Genomic inbreeding coefficients based on the distribution of the length of runs of homozygosity in a closed line of Iberian pigs
- Luis Gomez-Raya^{1}Email author,
- Carmen Rodríguez^{1},
- Carmen Barragán^{1} and
- Luis Silió^{1}
https://doi.org/10.1186/s12711-015-0153-1
© Gomez-Raya et al. 2015
Received: 28 November 2014
Accepted: 13 September 2015
Published: 16 October 2015
Abstract
Background
The increasing availability of DNA markers provides new metrics of inbreeding based on single nucleotide polymorphisms (SNPs), i.e. molecular inbreeding or the proportion of runs of homozygosity (ROH), as alternatives to traditional pedigree-based inbreeding coefficients. However, none of these metrics incorporate the length of ROH as an indicator of recent inbreeding. Novel inbreeding coefficients that incorporate length of ROH as a random variable with an associated density are investigated.
Methods
New inbreeding metrics based on the distribution of the length of ROH are proposed: (1) the Kolmolgorov–Smirnov test, (2) a function of the quantiles of the cumulative distribution function of an individual versus the population, and (3) fitting of an exponential distribution to ROH lengths (mean, variance, and the probability of drawing at random a ROH larger than a given threshold). The new inbreeding and pedigree-based metrics were compared using 217 sows of an Iberian line that belong to three groups: C1 (conservation), C2 (conservation derived from C1), and S (selected and derived from C1), with complete pedigrees and genotyped for 35,023 SNPs.
Results
Correlations between pedigree-based and the new genomic inbreeding coefficients ranged from 0.22 to 0.72 but most ranged from 0.60 to 0.70. The correlation between quantile chromosomal inbreeding coefficients (using molecular information of just one chromosome at the time) and chromosomal length was 0.84 (SE = 0.14), supporting the hypothesis that these coefficients incorporate information on ROH length as an indication of recent inbreeding. Kolmogorov–Smirnov and exponential chromosomal inbreeding coefficients were also correlated with chromosomal length (0.57). Chromosome 1 had the largest quantile ROH inbreeding coefficient (largest ROH sizes), whereas chromosome 10 had the lowest (shortest ROH sizes). Selection for lean growth increased ROH-based inbreeding coefficients for group S when compared to unselected groups C1 and C2. At the chromosomal level, this comparison showed that the level of autozygosity and the length of ROH for most of the autosomes increased in the selection line.
Conclusions
Quantile and exponential probability inbreeding coefficients using ROH length as a random variable provide additional information about recent inbreeding compared to existing inbreeding coefficients such as molecular, pedigree-based or total ROH content inbreeding coefficients.
Keywords
Background
The inbreeding coefficient of an individual is the probability that two alleles at a locus in that individual are identical by descent [1]. The inbreeding coefficient is a key parameter to understand the amount of matings between related individuals that have taken place in a population. Inbreeding leads to an increase in homozygosity, which, in turn, reduces performance of production traits (inbreeding depression), reduces fitness and compromises long-term viability of the population [2, 3]. Therefore, control of inbreeding is itself an objective in animal production or conservation genetics [4].
In farm animals, coefficients of inbreeding are systematically computed from pedigree records using path coefficients [5]. If pedigrees are not available, inbreeding coefficients can be calculated using molecular information. In particular, genome-wide single nucleotide polymorphism (SNP) bead chips are used to assess levels of homozygosity [6] or to estimate pedigree-based inbreeding coefficients [7, 8]. These approaches assume that SNPs are unlinked and they do not make use of all available information. However, SNPs are physically linked and alleles at linked markers on the same homologous chromosome are inherited together unless a recombination event occurs between them.
Runs of homozygosity (ROH) are defined as continuous and uninterrupted stretches of DNA sequences without heterozygosity in diploid state [9]. Presence of long ROH can imply recent inbreeding, which can be used to estimate genome-wide autozygosity and inbreeding coefficients, as suggested by Keller et al. [10]. ROH has been used to investigate inbreeding in human [11–13], cattle [14, 15], and pig populations [16, 17].
