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Symposium review: Exploiting homozygosity in the era of genomics—Selection, inbreeding, and mating programs

Open AccessPublished:April 21, 2020DOI:https://doi.org/10.3168/jds.2019-17846

      ABSTRACT

      The advent of genomic selection paved the way for an unprecedented acceleration in genetic progress. The increased ability to select superior individuals has been coupled with a drastic reduction in the generation interval for most dairy populations, representing both an opportunity and a challenge. Homozygosity is now rapidly accumulating in dairy populations. Currently, inbreeding depression is managed mostly by culling at the farm level and by controlling the overall accumulation of homozygosity at the population level. A better understanding of how homozygosity and recessive load are related will guarantee continued genetic improvement while curtailing the accumulation of harmful recessives and maintaining enough genetic variability to ensure the possibility of selection in the face of changing environmental conditions. In this review, we present a snapshot of the current dairy selection structure as it relates to response to selection and accumulation of homozygosity, briefly outline the main approaches currently used to manage inbreeding and overall variability, and present some approaches that can be used in the short term to control accumulation of harmful recessives while maintaining sustained selection pressure.

      Key words

      INBREEDING AND GENOMIC INFORMATION

       Genomic Selection as a Breeding Standard

      After its initial implementation in the US dairy population (
      • Wiggans G.R.
      • Cole J.B.
      • Hubbard S.M.
      • Sonstegard T.S.
      Genomic selection in dairy cattle: The USDA experience.
      ), genomic selection has become a consolidated approach, which is now the standard in many breeding domains, including the vast majority of livestock (
      • Georges M.
      • Charlier C.
      • Hayes B.
      Harnessing genomic information for livestock improvement.
      ), crop (
      • Wallace J.G.
      • Rodgers-Melnick E.
      • Buckler E.S.
      On the road to breeding 4.0: Unraveling the good, the bad, and the boring of crop quantitative genomics.
      ), and forestry (
      • Grattapaglia D.
      ) species. Although genomic selection has been hailed as a revolutionary shift in animal breeding, it represents the latest in a series of iterations in the improvement of efficiency of selection, which spans a good part of 2 centuries. The discovery of single-gene transmission by
      • Mendel G.
      Experiments in Plant Hybridisation.
      , the theorization of multiple gene inheritance by
      • Fisher R.A.
      The Genetical Theory of Natural Selection.
      , the introduction of pedigree relationships by
      • Wright S.
      Coefficients of inbreeding and relationship.
      , the formalization of the selection index by
      • Hazel L.N.
      • Lush J.L.
      The efficiency of three methods of selection.
      , and the implementation of linear mixed models by
      • Henderson C.R.
      Estimation of variance and covariance components.
      all represent key innovations in the efficiency of discriminating among individuals on the basis of their genetic value that precede the use of genome-wide marker maps in prediction (
      • Meuwissen T.H.E.
      • Hayes B.J.
      • Goddard M.E.
      Prediction of total genetic value using genome-wide dense marker maps.
      ).
      Each of these incremental improvements increased the efficiency of selection. Similarly, and inevitably, these improvements have also resulted in an increase in inbreeding. The accumulation of inbreeding in selected populations is unavoidable, and it is the consequence of intense directional selection, the high disparity of reproductive success introduced by AI and other reproductive advancements, and of the use of BLUP and truncation selection, which favor the overrepresentation of a few elite families (
      • Miglior F.
      • Beavers L.
      Genetic diversity and inbreeding: Before and after genomics.
      ), leading to large variability in family size and the consequent reduction of the effective population size and higher rates of inbreeding.

