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The Brazilian merganser (Mergus octosetaceus) is one of the most endangered bird species in South America that comprises less than 250 mature individuals in the wild environments. This is a species extremely sensitive to environmental disturbances and restricted to few “pristine” freshwater habitats in Brazil, and it has been classified as Critically Endangered on the IUCN Red List since 1994. Understanding its current genetic diversity to promote in situ and ex situ management strategies was considered urgent for conservation of the remaining populations. To understand the evolutionary dynamics of remaining Brazilian merganser populations we have used "Genotyping by Sequencing" approach to characterize 923 SNPs in 31 individuals from all known areas of occurrence. The remaining populations of the Brazilian merganser present a low genetic diversity and high inbreeding levels likely due to recent population decline associated to habitat loss. Furthermore, it revealed a moderate level of genetic differentiation between all populations located in four separated areas of the highly threatened Cerrado biome. The results indicate that urgent actions for conservation of the species should be accompanied by a careful genetic monitoring to allow appropriate in situ and ex situ management to increase the long-term species survival in its natural environment.

International audience; Many specificities single out HLA-F: its structure, expression regulation at cell membrane and function. HLA-F mRNA is detected in the most cell types and the protein is localized in the ER and Golgi apparatus. When expressed at cell surface, HLA-F may be associated to β2-microglobulin and peptide or expressed as an open-conformer molecule. HLA-F reaches the membrane upon activation of different primary cell types and cell-lines. HLA-F has its highest affinity for the KIR3DS1-activating NK receptor, but also binds inhibitory immune receptors. Some studies reported that HLA-F expression is associated with its genotype. Higher HLA-F mRNA expression associated with F*01:01:02, and 3 noncoding SNPs, rs1362126, rs2523405, and rs2523393, located in HLA-F-AS1 or upstream the HLA-F sequence were associated with HLA-F mRNA expression. Given the implication of HLA-F in many clinical setting, and the undisclosed process of its expression regulation, we aim to confirm the effect of the aforementioned SNPs with HLA-F transcriptional and protein expression. We analyzed the distribution, frequency and linkage disequilibrium of these SNPs at worldwide scale in the 1000 Genomes Project samples. Influence on the genotype of each SNP on HLA-F expression was explored using RNAseq data from the 1000 Genomes Project, and using Q-PCR and intracellular cytometry in PBMC from healthy individuals. Our results show that the SNPs under studied displayed remarkably different allelic proportion according to geography and confirm that rs1362126, rs2523405, and rs2523393 displayed the most concordant results, with the highest effect size and a double-dose effect.

Background: Genome-wide association studies (GWASs) have identified genes influencing skin ageing and mole count in Europeans, but little is known about the relevance of these (or other genes) in non-Europeans. - Objectives: To conduct a GWAS for facial skin ageing and mole count in adults

Repeated application of noxious stimuli leads to a progressively increased pain perception; this temporal summation is enhanced in and predictive of clinical pain disorders. Its electrophysiological correlate is “wind-up,” in which dorsal horn spinal neurons increase their response to repeated nociceptor stimulation. To understand the genetic basis of temporal summation, we undertook a GWAS of wind-up in healthy human volunteers and found significant association with SLC8A3 encoding sodium-calcium exchanger type 3 (NCX3). NCX3 was expressed in mouse dorsal horn neurons, and mice lacking NCX3 showed normal, acute pain but hypersensitivity to the second phase of the formalin test and chronic constriction injury. Dorsal horn neurons lacking NCX3 showed increased intracellular calcium following repetitive stimulation, slowed calcium clearance, and increased wind-up. Moreover, virally mediated enhanced spinal expression of NCX3 reduced central sensitization. Our study highlights Ca2+ efflux as a pathway underlying temporal summation and persistent pain, which may be amenable to therapeutic targeting., Neuron, 110 (16)

We report a genome-wide association study for facial features in > 6,000 Latin Americans. We placed 106 landmarks on 2D frontal photographs using the cloud service platform Face++. After Procrustes superposition, genome-wide association testing was performed for 301 inter-landmark distances. We detected nominally significant association (P-value − 8) for 42 genome regions. Of these, 9 regions have been previously reported in GWAS of facial features. In follow-up analyses, we replicated 26 of the 33 novel regions (in East Asians or Europeans). The replicated regions include 1q32.3, 3q21.1, 8p11.21, 10p11.1, and 22q12.1, all comprising strong candidate genes involved in craniofacial development. Furthermore, the 1q32.3 region shows evidence of introgression from archaic humans. These results provide novel biological insights into facial variation and establish that automatic landmarking of standard 2D photographs is a simple and informative approach for the genetic analysis of facial variation, suitable for the rapid analysis of large population samples.

