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Before availability of dense SNP data, genetic diversity was characterized and managed with pedigree-based information. Besides this classical approach, 2 methodologies have been proposed in recent years to characterize and manage diversity from dense SNP data: the SNP-by-SNP approach and the alternative based on runs of homozygosity (ROH). The establishment of criteria to identify ROH is a current constraint in the literature dealing with ROH. The objective of this study was, using a medium-density SNP chip, to quantify by 3 methods (pedigree, SNP-by-SNP, and ROH) the genetic diversity on 5 selected French dairy sheep subpopulations and breeds and to assess the effect of the definition of ROH on these estimates. The data set available included individuals from the breeds Basco-Béarnaise, Manech Tête Noire, Manech Tête Rousse, and 2 subpopulations of Lacaune: Lacaune Confederation and Lacaune Ovitest. Animals were genotyped with the Illumina OvineSNP50 BeadChip (Illumina Inc., San Diego, CA). After filtering, the genomic data included 38,287 autosomal SNP and 8,700 individuals, which comprised 72,803 animals in the pedigree. The results indicated that no significant differences were observed in effective population size estimates obtained from pedigree or genomic (SNP-by-SNP or ROH) information. In general, estimates of effective population size were above 200 in Lacaune Confederation and Lacaune Ovitest subpopulations and below 200 in Basco-Béarnaise, Manech Tête Noire, and Manech Tête Rousse breeds. The minimum length that constituted a ROH, the minimum number of SNP that constituted a ROH, as well as the minimum density and the maximum distance allowed between 2 homozygous SNP are ROH-defining factors with important implications in the estimation of the rate of inbreeding. The ROH-based rates of inbreeding in concordance with those obtained from pedigree information require a specific set of values. This particular set of values is different from that identified to obtain ROH-based rates of inbreeding similar to those obtained on a SNP-by-SNP basis. Factors to define ROH do not change the results much unless extreme values are considered, although further research on ROH-based inbreeding is still required.
The preservation of genetic diversity is usually achieved by maximizing the effective population size or, equivalently, by minimizing the rate of inbreeding in a population. Genomic selection can reduce the rate of inbreeding per generation but can lead to a higher rate of inbreeding per year (
). Such an increase in the rate of inbreeding can result in lower genetic diversity, lower response to selection, and a higher exposure of deleterious alleles (
). For this reason, controlling the rate of inbreeding is an important goal in breeding programs.
Before the widespread availability of dense SNP data, genetic diversity was characterized and managed with pedigree-based inbreeding estimates. This approximation refers to the proportion of the genome that is expected to be identical by descent (IBD). However, this pedigree-based approach has several constraints. First, pedigree completeness and quality are essential (
The realized proportion of the genome that 2 individuals share can be more accurately estimated from genome-based information than from pedigree-based information (
), which involves the estimation of the alleles that are identical by state (IBS) for each individual SNP. Consequently, it captures relationships caused by common ancestors going back to a base population where all alleles are supposed to be unique. The second is the segment-based approach (e.g.,
), which considers IBS segments, rather than individual SNP. The segments of homozygous genotypes are called runs of homozygosity (ROH). The ROH-based inbreeding estimates could capture the relatedness between nominally unrelated founders of the pedigree (
Effects of models with finite loci, selection, dominance, epistasis and linkage on inbreeding coefficients based on pedigree and genotypic information.
). The ROH could arise due to autozygosity, where the same chromosomal segment has been passed to an offspring from parents who inherited it from a common ancestor (
). Accordingly, ROH with ancient origin are expected to be shorter, because recombination from repeated meiosis breaks up IBD segments. On the other hand, ROH due to recent inbreeding are expected to be longer because the probability of breaking up IBD segments from recombination is reduced.