The approach used to compute inbreeding coefficients based on ROH requires calculating the total length of ROH covering the genome of an individual (for a given minimum number of contiguous homozygous SNPs) divided by the length of the genome [11, 18]. As stated above, recent inbreeding is associated to larger ROH fragments [10–19]. However, it is not well established either how to make a comparison between individuals with different numbers and lengths of ROH fragments or how to use the length of ROH to estimate recent inbreeding.
The objective of this paper was to investigate the use of ROH length as a random variable with an associated distribution or probability density to derive new inbreeding coefficients: (1) a method based on the Kolmogorov–Smirnov test, (2) a method based on quantiles of the distribution of the length of ROH, and (3) a method based on fitting an exponential distribution to the ROH-length distribution. These inbreeding coefficients were compared to SNP-based homozygosity metrics and pedigree inbreeding coefficients. It is shown that the new coefficients provide additional information on recent inbreeding. The new inbreeding coefficients were used to investigate inbreeding in a closed line of Iberian pigs maintained in a conservation program and to investigate the effect of selection on inbreeding.
Methods
Torbiscal line pedigree
Genotyping and SNP-based metrics of inbreeding
DNA was isolated from blood using a standard phenol/chloroform protocol and genotyped with the Illumina Porcine SNP60 BeadChip [25] and the Infinium HD Assay Ultra protocol (Illumina Inc.). Genotypes of 62,163 SNPs were called with the GenomeStudio software (Illumina). In addition, DNA from 17 Iberian pigs representing the main breeding nuclei of this breed were analyzed to identify SNPs of good quality that were monomorphic or had very low minor allele frequency (MAF) in the Torbiscal line. Quality control of genotypes was performed according to the following criteria: call rate for the individual >0.96; SNPs with a call rate >0.99; GenTrain score (measure of the reliability of the SNP detection based on the distribution of genotypic classes) >0.70; AB R mean (mean of the normalized intensity of the heterozygote cluster) >0.35; and MAF >0.05. SNPs located on sex chromosomes, those not mapped in the Sscrofa10.2 assembly (http://gbi.agrsci.dk/pig/sscrofa10_2_annotation/), or those with inconsistent inheritance from dam to daughter were also removed. Based on these criteria 35,023 SNPs were retained and used for further analyses.
Genomic inbreeding coefficients based on the distribution of the length of ROH
A minimum number of contiguous SNPs with homozygous genotypes are required for declaring a stretch of DNA as a ROH in an individual because short tracts of homozygosity are rather common due to strong linkage disequilibrium. ROH length can be expressed either as the number of contiguous homozygous SNPs, or as the length measured in units of physical distance in Mb. These two measures of ROH length are highly correlated and both represent estimates of autozygosity (two chromosomal segments inherited from each parent that are identical from a common ancestor) since only a limited number of SNPs are genotyped within a DNA segment. Because of the exploratory nature of this paper, several alternative minimum numbers of contiguous SNPs (5, 15, 25, and 35) were used to define a ROH in order to investigate their impact on the novel inbreeding coefficients based either on the length of ROH estimated as the number of contiguous homozygous SNPs or in physical distance (Mb). For the majority of the methods, estimates of individual autozygosity (I-ROH) were taken as a deviation from a reference population or group (A-ROH). Unless stated otherwise, the reference population will consist of all individuals with available genotypes. Source code in R language (http://www.r-project.org/) for estimating the inbreeding coefficients and a small example for two individuals are provided as supplementary material in Additional files 1, 2, 3, 4 and 5.
