of the same size causes fluctuations in genomic estimated breeding values (GEBVs) up to one additive standard deviation without affecting prediction accuracy. About 2% of the variation in the GRM is noise. In the recursion formula for APY, the error term modeling the noise is different for every set of core animals, creating changes in breeding values. While average changes are small, and correlations between breeding values estimated with different core animals are close to 1.0, based on the normal distribution theory, outliers can be several times bigger than the average. Tests included commercial datasets from beef and dairy cattle and from pigs. Beyond a certain number of core animals, the prediction accuracy did not improve, but fluctuations decreased with more animals. Fluctuations were much smaller than the possible changes based on prediction error variance. GEBVs change over time even for animals with no new data as genomic relationships ties all the genotyped animals, causing reranking of top animals. In contrast, changes in nongenomic models without new data are small. Also, GEBV can change due to details in the model, such as redefinition of contemporary groups or unknown parent groups. In particular, increasing the fraction of blending of the GRM with a pedigree relationship matrix from 5% to 20% caused changes in GEBV up to 0.45 SD, with a correlation of GEBV > 0.99. Fluctuations in genomic predictions are part of genomic evaluation models and are also present without the APY algorithm when genomic evaluations are computed with updated data. The best approach to reduce the impact of fluctuations in genomic evaluations is to make selection decisions not on individual animals with limited individual accuracy but on groups of animals with high average accuracy.

Accuracy of genomic BLUP when considering a genomic relationship matrix based on the number of the largest eigenvalues: a simulation study.

BACKGROUND: The dimensionality of genomic information is limited by the number of independent chromosome segments (Me), which is a function of the effective population size. This dimensionality can be determined approximately by singular value decomposition of the gene content matrix, by eigenvalue decomposition of the genomic relationship matrix (GRM), or by the number of core animals in the algorithm for proven and young (APY) that maximizes the accuracy of genomic prediction. In the latter, core animals act as proxies to linear combinations of Me. Field studies indicate that a moderate accuracy of genomic selection is achieved with a small dataset, but that further improvement of the accuracy requires much more data. When only one quarter of the optimal number of core animals are used in the APY algorithm, the accuracy of genomic selection is only slightly below the optimal value. This suggests that genomic selection works on clusters of Me. RESULTS: The simulation included datasets with different population sizes and amounts of phenotypic information. Computations were done by genomic best linear unbiased prediction (GBLUP) with selected eigenvalues and corresponding eigenvectors of the GRM set to zero. About four eigenvalues in the GRM explained 10% of the genomic variation, and less than 2% of the total eigenvalues explained 50% of the genomic variation. With limited phenotypic information, the accuracy of GBLUP was close to the peak where most of the smallest eigenvalues were set to zero. With a large amount of phenotypic information, accuracy increased as smaller eigenvalues were added. CONCLUSIONS: A small amount of phenotypic data is sufficient to estimate only the effects of the largest eigenvalues and the associated eigenvectors that contain a large fraction of the genomic information, and a very large amount of data is required to estimate the remaining eigenvalues that account for a limited amount of genomic information. Core animals in the APY algorithm act as proxies of almost the same number of eigenvalues. By using an eigenvalues-based approach, it was possible to explain why the moderate accuracy of genomic selection based on small datasets only increases slowly as more data are added.

Crossbred evaluations using single-step genomic BLUP and algorithm for proven and young with different sources of data1.