There is a need to establish consistent and reproducible criteria for identifying and quantifying ROH. The comparison between studies is challenging because inconsistency is high among the criteria used to identify ROH both within and also between species (
). This lack of standard criteria for identifying ROH enhances the probability of introducing bias on ROH-based inbreeding estimates. Accordingly, some parameters and thresholds imposed during the sequence analysis can affect ROH identification (
). In addition, pruning SNP that show low minor allele frequency, that deviate from Hardy-Weinberg equilibrium, or show high linkage disequilibrium can influence ROH characterization (
for a review]. However, further exploration is desirable to better understand the criteria for estimating ROH-based inbreeding.
Selection of French dairy sheep has been implemented for each local breed separately. The largest breed is the Lacaune, which consists of 2 subpopulations: Lacaune Confederation (LACCon) and Lacaune Ovitest (LACOvi). The population in the western Pyrenees Mountains consists of 3 breeds: Manech Tête Rousse (MTR), Manech Tête Noire (MTN), and Basco-Béarnaise (BB). Breeding programs, started in the sixties, are now clearly profitable (
); however, it is still unclear how to implement genomic management of diversity within these breeds.
The objectives of our study were the following. First, to quantify the genetic diversity in 5 selected French sheep subpopulations and breeds with several pedigree- and marker-based methods and to compare the existing results in terms of rate of inbreeding and on effective population size. Second, to establish the robustness of ROH-based measures of inbreeding to the criteria used to define a ROH. We used a medium-density SNP chip to complete these objectives.
MATERIALS AND METHODS
Data
Rams were genotyped with the OvineSNP50 BeadChip (Illumina Inc., San Diego, CA). Supplemental Figure S1 (https://doi.org/10.3168/jds.2018-15405) shows the distribution of progeny-tested rams genotyped per year of birth. The genotyped animals in the BB breed were born between 1999 and 2008; in the MTN breed between 1996 and 2007; in MTR breed between 1999 and 2009; in the LACCon subpopulation between 1996 and 2012; and in the LACOvi subpopulation between 1999 and 2012.
The SNP quality control included the absence of parent-offspring Mendelian segregation incompatibilities (<3%), SNP call rate >97%, and large deviations from Hardy-Weinberg equilibrium [SNP with P < 10−6 were discarded; see
for more details]. The final data set included 38,287 autosomal SNP and 8,700 genotyped animals. The pedigree data set was constructed with all known ancestors of the genotyped individuals and comprised 72,803 animals, with all breeds merged. Table 1 shows per subpopulation and breed the number of genotyped animals, the individuals included in the pedigree, and the equivalent number of complete generations.
Table 1Number of genotyped animals, individuals included in the pedigree, and equivalent number of complete generations per subpopulation and breed
PEDIG: A Fortran package for pedigree analysis suited for large populations. In Proceedings of the 7th World Congress of Genetics Applied to Livestock Production, France.
. The generation interval was also calculated using PEDIG and was 4.95, 4.51, 4.20, 3.61, and 3.55 for BB, MTN, MTR, LACCon, and LACOvi, respectively, in accordance with previous estimates (
, IBS relationships are twice the probability that 2 alleles taken at random, 1 per individual, are identical. For 1 individual with itself, the sampling is with replacement, and the relationship reduces to 1 + the probability that 1 allele is identical to the other. Thus, the inbreeding coefficient based on individual SNP (FSNP) of individual i
is simply the probability that the 2 alleles are identical, measured across the genome, and was equal to the proportion of typed loci at which this individual is homozygous (
). More specifically, the inbreeding estimator (FROH), is the proportion of the genome that is in ROH. For individual i,
was calculated as
where
is the total number of ROH in individual i,
is the length of the kth ROH in individual i in base pairs, and lg is the length of the genome in base pairs (which was 2,438,309,318 bp in the data set analyzed in the present study). An example of ROH is shown in Figure 1.