KS-ROH inbreeding coefficient
Quantile-ROH inbreeding coefficient
Exponential-ROH inbreeding coefficient
- (a)Using the mean of the exponential density:where \(\lambda_{I - ROH}\) and \(\lambda_{A - ROH}\) are the rates of the fitted exponential distribution for the individual and for all individuals, respectively.$$F_{{ROH - E^{m} }} = \frac{1}{{\lambda_{I - ROH} }} - \frac{1}{{\lambda_{A - ROH} }},$$
- (b)Using the variance of the exponential density:$$F_{{ROH - E^{v} }} = \frac{1}{{\lambda_{I - ROH}^{2} }} - \frac{1}{{\lambda_{A - ROH}^{2} }}.$$
- (c)Using the integral of the fitted exponential density for the individual from a threshold T to ∞ to calculate the inbreeding coefficient of the individual based on the probability of getting an ROH fragment with length larger than T as:where T is the threshold and x the length of the ROH. This genomic inbreeding coefficient is an estimate of the degree of autozygosity of an individual, and being a probability, it is forced to range from 0 to 1. The threshold is arbitrary but comparison between individuals is feasible when the same threshold is used for individuals from the same population typed with the same array.$$F_{{ROH - E^{p} }} = \int_{T}^{\infty } \lambda_{I - ROH} e^{{ - (\lambda_{I - ROH} )x}} d(x),$$
Note that in the above equations, terms that apply to all individuals (i.e. the exponential distribution with rate \(\lambda_{A - ROH}\)) is the same for all individuals and, therefore, does not affect the ranking of individuals based on their inbreeding coefficients. Results will be provided for all three coefficients comparing correlations of these coefficients with traditional inbreeding coefficients. However, only \(F_{{ROH - E^{m} }}\) or \(F_{{ROH - E^{p} }}\) coefficients will be discussed in other sections of the paper in order to reduce the number of tables and figures.
Traditional inbreeding coefficients
Correlations were estimated between the new inbreeding coefficients based on the length of ROH and the following traditional inbreeding coefficients: (1) pedigree-based inbreeding coefficient (F _{ ped }) computed for each individual by tracing the pedigree back to the founder animals; (2) pedigree-based new inbreeding coefficient (F _{ ped-new}) based on the equations proposed by Hinrichs et al. [23] with breeding animals born in 1980 as the intermediate base generation; (3) pedigree-based old inbreeding coefficient (F _{ ped-old}) based on the equations proposed by Hinrichs et al. [23] after ignoring all inbreeding generated from 1980 on; (4) molecular inbreeding coefficient (F _{ Mol }), defined as the proportion of genotyped SNPs at which an individual is homozygous (identical by state) [6]; and (5) total ROH content based metric of homozygosity [11] calculated for the autosomal genome as \({F_{ROH} = L_{ROH} /L_{AUTO} }\), where \({L_{ROH} }\) is the total ROH length of the individual and \({L_{AUTO} }\) is the length of the autosomal genome [11]. Identification of ROH was performed with the program PLINK (http://pngu.mgh.harvard.edu/purcell/plink/). In order to adapt to the much lower density of SNPs than those used by McQuillan [11], the conditions for declaring a ROH included a sliding window of 15 SNPs, allowing two missing calls and one heterozygous SNP per window; a ROH was declared if it had a length of at least 100 kb and contained 15 or more SNPs. The minimum required density was one SNP per 500 kb and the maximum gap allowed between any two consecutive SNPs was 1000 kb. Other options were according to the default settings in the program.
Results
Correlations between current and new genomic inbreeding coefficients measured in number of SNPs and using alternative minimum numbers of SNPs when declaring a ROH
F _{ ROH-KS } | F _{ ROH-Q } | F _{ ROH-E } ^{ m } | F _{ ROH-E } ^{ v } | F _{ ROH-E } ^{ p } | |