International audience; Red cell blood group systems are crucial for safe transfusion, transplantation, and pregnancy monitoring. In addition, blood groups have long been investigated to decipher the origin of human populations, migration, adaptation, and admixture. However, since the extensive use of DNA polymorphisms in Anthropology, blood groups have been relegated to their primary application, blood transfusion. The finer genomic mapping of some Neanderthal and Denisova individuals about modern humans has provided significant evidence on the evolutionary history of both archaic and modern humans. However, despite their medical and anthropological interest, little is known about blood groups in archaic populations. To better understand the origin, expansion and encounter with Homo sapiens, we reappraised the available high-quality sequences of three Neanderthals (Vindija 33.19, Chagyrskaya 8, Altai Neandertal) and one Denisovan (Denisova 3) for 11 genes of the 7 blood group systems that are routinely screened in transfusion: ABO including H/ Se, Rh (Rhesus), Kell, Duffy, Kidd, MNS, and Diego. We show that Neanderthals and Denisova were polymorphic for ABO and shared blood group alleles recurrent in modern Sub-Saharan populations. Furthermore, we found ABO-related alleles currently preventing viral gut infection and all Neanderthal shared RHD and RHCE alleles nowadays associated with a high risk of hemolytic disease of the fetus and newborn. Such a common blood group pattern across time and space is coherent with a Neanderthal population of low genetic diversity exposed to possible pregnancies with complications. Lastly, we connect the Neanderthal RHD allele to two present-day Aboriginal Australians and Papuan, suggesting that a segment of the archaic genome was introgressed in this gene in non-Eurasian populations before their expansion towards Oceania. While contributing to both the origin and late evolutionary history of Neanderthal and Denisova, our results further illustrate that blood group systems remain effective anthropological markers.