Figure 1Example of run of homozygosity (ROH) within the dotted squares. The first allele is indicated by 1 and the second allele is indicated by 2 within the circles. The minimum length that constituted a ROH was 4 Mb, the minimum number of SNP was 10, the minimum density was 1 SNP per 10 kb, the maximum distance allowed between 2 consecutive homozygous SNP in a run was 1 Mb, a maximum of 2 missing genotypes were allowed (empty circles,) and 1 heterozygous genotype within a particular ROH was permitted (alleles indicated in black). nROH refers to the number of ROH, lROH indicates the length of the ROH, and lg is the length of the genome.
There are 6 criteria for identifying a ROH, which consider the information provided by the SNP itself (i.e., homozygous, heterozygous, or missing genotype) and its map position in the chromosome. These 6 criteria are (1) the minimum length, in megabases, that constituted a ROH; (2) the minimum number of SNP that constituted a ROH; (3) the minimum density, at least 1 SNP in each direction, in kilobases; (4) the maximum distance allowed between 2 consecutive homozygous SNP, in megabases; (5) the maximum number of missing genotypes allowed; and (60 the maximum number of heterozygous genotypes permitted within a particular ROH. Table 2 shows the different values tested for each ROH defining factor and their default values (based on
Rates of inbreeding (ΔF) per year
were computed from the regression coefficient of the inbreeding coefficient for each individual on the year of birth, taking into account the 8,700 animals. Rates of inbreeding per generation (ΔFPED, ΔFSNP, and ΔFROH) were calculated by multiplying the rates of inbreeding per year by the generation interval (L). Finally, estimates of effective population size (Ne) were obtained from the rate of inbreeding per generation as NePED = 1/2ΔFPED, NeSNP = 1/2ΔFSNP, and NeROH = 1/2ΔFROH (
). Confidence intervals for effective population sizes were obtained from the standard error of the rates of inbreeding per year; for example, the estimator of NeSNP is
and its confidence interval is
RESULTS
Comparison of Pedigree- and Genome-Based Inbreeding Estimators
In this section, the default values used for identifying a ROH were (1) 4 Mb as the minimum length that constituted a ROH, (2) 30 as the minimum number of SNP, (3) 1 SNP/100 kb as the minimum density, (4) 1 Mb as the maximum distance allowed between 2 consecutive homozygous SNP in a run, (5) 2 missing genotypes maximum, and (6) 1 heterozygous genotype within a particular ROH. These default values are highlighted in bold in Table 2.
Table 3 shows the average inbreeding values for each evaluated subpopulation and breed. The ROH-based inbreeding estimates were slightly higher than those obtained from pedigree-based information. Inbreeding estimates obtained on a SNP-by-SNP basis (IBS) result in higher values than other estimators because they cannot distinguish between IBD and IBS. The difference is roughly a constant [e.g., for a single locus IBS = IBD + (1 − IBD)(p2 + q2), where p and q are the allele frequencies] that vanishes when computing the rates of inbreeding (
). The lowest values of inbreeding were observed in LACCon subpopulation. In addition, the highest values of inbreeding were obtained for LACOvi subpopulation (FPED) and MTN breed (FSNP and FROH).
Table 3Mean ± SE of the inbreeding coefficient, rate of inbreeding per generation (ΔF) ± SE, and effective population size (Ne; 95% CI) for each evaluated subpopulation and breed
ROH identifying values were: (1) the minimum length that constituted a ROH was 4 Mb; (2) the minimum number of SNP was 30; (3) the minimum density was 1 SNP per 100 kb; (4) the maximum distance allowed between 2 consecutive homozygous SNP in a run was 1 Mb; (5) a maximum of 2 missing genotypes; and (6) 1 heterozygous genotype within a particular ROH were permitted.
ROH identifying values were: (1) the minimum length that constituted a ROH was 4 Mb; (2) the minimum number of SNP was 30; (3) the minimum density was 1 SNP per 100 kb; (4) the maximum distance allowed between 2 consecutive homozygous SNP in a run was 1 Mb; (5) a maximum of 2 missing genotypes; and (6) 1 heterozygous genotype within a particular ROH were permitted.