Genomic selection (GS) is routinely applied to many purebreds and lines of farm species. However, this method can be extended to predictions across purebreds as well as for crossbreds. This is useful for swine and poultry, for which selection in nucleus herds is typically performed on purebred animals, whereas the commercial product is the crossbred animal. Single-step genomic BLUP (ssGBLUP) is a widely applied method that can explore the recently developed algorithm for proven and young (APY). The APY allows for greater efficiency in computing BLUP solutions by exploiting the theory of limited dimensionality of genomic information and chromosome segments (Me). This study investigates the predictivity as a proxy for accuracy across and within 2 purebred pig lines and their crosses, under the application of APY in ssGBLUP setup, and different levels of Me overlapping across populations. The data consisted of approximately 210k phenotypic records for 2 traits (T1 and T2) with moderate heritability. Genotypes for 43k SNP markers were available for approximately 46k animals, from which 26k and 16k belong to 2 pure lines (L1 and L2), and approximately 4k are crossbreds. The complete pedigree had more than 720k animals. Different multivariate ssGBLUP models were applied, either with the regular or APY inverse of the genomic relationship matrix (G). The models included a standard bivariate animal model with 3 lines evaluated as 1 joint line, and for each trait individually, a 3-trait animal model with each line treated as a separate trait. Both models provided the same predictivity across and within the lines. Using either of the pure lines data as a training set resulted in a similar predictivity for the crossbreed animals (0.18 to 0.21). Across-line predictive ability was limited to less than half of the maximum predictivity for each line (L1T1 0.33, L1T2 0.25, L2T1 0.35, L2T2 0.36). For crossbred predictions, APY performed equivalently to regular G inverse when the number of core animals was equal to the number of eigenvalues explaining between 98% and 99% of the variance of G (4k to 8k) including all lines. Predictivity across the lines is achievable because of the shared Me between them. The number of those shared segments can be obtained via eigenvalue decomposition of genomic information available for each line.

Bias in heritability estimates from genomic restricted maximum likelihood methods under different genotyping strategies.

We investigated the effects of different strategies for genotyping populations on variance components and heritabilities estimated with an animal model under restricted maximum likelihood (REML), genomic REML (GREML), and single-step GREML (ssGREML). A population with 10 generations was simulated. Animals from the last one, two or three generations were genotyped with 45,116 SNP evenly distributed on 27 chromosomes. Animals to be genotyped were chosen randomly or based on EBV. Each scenario was replicated five times. A single trait was simulated with three heritability levels (low, moderate, high). Phenotypes were simulated for only females to mimic dairy sheep and also for both sexes to mimic meat sheep. Variance component estimates from genomic data and phenotypes for one or two generations were more biased than from three generations. Estimates in the scenario without selection were the most accurate across heritability levels and methods. When selection was present in the simulations, the best option was to use genotypes of randomly selected animals. For selective genotyping, heritabilities from GREML were more biased compared to those estimated by ssGREML, because ssGREML was less affected by selective or limited genotyping.

Metafounders are related to F st fixation indices and reduce bias in single-step genomic evaluations.

BACKGROUND: Metafounders are pseudo-individuals that encapsulate genetic heterozygosity and relationships within and across base pedigree populations, i.e. ancestral populations. This work addresses the estimation and usefulness of metafounder relationships in single-step genomic best linear unbiased prediction (ssGBLUP). RESULTS: We show that ancestral relationship parameters are proportional to standardized covariances of base allelic frequencies across populations, such as [Formula: see text] fixation indexes. These covariances of base allelic frequencies can be estimated from marker genotypes of related recent individuals and pedigree. Simple methods for their estimation include naïve computation of allele frequencies from marker genotypes or a method of moments that equates average pedigree-based and marker-based relationships. Complex methods include generalized least squares (best linear unbiased estimator (BLUE)) or maximum likelihood based on pedigree relationships. To our knowledge, methods to infer [Formula: see text] coefficients from marker data have not been developed for related individuals. We derived a genomic relationship matrix, compatible with pedigree relationships, that is constructed as a cross-product of {-1,0,1} codes and that is equivalent (apart from scale factors) to an identity-by-state relationship matrix at genome-wide markers. Using a simulation with a single population under selection in which only males and youngest animals are genotyped, we observed that generalized least squares or maximum likelihood gave accurate and unbiased estimates of the ancestral relationship parameter (true value: 0.40) whereas the naïve method and the method of moments were biased (average estimates of 0.43 and 0.35). We also observed that genomic evaluation by ssGBLUP using metafounders was less biased in terms of estimates of genetic trend (bias of 0.01 instead of 0.12), resulted in less overdispersed (0.94 instead of 0.99) and as accurate (0.74) estimates of breeding values than ssGBLUP without metafounders and provided consistent estimates of heritability. CONCLUSIONS: Estimation of metafounder relationships can be achieved using BLUP-like methods with pedigree and markers. Inclusion of metafounder relationships reduces bias of genomic predictions with no loss in accuracy.