---|---|---|---|---|---|
Minimum number of SNPs >5 | |||||
F _{ ped } | 0.223 | 0.548 | 0.716 | 0.723 | 0.690 |
F _{ ped-new } | 0.226 | 0.548 | 0.717 | 0.724 | 0.691 |
F _{ ped-old } | −0.056 | 0.170 | 0.171 | 0.164 | 0.174 |
F _{ Mol } | 0.406 | 0.749 | 0.963 | 0.945 | 0.969 |
F _{ ROH } | 0.407 | 0.749 | 0.948 | 0.927 | 0.960 |
Minimum number of SNPs >15 | |||||
F _{ ped } | 0.472 | 0.663 | 0.672 | 0.677 | 0.630 |
F _{ ped-new } | 0.473 | 0.663 | 0.672 | 0.677 | 0.630 |
F _{ ped-old } | 0.081 | 0.190 | 0.187 | 0.183 | 0.176 |
F _{ Mol } | 0.675 | 0.892 | 0.902 | 0.885 | 0.892 |
F _{ ROH } | 0.897 | 0.877 | 0.884 | 0.870 | 0.877 |
Minimum number of SNPs >25 | |||||
F _{ ped } | 0.500 | 0.655 | 0.651 | 0.667 | 0.587 |
F _{ ped-new } | 0.501 | 0.655 | 0.651 | 0.668 | 0.587 |
F _{ ped-old } | 0.113 | 0.199 | 0.199 | 0.188 | 0.199 |
F _{ Mol } | 0.688 | 0.866 | 0.857 | 0.850 | 0.830 |
F _{ ROH } | 0.676 | 0.837 | 0.828 | 0.818 | 0.802 |
Minimum number of SNPs >35 | |||||
F _{ ped } | 0.470 | 0.631 | 0.621 | 0.650 | 0.544 |
F _{ ped-new } | 0.470 | 0.630 | 0.620 | 0.650 | 0.543 |
F _{ ped-old } | 0.167 | 0.224 | 0.225 | 0.212 | 0.231 |
F _{ Mol } | 0.655 | 0.829 | 0.813 | 0.815 | 0.774 |
F _{ ROH } | 0.638 | 0.796 | 0.780 | 0.780 | 0.744 |
Correlations between current and new genomic inbreeding coefficients measured in length of ROH in Mb and using alternative minimum numbers of SNPs when declaring a ROH
F _{ ROH-KS } | F _{ ROH-Q } | F _{ ROH-E } ^{ m } | F _{ ROH-E } ^{ v } | F _{ ROH-E } ^{ p } | |
---|---|---|---|---|---|
Minimum number of SNPs >5 | |||||
F _{ ped } | 0.166 | 0.510 | 0.701 | 0.713 | 0.704 |
F _{ ped-new } | 0.169 | 0.510 | 0.707 | 0.714 | 0.705 |
F _{ ped-old } | −0.081 | 0.150 | 0.158 | 0.151 | 0.161 |
F _{ Mol } | 0.317 | 0.696 | 0.960 | 0.939 | 0.960 |
F _{ ROH } | 0.295 | 0.717 | 0.956 | 0.931 | 0.956 |
Minimum number of SNPs >15 | |||||
F _{ ped } | 0.447 | 0.645 | 0.652 | 0.656 | 0.625 |
F _{ ped-new } | 0.447 | 0.645 | 0.653 | 0.657 | 0.625 |
F _{ ped-old } | 0.110 | 0.176 | 0.176 | 0.171 | 0.172 |
F _{ Mol } | 0.613 | 0.878 | 0.894 | 0.875 | 0.890 |
F _{ ROH } | 0.897 | 0.883 | 0.893 | 0.865 | 0.893 |
Minimum number of SNPs >25 | |||||
F _{ ped } | 0.459 | 0.618 | 0.614 | 0.631 | 0.561 |
F _{ ped-new } | 0.458 | 0.619 | 0.614 | 0.632 | 0.560 |
F _{ ped-old } | 0.168 | 0.184 | 0.185 | 0.171 | 0.194 |
F _{ Mol } | 0.587 | 0.850 | 0.840 | 0.835 | 0.813 |
F _{ ROH } | 0.580 | 0.843 | 0.832 | 0.823 | 0.808 |
Minimum number of SNPs >35 | |||||
F _{ ped } | 0.445 | 0.586 | 0.576 | 0.607 | 0.507 |
F _{ ped-new } | 0.443 | 0.585 | 0.576 | 0.607 | 0.506 |
F _{ ped-old } | 0.244 | 0.197 | 0.198 | 0.182 | 0.140 |
F _{ Mol } | 0.607 | 0.809 | 0.792 | 0.797 | 0.675 |
F _{ ROH } | 0.599 | 0.801 | 0.794 | 0.786 | 0.747 |
Correlations between pairs of chromosomal genomic inbreeding coefficients and length (number of SNPs per chromosome)
Length | F _{ Mol } | F _{ ROH } | F _{ ROH-KS } | F _{ ROH-Q } | F _{ ROH-E } ^{ m } | F _{ ROH-E } ^{ p } | |
---|---|---|---|---|---|---|---|
Length | 0.04 | 0.16 | 0.57 | 0.84 | 0.57 | 0.57 | |
F _{ Mol } | 0.25 | 0.45 | 0.01 | −0.07 | 0.44 | 0.45 | |
F _{ ROH } | 0.25 | 0.25 | 0.32 | 0.13 | 0.51 | 0.52 | |
F _{ ROH-KS } | 0.21 | 0.25 | 0.24 | 0.60 | 0.83 | 0.82 | |
F _{ ROH-Q } | 0.14 | 0.25 | 0.25 | 0.20 | 0.59 | 0.58 | |
F _{ ROH-E } ^{ m } | 0.20 | 0.22 | 0.21 | 0.14 | 0.20 | 0.99 | |
F _{ ROH-E } ^{ p } | 0.21 | 0.22 | 0.21 | 0.14 | 0.20 | 0.00 |
Discussion