ROH identifying values were: (1) the minimum length that constituted a ROH was 4 Mb; (2) the minimum number of SNP was 30; (3) the minimum density was 1 SNP per 100 kb; (4) the maximum distance allowed between 2 consecutive homozygous SNP in a run was 1 Mb; (5) a maximum of 2 missing genotypes; and (6) 1 heterozygous genotype within a particular ROH were permitted.
59 (38–132)
81 (52–174)
109 (87–146)
227 (179–310)
357 (252–616)
1 FPED = inbreeding calculated from pedigree-based information; FSNP = inbreeding calculated on a SNP-by-SNP basis; FROH = ROH-based inbreeding.
3 ROH identifying values were: (1) the minimum length that constituted a ROH was 4 Mb; (2) the minimum number of SNP was 30; (3) the minimum density was 1 SNP per 100 kb; (4) the maximum distance allowed between 2 consecutive homozygous SNP in a run was 1 Mb; (5) a maximum of 2 missing genotypes; and (6) 1 heterozygous genotype within a particular ROH were permitted.
The correlation coefficient between the inbreeding estimates is shown in Table 4. For all the evaluated subpopulations and breeds the correlation coefficient between pedigree- and genomic-based inbreeding estimates is moderate (ranged between 0.38 and 0.58). The highest correlation was observed between both genomic inbreeding estimates (ranged between 0.78 and 0.88). Moreover, the lowest correlation was observed between FPED and FROH, with the exception of MTR breed, where the lowest correlation was observed between FPED and FSNP. Differences are, however, very small.
Table 4Correlation coefficient of the inbreeding estimates for each evaluated subpopulation and breed
ROH identifying values were: (1) the minimum length that constituted a ROH was 4 Mb; (2) the minimum number of SNP was 30; (3) the minimum density was 1 SNP per 100 kb; (4) the maximum distance allowed between 2 consecutive homozygous SNP in a run was 1 Mb; (5) a maximum of 2 missing genotypes; and (6) 1 heterozygous genotype within a particular ROH were permitted.
ROH identifying values were: (1) the minimum length that constituted a ROH was 4 Mb; (2) the minimum number of SNP was 30; (3) the minimum density was 1 SNP per 100 kb; (4) the maximum distance allowed between 2 consecutive homozygous SNP in a run was 1 Mb; (5) a maximum of 2 missing genotypes; and (6) 1 heterozygous genotype within a particular ROH were permitted.
BB
0.53
0.51
0.86
MTN
0.50
0.48
0.88
MTR
0.56
0.58
0.84
LACCon
0.38
0.38
0.78
LACOvi
0.42
0.40
0.79
1 FPED = inbreeding calculated from pedigree-based information; FSNP = inbreeding calculated on a SNP-by-SNP basis; FROH = ROH-based inbreeding.
3 ROH identifying values were: (1) the minimum length that constituted a ROH was 4 Mb; (2) the minimum number of SNP was 30; (3) the minimum density was 1 SNP per 100 kb; (4) the maximum distance allowed between 2 consecutive homozygous SNP in a run was 1 Mb; (5) a maximum of 2 missing genotypes; and (6) 1 heterozygous genotype within a particular ROH were permitted.
The rate of inbreeding per generation is also shown in Table 3 for each evaluated subpopulation and breed. Similar estimates of rate of inbreeding were obtained both with pedigree- and genomic-based information, in contrast to the average inbreeding estimates. The highest values were observed for ΔFPED (in BB, MTN, and LACOvi) and ΔFROH (in MTR and LACCon). The lowest values of rate of inbreeding were obtained with ΔFSNP, except for LACOvi, where the lowest values were also observed with ΔFROH. For Lacaune, values of ΔF are consistent with the 3 methods; this was not the case for BB, MTN, and MTR, where ΔFSNP were consistently lowest.