       How Genomic Selection Affects Inbreeding

      Several authors have discussed the influence of genomic selection on inbreeding (
      • Howard J.T.
      • Pryce J.E.
      • Baes C.
      • Maltecca C.
      Invited review: Inbreeding in the genomics era: Inbreeding, inbreeding depression, and management of genomic variability.
      ;
      • Varona L.
      • Legarra A.
      • Toro M.A.
      • Vitezica Z.G.
      Non-additive effects in genomic selection.
      ;
      • Baes C.F.
      • Makanjuola B.O.
      • Miglior F.
      • Marras G.
      • Howard J.T.
      • Fleming A.
      • Maltecca C.
      Symposium review: The genomic architecture of inbreeding: How homozygosity affects health and performance.
      ). Here, we will briefly recap a few of the main concepts. On one side, under genomic selection, we can observe an increased rate of inbreeding per year due to shortening of the generation interval. At the same time, the rate of inbreeding per generation should decrease because of our increased ability to discriminate Mendelian sampling among individuals, as well as the ability to access a larger pool of genotyped individuals compared with traditional progeny test schemes (
      • Daetwyler H.D.
      • Villanueva B.
      • Bijma P.
      • Woolliams J.A.
      Inbreeding in genome-wide selection.
      ). In general terms, all these phenomena are real. The net result of these combined processes, though, is that under genomic selection, homozygosity accumulates at a faster rate than under pedigree selection. Young bulls' pedigree inbreeding in Holstein has increased from 7.06% in 2012 to 9.59% in 2019. In the same period, genomic inbreeding has increased from 7.89 to 13.02%. Similar estimates can be seen for Jersey (from 6.49 to 8.76% pedigree and 8.93 to 10.87% genomic) and for Brown Swiss (from 7.30 to 9.22% pedigree, and from 8.20 to 10.87% genomic; CDCB April 2019, https://queries.uscdcb.com/eval/summary/inbrd.cfm). Another example of this phenomenon has been documented in French cattle, with a significant increase in pedigree inbreeding for Normande (0.059 to 0.088% per year) and Holstein (0.19 to 0.49% per year) and genomic inbreeding for Holstein (0.080 to 0.55% per year) under genomic selection compared with selection by progeny testing (
      • Doublet A.C.
      • Croiseau P.
      • Fritz S.
      • Michenet A.
      • Hozé C.
      • Danchin-Burge C.
      • Laloë D.
      • Restoux G.
      The impact of genomic selection on genetic diversity and genetic gain in three French dairy cattle breeds.
      ).

      WHAT DOES INBREEDING MEASURE?

      In the previous section, we discussed how the process of selection affects the accumulation of inbreeding. Often, the implicit assumption made concerning inbreeding is that its accumulation is harmful tout court. It is important to note that, in itself, inbreeding is neither good nor bad. In selecting for the improvement of a particular trait (in most cases, we are interested in increasing the yield of a particular production trait), the accumulation of homozygosity at favorable variants is the primary objective. This, in turn, has implications for the amount of genetic variability and the response to selection in future generations, which will be discussed later. Accumulation of inbreeding depression is, for the most part, the unintended result of how selection is conducted in breeding programs.

       Inbreeding and Inbreeding Depression

      A working definition of inbreeding, following that of
      • Malécot G.
      Les Mathematiques de I'Heredite.
      , was given by
      • Kimura M.
      • Crow J.F.
      On the maximum avoidance of inbreeding.
      as the probability that 2 random alleles at the same locus from 2 uniting gametes are identical by descent from a common ancestor. At a single locus, in a random mating population, the mean of a population is defined as μ = a(pq) + 2dpq, where p and q are the allele frequencies of the locus and a and d are the genotypic values for additive and dominance, respectively (
      • Falconer D.S.
      • Mackay T.F.C.
      Introduction to Quantitative Genetics.
      ). Under inbreeding, the previous equation is modified to μ = a(pq) + 2d(1 – F)pq, where F is the inbreeding coefficient. The population mean, therefore, under inbreeding, is reduced by a quantity of −2pqFd. This reduction is usually referred to as inbreeding depression. The first thing to notice is that the insurgence of inbreeding depression depends on dominance. If no dominance is present, the change in population mean will be zero, and inbreeding will not have an effect on the population. Conversely, for a single locus, if d > 0, inbreeding will decrease the mean of the population and if d < 0, inbreeding will increase it. If we generalize this to multiple loci, the insurgence of inbreeding depression requires dominance to be directional (dominance effects are, on average, negative). This agrees with empirical results, and recessive deleterious mutations and partial directional dominance are normally considered the drivers of inbreeding depression (
      • Charlesworth D.
      • Willis J.H.
      The genetics of inbreeding depression.
      ) and are usually referred to as genomic or recessive load. Under this scenario, deleterious alleles are (partially) recessive and are generated by recurrent mutation so that deleterious alleles in the “base” population are present in the heterozygous state. Inbreeding increases the frequency of homozygotes for deleterious alleles as a result of selection and drift, which results in inbreeding depression (
      • Falconer D.S.
      • Mackay T.F.C.
      Introduction to Quantitative Genetics.
      ).

       Genetic Variance Under Inbreeding

      The relationship of inbreeding with genetic variance is nuanced. The total genetic variance under inbreeding as defined by
      • Weir B.S.
      • Cockerham C.
      Two-locus theory in quantitative genetics.
      can be given by the formula
      VGF = (1 + F)VA + (1 – F)VD + …,


      where VA and VD are the additive and dominance variances and “…” are the remaining terms related to the covariance between additive and dominance as well as the variance of inbreeding depression itself; they are omitted here for simplicity but an extensive treatment of the subject can be found in
      • Abney M.
      • McPeek M.S.
      • Ober C.
      Estimation of variance components of quantitative traits in inbred populations.
      . It should be noted that in the absence of dominance variation, the total genetic variance is given by (1 + F)VA and is larger than that for the founder population. This holds only in the absence of dominance, and results with nonadditive variation are more complex (
      • Walsh B.
      • Lynch M.
      Evolution and Selection of Quantitative Traits.
      ).