By “genomic inbreeding coefficient”, we denote a parameter that uses genomic information on autozygosity as a measure of relatedness among ancestors of an individual. It includes molecular inbreeding coefficients, ROH inbreeding coefficients [10–19, 28, 29] and coefficients that make use of the length of ROH as a random variable with an associated probability distribution or probability density function, as proposed in this paper. One of the first issues that had to be addressed is how to estimate ROH. DNA sequencing methods are required to observe autozygosity but often ROH are estimated based on genotypes obtained with BeadChip arrays of SNPs. Stretches of DNA are declared as ROH if a minimum number of consecutive SNPs from an array are homozygous. We explored four different minimum numbers of SNPs to declare a ROH (5, 15, 25, and 35) and considered two alternative measures of length, the number of SNPs and physical length in Mb. Our results suggest that the minimum number of SNPs can affect correlations between genomic and pedigree inbreeding coefficients. On the one hand, Quantile and Kolmolgorov–Smirnov ROH inbreeding coefficients were less correlated with pedigree inbreeding coefficients when the minimum number was small, in contrast to exponential inbreeding coefficients. Nevertheless, differences between inbreeding coefficients based on ROH length were not large, except for F _{ ROH-KS }. On the other hand, correlations between pedigree and genomic inbreeding coefficients were slightly higher when using the ROH length based on number of SNPs instead of physical distance. An explanation is that only some SNPs in a DNA fragment are genotyped and errors in declaring a fragment autozygous add another source of error to the usual genotyping errors, such as SNP location or distance between SNPs in the array. Nevertheless, the correlations based either on the number of SNPs or on physical distance were rather similar across all situations investigated.
All inbreeding coefficients (traditional and newly developed) have advantages and disadvantages. The advantage of the pedigree inbreeding coefficient is that it is simple and only requires recording of pedigrees but it does not account for the sampling that occurs when gametes are produced during meiosis. That is, pedigree inbreeding coefficients are probabilistic and do not account for the fact that individuals with the same inbreeding history can differ in autozygosity. For example, two full-sibs can have different numbers of fragments of autozygosity (and at different locations) just by sampling. In contrast, all genomic inbreeding coefficients account for sampling and they measure the “realized inbreeding” of an individual.
Genomic inbreeding coefficients differ in the way they use the genotype information. Molecular inbreeding coefficients are calculated as the proportion of homozygous sites that are genotyped with an array. They assume that the genotyped SNPs are randomly located across the genome and do not distinguish old from recent inbreeding. This coefficient incorporates the entire breeding history of the individual, including new mutations and old inbreeding. The total ROH content inbreeding coefficient is the proportion of the genome of an individual that comprises autozygous fragments. This coefficient does incorporate regions of autozygosity but, in contrast to the molecular coefficient, it ignores fragments consisting of a single or a few contiguous homozygous SNPs in its computation. Total ROH content inbreeding coefficient does distinguish old from recent inbreeding but with the limitation that direct information on the length of ROH fragments is not used. In principle, two individuals with the same total ROH content inbreeding coefficients can have a different proportion of large and short ROH fragments. However, total ROH content inbreeding coefficients may indirectly account for the length of ROH because highly inbred animals, such as progeny from the mating between two full-sibs, should have larger total ROH content inbreeding coefficients made up by a large number of ROH of larger size.