Table 3 also shows estimates of Ne with confidence intervals. The lowest values of effective population size were obtained from ΔFPED (in BB, MTN and LACOvi) and ΔFROH (in MTR and LACCon). The highest values of effective population size were observed with ΔFSNP, except for LACOvi, where the highest values were also observed with ΔFROH. The 3 rates of inbreeding agree, ranking subpopulations and breeds by effective population size. In order of decreasing Ne, the breeds and subpopulations were LACOvi, LACCon, MTR, MTN, and BB. The only exception was observed with ΔFPED, which inverted LACCon and LACOvi. In general, Ne estimates were above 200 in LACCon and LACOvi subpopulations and below 200 in BB, MTN, and MTR breeds. However, no significant differences were observed in the estimates of Ne obtained from the 3 evaluated inbreeding estimates. This highlights the agreement between pedigree-based and SNP-by-SNP estimates of inbreeding with those obtained from ROH with the default values.
Effect on Estimates of Factors Defining ROH
In the evaluation of each ROH-defining factor, the other 5 ROH-defining factors remained the default value highlighted in bold in Table 2.
Figure 2, Figure 3 and Supplemental Figure S2 (https://doi.org/10.3168/jds.2018-15405) show the evolution of the rate of inbreeding in all evaluated breeds and subpopulations for each ROH-defining factor. The 6 evaluated factors showed, in general, the same behavior independently of the tested subpopulation or breed. Four ROH-defining factors have implications on the rate of inbreeding. These factors are (1) the minimum length that constituted a ROH, (2) the minimum number of SNP that constituted a ROH, (3) the minimum density (at least 1 SNP every some specific number of bases), and (4) the maximum distance allowed between 2 consecutive homozygous SNP. Figure 2 shows that, if the minimum length that constituted a ROH is equal or lower than 4 Mb (which could probably reflect ancient inbreeding), ΔFROH are, in general, in concordance with ΔFPED. However, if the minimum length that constituted a ROH is higher than 4 Mb (which could probably reflect more recent inbreeding), ΔFROH are close to ΔFSNP. In addition, reduced ROH lengths provided higher rates of inbreeding than greater ROH lengths. Accordingly, ΔFROH obtained with ROH of ≤80 SNP are consistent with ΔFPED, and ΔFROH estimated from ROH of more than 80 SNP are, overall, similar to ΔFSNP. The ΔFROH assessed with a minimum density equal or lower than 1 SNP every 90 kb is close to ΔFSNP, and the ΔFROH estimated with a minimum density higher than 1 SNP every 90 kb is close to ΔFPED. Finally, a maximum distance between 2 homozygous SNP higher than 0.3 Mb makes ΔFROH agree with ΔFPED, and equal or lower to 0.3 Mb makes ΔFROH match ΔFSNP (Figure 3).
Figure 2Evolution of the rate of inbreeding per generation (ΔF) in relation to the minimum length that constituted a run of homozygosity (ROH; Mb). BB = Basco-Béarnaise; MTN = Manech Tête Noire; MTR = Manech Tête Rousse; LACCon = Lacaune Confederation; LACOvi = Lacaune Ovitest. Gray point indicates the default value. Bars indicate the SE. Dashed lines indicate the 95% CI of pedigree-based inbreeding. Dotted lines indicate the 95% CI of SNP-by-SNP–based inbreeding.
Figure 3Evolution of the rate of inbreeding per generation (ΔF) in relation to the minimum number of SNP, the minimum density, and the maximum distance between 2 homozygous SNP. BB = Basco-Béarnaise; MTN = Manech Tête Noire; MTR = Manech Tête Rousse; LACCon = Lacaune Confederation; LACOvi = Lacaune Ovitest. Gray point indicates the default value. Bars indicate the SE. Dashed lines indicate the 95% CI of pedigree-based inbreeding. Dotted lines indicate the 95% CI of SNP-by-SNP–based inbreeding.