Here we evaluate the accuracy of prediction for eye, hair and skin pigmentation in a dataset of > 6500 individuals from Mexico, Colombia, Peru, Chile and Brazil (including genome-wide SNP data and quantitative/categorical pigmentation phenotypes - the CANDELA dataset CAN). We evaluated accuracy in relation to different analytical methods and various phenotypic predictors. As expected from statistical principles, we observe that quantitative traits are more sensitive to changes in the prediction models than categorical traits. We find that Random Forest or Linear Regression are generally the best performing methods. We also compare the prediction accuracy of SNP sets defined in the CAN dataset (including 56, 101 and 120 SNPs for eye, hair and skin colour prediction, respectively) to the well-established HIrisPlex-S SNP set (including 6, 22 and 36 SNPs for eye, hair and skin colour prediction respectively). When training prediction models on the CAN data, we observe remarkably similar performances for HIrisPlex-S and the larger CAN SNP sets for the prediction of hair (categorical) and eye (both categorical and quantitative), while the CAN sets outperform HIrisPlex-S for quantitative, but not for categorical skin pigmentation prediction. The performance of HIrisPlex-S, when models are trained in a world-wide sample (although consisting of 80% Europeans, https://hirisplex.erasmusmc.nl), is lower relative to training in the CAN data (particularly for hair and skin colour). Altogether, our observations are consistent with common variation of eye and hair colour having a relatively simple genetic architecture, which is well captured by HIrisPlex-S, even in admixed Latin Americans (with partial European ancestry). By contrast, since skin pigmentation is a more polygenic trait, accuracy is more sensitive to prediction SNP set size, although here this effect was only apparent for a quantitative measure of skin pigmentation. Our results support the use of HIrisPlex-S in the prediction of categorical pigmentation traits for forensic purposes in Latin America, while illustrating the impact of training datasets on its accuracy. Fil: Palmal, Sagnik. Centre National de la Recherche Scientifique; Francia. Aix-Marseille Université; Francia Fil: Kaustubh Adhikari. The Open University; Reino Unido. University College London; Estados Unidos Fil: Mendoza Revilla, Javier. Universidad Peruana Cayetano Heredia; Perú. Institut Pasteur de Paris.; Francia Fil: Fuentes Guajardo, Macarena. Universidad de Tarapacá; Chile Fil: Silva de Cerqueira, Caio Cesar. Scientific Police of São Paulo State; Brasil Fil: Bonfante, Betty. Aix-Marseille Université; Francia. Centre National de la Recherche Scientifique; Francia Fil: Chacón Duque, Juan Camilo. Natural History Museum; Reino Unido Fil: Sohail, Anood. Kinnaird College for Women. Department of Biotechnology; Pakistán Fil: Hurtadeo, Malena. Universidad Peruana Cayetano Heredia; Perú Fil: Villegas, Valeria. Universidad Peruana Cayetano Heredia; Perú Fil: Granja, Vanessa. Universidad Peruana Cayetano Heredia; Perú Fil: Jaramillo, Claudia. Kinnaird College for Women. Department of Biotechnology; Pakistán. Universidad de Antioquia; Colombia Fil: Arias, Williams. Universidad de Antioquia; Colombia Fil: Barquera Lozano, Rodrigo. Instituto Nacional de Antropología e Historia; México. Max Planck Institute for the Science of Human History. Department of Archaeogenetics; Alemania Fil: Everardo Martínez, Paola. Instituto Nacional de Antropología e Historia; México Fil: Gómez Valdés, Jorge. Instituto Nacional de Antropología e Historia; México Fil: Villamil Ramirez, Hugo. Universidad Nacional Autónoma de México; México Fil: Hünemeier, Tábita. Universidade de Sao Paulo; Brasil Fil: Ramallo, Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Centro Nacional Patagónico. Instituto Patagónico de Ciencias Sociales y Humanas; Argentina. Universidade Federal do Rio Grande do Sul; Brasil Fil: Parolin, María Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Centro Nacional Patagónico. Instituto de Diversidad y Evolución Austral; Argentina Fil: Gonzalez, Rolando Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Centro Nacional Patagónico. Instituto Patagónico de Ciencias Sociales y Humanas; Argentina Fil: Schüler-Faccini, Lavinia. Universidade Federal do Rio Grande do Sul, Porto Alegre; Brasil Fil: Bortolini, María Cátira. Universidade Federal do Rio Grande do Sul; Brasil Fil: Acuña Alonzo, Victor. Instituto Nacional de Antropología e Historia; México. Universidade Federal do Rio Grande do Sul; Brasil Fil: Canizales Quinteros, Samuel. Universidad Nacional Autónoma de México; México Fil: Gallo, Carla. Universidad Peruana Cayetano Heredia; Perú Fil: Poletti, Giovanni. Universidad Peruana Cayetano Heredia; Perú Fil: Bedoya, Gabriel. Universidad de Antioquia; Colombia Fil: Rothhammer, Francisco. Universidad de Tarapacá; Chile. Universidad de Chile; Chile Fil: Balding, David. University College London; Reino Unido. University of Melbourne; Australia Fil: Faux, Pierre. Aix-Marseille Université; Francia. Centre National de la Recherche Scientifique; Francia Fil: Ruiz Linares, Andrés. Aix-Marseille Université; Francia. Centre National de la Recherche Scientifique; Francia. University College London; Reino Unido. Fudan University; República de China

We carried out a genome-wide association study in Latin Americans and identified novel face morphology loci.., To characterize the genetic basis of facial features in Latin Americans, we performed a genome-wide association study (GWAS) of more than 6000 individuals using 59 landmark-based measurements from two-dimensional profile photographs and ~9,000,000 genotyped or imputed single-nucleotide polymorphisms. We detected significant association of 32 traits with at least 1 (and up to 6) of 32 different genomic regions, more than doubling the number of robustly associated face morphology loci reported until now (from 11 to 23). These GWAS hits are strongly enriched in regulatory sequences active specifically during craniofacial development. The associated region in 1p12 includes a tract of archaic adaptive introgression, with a Denisovan haplotype common in Native Americans affecting particularly lip thickness. Among the nine previously unidentified face morphology loci we identified is the VPS13B gene region, and we show that variants in this region also affect midfacial morphology in mice.