Comparison of the new metrics to existing methods provides little information on their ability to detect long ROH (as an aid to detect recent inbreeding) since existing methods cannot. Thus, in order to investigate the ability of the new methods to detect long ROH fragments, correlations between chromosomal inbreeding and chromosomal length were performed. A recent common ancestor of the parents of an individual is expected to result in entire chromosomes or long DNA fragments (as a result of single or multiple recombination events in the different paths leading to the parents of the individual) to be identical by descent in the individual. Therefore, long chromosomes are expected to result in longer ROH fragments. In addition, longer chromosomes have been shown to have a lower recombination rate (cM/Mb) in swine [30], which would also result in longer ROH fragments. Our results show that chromosomal length was highly correlated with quantile chromosomal inbreeding coefficients and to a lesser extent with other proposed metrics. Thus, quantile inbreeding coefficients are sensitive to long ROH fragments and, therefore, improve detection of recent inbreeding.
The largest limitation of the newly proposed metrics is that they do not allow for straightforward comparison of the level of inbreeding of individuals from different species. Genomes with different number and size of chromosomes (or recombination rate) may lead to distributions of individual inbreeding coefficients based on ROH length that are not comparable. This may be overcome by using exponential-p inbreeding coefficients and by setting appropriate thresholds that facilitate comparisons across species. For example, thresholds could be chosen based on the distributions of ROH length for each species relative to the distribution of ROH length of several species together.
Traditional and new inbreeding coefficients allowed for the detection of the effect of selection on inbreeding [27]. However, the genomic inbreeding coefficients can pinpoint chromosomal regions where autozygosity is more extensive. Selection has two effects on inbreeding: one is its direct action to increase the frequency of alleles that favorably affect the trait under selection; the other is the increase in inbreeding and autozygosity for all loci regardless of their effects on the trait, which is attributed to co-selection of individuals with high breeding values which tend to share not just alleles at loci with an effect on the trait but at all loci, i.e., to be relatives [31]. Our results for chromosomes 5, 9 and 16 support the hypothesis that autozygosity affects both loci that are related to the selected traits as well as neutral loci scattered over the genome. In addition, the increased autozygosity in the S group is apparent for all chromosomes except chromosome 4. The method can identify chromosomal inbreeding but not the reasons for its occurrence.
In conservation genetics, coancestry coefficients are used to optimize genetic management in a conservation program and several estimators of coancestries based on molecular information have been proposed, e.g., [32, 33]. These methods ignore that linked SNPs are inherited together, and consequently, the information provided by ROH. Pryce et al. [34] showed that ROH could provide additional information on coancestry when mating relatives. However, their approach consisted in estimating the proportion of haplotypes at a given length of ROH that are common between individuals. A novel alternative would be to make use of the expected distribution of the length of the ROH among progeny of related parents, in line with our proposed use of ROH to quantify inbreeding. In other words, to use coancestry coefficients based on the expected shape of the distribution of ROH lengths in the progeny of the two parents.
Conclusions
The proposed inbreeding coefficients add to existing methods to estimate inbreeding by accounting for the length of ROH, which incorporates information on recent inbreeding. Among the proposed metrics, quantile inbreeding coefficients are the most sensitive for identifying individuals with longer ROH fragments. Exponential-p inbreeding coefficients are less sensitive for detecting long ROH fragments but are defined as a probability (they range from 0 to 1) and are, therefore, suitable for comparison of individuals across populations.
Declarations
Authors’ contributions
LS and CR conceived and carried out the genotyping experiments, helped in the data analysis, and contributed greatly with the writing of the manuscript; LGR conceived the idea of using the fragments of ROH as a random variable, analyzed the data and wrote the first version of the manuscript; CB selected the genotyped samples, edited the raw SNP data and helped to write the manuscript. All authors read and approved the final manuscript.
Acknowledgements
The authors are grateful to Wendy M. Rauw for criticism of the manuscript. Technical assistance of Fabián García is gratefully acknowledged. Financial support was provided by RTA2011-00113 and RZ2012-00006 grants. We acknowledge the effort of Jaime Rodrigáñez and all the staff of the Iberian pig farm ‘Dehesón del Encinar’ for maintaining strict pedigree and data recording on the Torbiscal pigs and their ancestors since 1944 until the recent closure of the farm facilities. The authors are thankful to two anonymous reviewers for their comments to improve the manuscript.
Consent for publication
The cover image belongs to the author and therefore no consent is required.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
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