Dimensionality of genomic information and performance of the Algorithm for Proven and Young for different livestock species.

BACKGROUND: A genomic relationship matrix (GRM) can be inverted efficiently with the Algorithm for Proven and Young (APY) through recursion on a small number of core animals. The number of core animals is theoretically linked to effective population size (N e ). In a simulation study, the optimal number of core animals was equal to the number of largest eigenvalues of GRM that explained 98% of its variation. The purpose of this study was to find the optimal number of core animals and estimate N e for different species. METHODS: Datasets included phenotypes, pedigrees, and genotypes for populations of Holstein, Jersey, and Angus cattle, pigs, and broiler chickens. The number of genotyped animals varied from 15,000 for broiler chickens to 77,000 for Holsteins, and the number of single-nucleotide polymorphisms used for genomic prediction varied from 37,000 to 61,000. Eigenvalue decomposition of the GRM for each population determined numbers of largest eigenvalues corresponding to 90, 95, 98, and 99% of variation. RESULTS: The number of eigenvalues corresponding to 90% (98%) of variation was 4527 (14,026) for Holstein, 3325 (11,500) for Jersey, 3654 (10,605) for Angus, 1239 (4103) for pig, and 1655 (4171) for broiler chicken. Each trait in each species was analyzed using the APY inverse of the GRM with randomly selected core animals, and their number was equal to the number of largest eigenvalues. Realized accuracies peaked with the number of core animals corresponding to 98% of variation for Holstein and Jersey and closer to 99% for other breed/species. N e was estimated based on comparisons of eigenvalue decomposition in a simulation study. Assuming a genome length of 30 Morgan, N e was equal to 149 for Holsteins, 101 for Jerseys, 113 for Angus, 32 for pigs, and 44 for broilers. CONCLUSIONS: Eigenvalue profiles of GRM for common species are similar to those in simulation studies although they are affected by number of genotyped animals and genotyping quality. For all investigated species, the APY required less than 15,000 core animals. Realized accuracies were equal or greater with the APY inverse than with regular inversion. Eigenvalue analysis of GRM can provide a realistic estimate of N e .

The Dimensionality of Genomic Information and Its Effect on Genomic Prediction.

The genomic relationship matrix (GRM) can be inverted by the algorithm for proven and young (APY) based on recursion on a random subset of animals. While a regular inverse has a cubic cost, the cost of the APY inverse can be close to linear. Theory for the APY assumes that the optimal size of the subset (maximizing accuracy of genomic predictions) is due to a limited dimensionality of the GRM, which is a function of the effective population size (Ne). The objective of this study was to evaluate these assumptions by simulation. Six populations were simulated with approximate effective population size (Ne) from 20 to 200. Each population consisted of 10 nonoverlapping generations, with 25,000 animals per generation and phenotypes available for generations 1-9. The last 3 generations were fully genotyped assuming genome length L = 30. The GRM was constructed for each population and analyzed for distribution of eigenvalues. Genomic estimated breeding values (GEBV) were computed by single-step GBLUP, using either a direct or an APY inverse of GRM. The sizes of the subset in APY were set to the number of the largest eigenvalues explaining x% of variation (EIGx, x = 90, 95, 98, 99) in GRM. Accuracies of GEBV for the last generation with the APY inverse peaked at EIG98 and were slightly lower with EIG95, EIG99, or the direct inverse. Most information in the GRM is contained in ∼NeL largest eigenvalues, with no information beyond 4NeL Genomic predictions with the APY inverse of the GRM are more accurate than by the regular inverse.