Rates of inbreeding higher than those obtained with ROH default values have implications on the estimation of diversity because a ΔF of 0.1% means that 0.1% of heterozygosity is lost, and the actual constraints on management of inbreeding (e.g., using optimal contributions) are typically based on ΔF (
). Thus, different factors for ROH will lead to dissimilar ΔFROH, which will lead to diverse selection decisions with more or less emphasis on genetic diversity.
Two ROH-defining factors generally have no consequences on the estimation of the rate of inbreeding across the evaluated subpopulations and breeds. These 2 factors are (1) the maximum number of missing genotypes allowed and (2) the maximum number of heterozygous permitted (Supplemental Figure S2; https://doi.org/10.3168/jds.2018-15405).
The ranking of subpopulations and breeds regarding the rate of inbreeding is the same when evaluating the 6 ROH-defining factors, where BB has the highest ΔF followed by MTN, MTR, LACCon, and, finally, LACOvi. This ranking is only disrupted when the minimum length that constituted a ROH is higher than 10 Mb and when the minimum number of SNP is higher than 300, probably due to the difficulty in finding these types of ROH; consequently, ROH-based inbreeding might be close to 0.
DISCUSSION
Inbreeding happens when an individual inherits chromosomal fragments that are IBD from both parents, leading to faster allele fixation, reduction of additive genetic variance (in principle), inbreeding depression, and a decline in the response to selection (
proposed to estimate inbreeding on a SNP-by-SNP basis, where each SNP is considered individually. An alternative way to estimate inbreeding coefficients is to determine the IBD probability of chromosome segments (ROH) instead of each SNP individually (
Inbreeding coefficients evaluated in the present study are defined in relation to the base population. In FPED, it is relative to the pedigree depth; for FROH, it is dependent on the ROH length; finally, in FSNP, it is relative to Hardy-Weinberg equilibrium. Thus, some differences arise from the different definitions. The FPED estimates were lower than FSNP and FROH, suggesting that FPED may possibly be underestimating inbreeding. This can be explained considering that FPED is an expectation and variability exists around this expectation (
). In addition, when calculating FPED, it is assumed that founder animals are unrelated. This assumption may also lead to the underestimation of FPED if the recorded pedigree is not deep enough (depth of pedigree is very heterogeneous in sheep breeds, as shown in Table 1), is incomplete, or has errors due to misidentification (8% in these sheep breeds;
) and incorrect recording. In addition, FPED assumes that the loci are neutral, so it does not consider loci submitted to selection. As pedigree information has been used extensively to measure the proportion of the genome that is IBD, the relatively moderate correlation between FPED and FROH supports that FROH can be used to predict IBD in sheep populations (
indicated a correlation between FPED and FROH longer than 1 Mb and FROH longer than 5 Mb of 0.78 and 0.82, respectively.
The absolute value of the inbreeding coefficient is not a valuable alternative to consider whether there is too much inbreeding or not because it is affected by several factors, such as (1) the number of generations considered, (2) if markers are used, (3) the allele frequency spectrum of those markers, or (4) factors defining ROH. The rate of inbreeding is a better criterion to handle inbreeding management, as it translates to the effective size of a population (
Genomic management of inbreeding in breeding schemes.
in: Proceedings of the 11th World Congress of Genetics Applied to Livestock Production, ICAR and Interbull, New Zealand. Am. Soc., Anim. Sci.,
Champaign, IL2018
Sheep have kept a considerable level of genetic diversity. The estimates of effective population size shown in our study are similar to those previously reported in the same breeds (
International Sheep Genomics Consortium Genome-wide analysis of the world's sheep breeds reveals high levels of historic mixture and strong recent selection.