We report an evaluation of prediction accuracy for eye, hair and skin pigmentation based on genomic and phenotypic data for over 6,500 admixed Latin Americans (the CANDELA dataset). We examined the impact on prediction accuracy of three main factors: (i) The methods of prediction, including classical statistical methods and machine learning approaches, (ii) The inclusion of non-genetic predictors, continental genetic ancestry and pigmentation SNPs in the prediction models, and (iii) Compared two sets of pigmentation SNPs: the commonly-used HIrisPlex-S set (developed in Europeans) and novel SNP sets we defined here based on genome-wide association results in the CANDELA sample. We find that Random Forest or regression are globally the best performing methods. Although continental genetic ancestry has substantial power for prediction of pigmentation in Latin Americans, the inclusion of pigmentation SNPs increases prediction accuracy considerably, particularly for skin color. For hair and eye color, HIrisPlex-S has a similar performance to the CANDELA-specific prediction SNP sets. However, for skin pigmentation the performance of HIrisPlex-S is markedly lower than the SNP set defined here, including predictions in an independent dataset of Native American data. These results reflect the relatively high variation in hair and eye color among Europeans for whom HIrisPlex-S was developed, whereas their variation in skin pigmentation is comparatively lower. Furthermore, we show that the dataset used in the training of prediction models strongly impacts on the portability of these models across Europeans and Native Americans.

The estimation of the inbreeding coefficient (F) is essential for the study of inbreeding depression (ID) or for the management of populations under conservation. Several methods have been proposed to estimate the realizedFusing genetic markers, but it remains unclear which one should be used. Here we used whole-genome sequence data for 245 individuals from a Holstein cattle pedigree to empirically evaluate which estimators best capture homozygosity at variants causing ID, such as rare deleterious alleles or loci presenting heterozygote advantage and segregating at intermediate frequency. Estimators relying on the correlation between uniting gametes (FUNI) or on the genomic relationships (FGRM) presented the highest correlations with these variants. However, homozygosity at rare alleles remained poorly captured. A second group of estimators relying on excess homozygosity (FHOM), homozygous-by-descent segments (FHBD), runs-of-homozygosity (FROH) or on the known genealogy (FPED) was better at capturing whole-genome homozygosity, reflecting the consequences of inbreeding on all variants, and for young alleles with low to moderate frequencies (0.10 < . < 0.25). The results indicate that FUNIand FGRMmight present a stronger association with ID. However, the situation might be different when recessive deleterious alleles reach higher frequencies, such as in populations with a small effective population size. For locus-specific inbreeding measures or at low marker density, the ranking of the methods can also change as FHBDmakes better use of the information from neighboring markers. Finally, we confirmed that genomic measures are in general superior to pedigree-based estimates. In particular, FPEDwas uncorrelated with locus-specific homozygosity.

We herein report the result of a large-scale, next generation sequencing (NGS)-based screen for embryonic lethal (EL) mutations in Belgian beef and New Zealand dairy cattle. We estimated by simulation that cattle might carry, on average, ∼0.5 recessive EL mutations. We mined exome sequence data from >600 animals, and identified 1377 stop-gain, 3139 frame-shift, 1341 splice-site, 22,939 disruptive missense, 62,399 benign missense, and 92,163 synonymous variants. We show that cattle have a comparable load of loss-of-function (LoF) variants (defined as stop-gain, frame-shift, or splice-site variants) as humans despite having a more variable exome. We genotyped >40,000 animals for up to 296 LoF and 3483 disruptive missense, breed-specific variants. We identified candidate EL mutations based on the observation of a significant depletion in homozygotes. We estimated the proportion of EL mutations at 15% of tested LoF and 6% of tested disruptive missense variants. We confirmed the EL nature of nine candidate variants by genotyping 200 carrier × carrier trios, and demonstrating the absence of homozygous offspring. The nine identified EL mutations segregate at frequencies ranging from 1.2% to 6.6% in the studied populations and collectively account for the mortality of ∼0.6% of conceptuses. We show that EL mutations preferentially affect gene products fulfilling basic cellular functions. The resulting information will be useful to avoid at-risk matings, thereby improving fertility.

Population genomics is transforming the analyses of biodiversity, particularly the studies in conservation genetics. However, genomic approaches based on short sequencing reads are often subjected to complex molecular protocols and bioinformatics procedures, which are prone to many artifactual biases. In preliminary analyses using common pipelines for handling, filtering and processing genotyping-by-sequencing (GBS) data from three aquatic bird species, we detected a bias likely associated to the sex of individuals of the genus Sula, which could be due to artifacts with sex chromosome derived reads. Thus, we have developed GBirdS, a new pipeline for avian population genetics from GBS data, implementing a new approach to identify molecular markers likely to be linked to the avian W chromosome. The pipeline was applied to a total of 113 samples from three avian species (Sula leucogaster, Sula dactylatra and Mergus octosetaceus), including 54 samples for which the molecular sexing was available. For 53 out of these 54 samples, the sex determination achieved using GBirdS agreed with molecular sexing. We have then removed from subsequent population analyses the sequences observed only in individuals determined as heterogametic (likely to be females) by our pipeline. Removing these sequences resulted in greater average fixation indexes between subpopulations of these three species. Therefore, we conclude that the sequences removed by our pipeline had an artificial effect on interindividual differences and population structure.

The objective of this study was to estimate the dominance variance for repeated live BW records in a crossbred population of pigs. Data were provided by the Walloon Pig Breeding Association and included 22,197 BW records of 2,999 crossbred Pietrain × Landrace K+ pigs from 50 to 210 d of age. The BW records were standardized and adjusted to 210 d of age for analysis. Three single-trait random regression animal models were used: Model 1 without parental subclass effect, Model 2 with parental subclasses considered unrelated, and Model 3 with the complete parental dominance relationship matrix. Each model included sex, contemporary group, and heterosis as fixed effects as well as additive genetic, permanent environment, and residual as random effects. Variance components and their SE were estimated using a Gibbs sampling algorithm. Heritability tended to increase with age: from 0.50 to 0.64 for Model 1, from 0.19 to 0.42 for Model 2, and from 0.31 to 0.53 for Model 3. Permanent environmental variance tended to decrease with age and accounted for 29 to 44% of total variance for Model 1, 29 to 37% of total variance for Model 2, and 34 to 51% of total variance for Model 3. Residual variance explained

Background Inbreeding coefficients can be estimated either from pedigree data or from genomic data, and with genomic data, they are either global or local (when the linkage map is used). Recently, we developed a new hidden Markov model (HMM) that estimates probabilities of homozygosity-by-descent (HBD) at each marker position and automatically partitions autozygosity in multiple age-related classes (based on the length of HBD segments). Our objectives were to: (1) characterize inbreeding with our model in an intensively selected population such as the Belgian Blue Beef (BBB) cattle breed; (2) compare the properties of the model at different marker densities; and (3) compare our model with other methods. Results When using 600 K single nucleotide polymorphisms (SNPs), the inbreeding coefficient (probability of sampling an HBD locus in an individual) was on average 0.303 (ranging from 0.258 to 0.375). HBD-classes associated to historical ancestors (with small segments ≤ 200 kb) accounted for 21.6% of the genome length (71.4% of the total length of the genome in HBD segments), whereas classes associated to more recent ancestors accounted for only 22.6% of the total length of the genome in HBD segments. However, these recent classes presented more individual variation than more ancient classes. Although inbreeding coefficients obtained with low SNP densities (7 and 32 K) were much lower (0.060 and 0.093), they were highly correlated with those obtained at higher density (r = 0.934 and 0.975, respectively), indicating that they captured most of the individual variation. At higher SNP density, smaller HBD segments are identified and, thus, more past generations can be explored. We observed very high correlations between our estimates and those based on homozygosity (r = 0.95) or on runs-of-homozygosity (r = 0.95). As expected, pedigree-based estimates were mainly correlated with recent HBD-classes (r = 0.56). Conclusions Although we observed high levels of autozygosity associated with small HBD segments in BBB cattle, recent inbreeding accounted for most of the individual variation. Recent autozygosity can be captured efficiently with low-density SNP arrays and relatively simple models (e.g., two HBD classes). The HMM framework provides local HBD probabilities that are still useful at lower SNP densities. Electronic supplementary material The online version of this article (10.1186/s12711-017-0370-x) contains supplementary material, which is available to authorized users.