Estimations of linkage disequilibrium, effective population size and ROH-based inbreeding coefficients in Spanish Churra sheep using imputed high-density SNP genotypes.
indicated the Border Leicester breed has the largest total number of ROH, followed by Poll Dorset and, finally, Merino; those authors also identified ROH within autosomes.
used the haplotype homozygosity method to infer population history and structure of Welsh sheep breeds. This approach is based on the genome-wide distribution of ROH. Finally,
related the ROH regions with subvital performance in Swakara breed. In addition, relatively few studies have assessed which set of parameters is optimal for identifying ROH to better understand their effects on detecting inbreeding. Accordingly, FROH does not accumulate over generations, as pedigree-based inbreeding estimates, because ROH break down due to recombination (
Genomic management of inbreeding in breeding schemes.
in: Proceedings of the 11th World Congress of Genetics Applied to Livestock Production, ICAR and Interbull, New Zealand. Am. Soc., Anim. Sci.,
Champaign, IL2018
). Finally, the probability of finding long ROH could be higher in regions surrounding the centromere, where the recombination rate is supposed to be reduced. Thus, efforts should be made to obtain correct ROH-based inbreeding estimates when defining ROH. It has been shown that 4 defining factors influence the identification of ROH-based inbreeding. The minimum length that should constitute a ROH has been previously studied by
, who considered a minimum length of 4 Mb to obtain reliable estimates of inbreeding. In addition, ROH-based rates of inbreeding were higher with short ROH than with long ROH, in agreement with results obtained from pedigree-based information in the same breeds (
indicated that a minimum ROH length of 20 to 50 SNP gave the most accurate and efficient estimates of ROH-based inbreeding estimates. The other 2 important ROH-defining factors identified in our study were the maximum distance between 2 homozygous SNP and the minimum density between 2 SNP. The ROH-based rates of inbreeding in concordance to those obtained from pedigree-based information require a specific set of values in the other ROH-defining factors. This particular set of values is different to that identified to obtain ROH-based rates of inbreeding similar to those obtained on a SNP-by-SNP basis.
Detecting ROH based on 50K chip data gave estimates similar to ROH from sequence data (
). Consequently, in the absence of full sequence data, ROH based on 50K can be used to assess inbreeding. Notwithstanding, genotypes denser than 50K could be required to accurately detect short ROH.
In conclusion, our results show that rates of inbreeding and effective population sizes are empirically comparable across methods (pedigree, SNP-by-SNP, and ROH). Effective population sizes of these dairy sheep breeds are in the low hundreds. In addition, factors to define ROH do not change much unless extreme values are considered, although further research on ROH-based inbreeding is still required.
ACKNOWLEDGMENTS
We thank Carole Moreno (INRA, Castanet Tolosan, France) and 2 anonymous referees for useful suggestions on the manuscript. This project has received funding from the European Unions' Horizon 2020 Research & Innovation programme under grant agreement no. 772787 – SMARTER (Small Ruminants Breeding for Efficiency and Resilience, Castanet Tolosan, France). This work was also supported by ARDI (Research, Development and Innovation, Vitoria, Spain; grant agreement EFA 208/16) from POCTEFA funds, and GDivSelGen (Efficient Use of Genetic Diversity in Genomic Selection, Paris, France) action (INRA SelGen metaprogram). Authors are also grateful to the GenoToul bioinformatics platform Toulouse Midi-Pyrenees (Castanet Tolosan, France) for providing computing and storage resources.
PEDIG: A Fortran package for pedigree analysis suited for large populations. In Proceedings of the 7th World Congress of Genetics Applied to Livestock Production, France.
Estimations of linkage disequilibrium, effective population size and ROH-based inbreeding coefficients in Spanish Churra sheep using imputed high-density SNP genotypes.
Effects of models with finite loci, selection, dominance, epistasis and linkage on inbreeding coefficients based on pedigree and genotypic information.
Genomic management of inbreeding in breeding schemes.
in: Proceedings of the 11th World Congress of Genetics Applied to Livestock Production, ICAR and Interbull, New Zealand. Am. Soc., Anim. Sci.,
Champaign, IL2018
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