We herein study genetic recombination in three cattle populations from France, New Zealand, and the Netherlands. We identify 2,395,177 crossover (CO) events in 94,516 male gametes, and 579,996 CO events in 25,332 female gametes. The average number of COs was found to be larger in males (23.3) than in females (21.4). The heritability of global recombination rate (GRR) was estimated at 0.13 in males and 0.08 in females, with a genetic correlation of 0.66 indicating that shared variants are influencing GRR in both sexes. A genome-wide association study identified seven quantitative trait loci (QTL) for GRR. Fine-mapping following sequence-based imputation in 14,401 animals pinpointed likely causative coding (5) and noncoding (1) variants in genes known to be involved in meiotic recombination (HFM1, MSH4, RNF212, MLH3, MSH5) for 5/7 QTL, and noncoding variants (3) in RNF212B for 1/7 QTL. This suggests that this RNF212 paralog might also be involved in recombination. Most of the identified mutations had significant effects in both sexes, with three of them each accounting for ∼10% of the genetic variance in males.

Single-step genomic predictions need the inverse of the part of the additive relationship matrix between genotyped animals (A22 ). Gains in computing time are feasible with an algorithm that sets up the sparsity pattern of A22-1 (SP algorithm) using pedigree searches, when A22-1 is close to sparse. The objective of this study is to present a modification of the SP algorithm (RSP algorithm) and to assess its use in approximating A22-1 when the actual A22-1 is dense. The RSP algorithm sets up a restricted sparsity pattern of A22-1 by limiting the pedigree search to a maximum number of searched branches. We have tested its use on four different simulated genotyped populations, from 10 000 to 75 000 genotyped animals. Accuracy of approximation is tested by replacing the actual A22-1 by its approximation in an equivalent mixed model including only genotyped animals. Results show that limiting the pedigree search to four branches is enough to provide accurate approximations of A22-1, which contain approximately 80% of zeros. Computing approximations is not expensive in time but may require a great amount of memory (at maximum, approximately 81 min and approximately 55 Gb of RAM for 75 000 genotyped animals using parallel processing on four threads).

In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on might be minor. This hypothesis was also tested. The inverse of A22 can be computed from the inverse of the triangular factor (T-1) obtained by Cholesky root-free decomposition of A22. We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Depending on the size and structure of the selected sub-population, gains in time to compute are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations.

Some genomic evaluation models require creation and inversion of a genomic relationship matrix ( G ). As the number of genotyped animals increases, G becomes larger and thus requires more time for inversion. A single-step genomic evaluation also requires inversion of the part of the pedigree relationship matrix for genotyped animals ( A 22 ). A strategy was developed to provide an approximation of the inverse of G G ˜ - 1 that may also be applied to the inverse of A 22 \( A ˜ 22 − 1 \) The algorithm proceeds by creation of an incomplete Cholesky factorization \( T ˜ − 1 \) of G −1 . For this purpose, a genomic relationship threshold determines whether 2 animals are closely related. For any animal, the sparsity pattern of the corresponding line in T ˜ − 1 will thus gather elements corresponding to all close relatives of that animal. Any line of T ˜ − 1 is filled in with resulting estimators of the least-squares regression of genomic relationships between close relatives on genomic relationship between the animal considered and those close relatives. The G ˜ − 1 was computed as the matrix product \( T ˜ − 1 \) ′ D − 1 T ˜ − 1 , where D −1 is a diagonal matrix. Then, T − 1 G \( T − 1 \) ′ resulted in a new matrix that is close to diagonal and also needs to be inverted. The inverse of that matrix was approximated with the same decomposition as for approximation of the inverse of G \( G ˜ − 1 \) and the procedure was repeated in successive rounds of recursion until a matrix was obtained that was close enough to diagonal to be inverted element by element. Two applications of the approximation algorithm were tested in a single-step genomic evaluation of US Holstein final score, and correlation coefficients between estimated breeding values based on either real or approximated G −1 were compared. Approximations came closer to G −1 as the number of recursion rounds increased. Approximations were even more accurate and expected to be faster for A 22 . Timesaving strategies are needed to reduce the computing time required for the algorithm.