      PRIMARY QUESTION

      Given what we have outlined above, it should be evident that inbreeding is an imperfect measure of the underlying recessive load of an individual because it cannot distinguish the accumulation of homozygosity for favorable variants, compared with neutral or deleterious loci. Some populations, such as US Jersey cattle, have even undergone purging inbreeding (
      • Gulisija D.
      • Crow J.F.
      Inferring purging from pedigree data.
      ). Two individuals could therefore, in principle, have the same inbreeding coefficient but a different deleterious load, simply because inbreeding has been accumulated in different regions of the genome. A perfect inbreeding management strategy would allow discrimination between these 2 individuals based on the amount of deleterious recessive each carries.

       Identifying Lethals and Sublethals

      Genomic information has made the identification of lethal recessives extremely effective. To date, at least 16 known recessives are tracked in the US dairy population (
      • Cole J.B.
      • VanRaden P.M.
      • Null D.J.
      • Hutchinson J.L.
      • Cooper T.A.
      • Hubbard S.M.
      AIP research report Genomic4: Haplotype tests for economically important traits of dairy cattle.
      ). This is partly due to the increased resolution that larger marker panels and sequence information provide, facilitating the detection of lethals via reverse genetic screening (
      • Charlier C.
      • Li W.
      • Harland C.
      • Littlejohn M.
      • Coppieters W.
      • Creagh F.
      • Davis S.
      • Druet T.
      • Faux P.
      • Guillaume F.
      • Karim L.
      • Keehan M.
      • Kadri N.K.
      • Tamma N.
      • Spelman R.
      • Georges M.
      NGS-based reverse genetic screen for common embryonic lethal mutations compromising fertility in livestock.
      ), but it also stems from the fact that recessives can be identified, at least in the first instance, with simple statistical tools, essentially by tracking distortions from the expected genotypic frequencies (
      • VanRaden P.M.
      • Olson K.M.
      • Null D.J.
      • Hutchison J.L.
      Harmful recessive effects on fertility detected by absence of homozygous haplotypes.
      ). When recessives are identified with a high degree of accuracy, then mating avoidance can be effectively deployed.
      • Cole J.B.
      • Null D.J.
      • VanRaden P.M.
      Phenotypic and genetic effects of recessive haplotypes on yield, longevity, and fertility.
      estimated annual losses of at least $10.7 million due to known recessives. As the number of recessives identified increases, managing them through mating becomes more involved. Heuristic methods have been proposed by
      • Cole J.B.
      A simple strategy for managing many recessive disorders in a dairy cattle breeding program.
      to manage the total lethal recessive load. More recently,
      • Johnsson M.
      • Gaynor R.C.
      • Jenko J.
      • Gorjanc G.
      • de Koning D.J.
      • Hickey J.M.
      Removal of alleles by genome editing (RAGE) against deleterious load.
      proposed the use of genome editing to remove deleterious recessives. When mutations in the population are partially dominant and harmful but have small to moderate-sized effects, methods based on genotype frequency distortions are not a viable solution. The identification of partially detrimental recessives then has to rely on the estimation of dominance effects. Unfortunately, this presents several challenges. The proportion of genetic variance at a causal variant that is captured by markers is ρ2 for additive variants, but ρ4 for dominant variants, where ρ is the allelic correlation (
      • Zhu Z.
      • Bakshi A.
      • Vinkhuyzen A.A.E.
      • Hemani G.
      • Lee S.H.
      • Nolte I.M.
      • van Vliet-Ostaptchouk J.V.
      • Snieder H.
      • Esko T.
      • Milani L.
      • Mägi R.
      • Metspalu A.
      • Hill W.G.
      • Weir B.S.
      • Goddard M.E.
      • Visscher P.M.
      • Yang J.
      Dominance genetic variation contributes little to the missing heritability for human complex traits.
      ). Additive and dominance effects are, in general, not independent either because of linkage disequilibrium or by virtue of true covariance between the 2 effects (
      • Huang W.
      • Mackay T.F.C.
      The genetic architecture of quantitative traits cannot be inferred from variance component analysis.
      ). Finally, given the need for directionality of dominance variation, the effect of dominant variants should already be partially accounted for by inbreeding (
      • Xiang T.
      • Christensen O.F.
      • Vitezica Z.G.
      • Legarra A.
      Genomic evaluation by including dominance effects and inbreeding depression for purebred and crossbred performance with an application in pigs.
      ). To the last point, a better formulation of models including dominance has been recently proposed by
      • Vitezica Z.G.
      • Legarra A.
      • Toro M.A.
      • Varona L.
      Orthogonal estimates of variances for additive, dominance, and epistatic effects in populations.
      , which makes dominance estimates free of inbreeding effects. In spite of this, the identification of partial dominance variants remains a difficult task. As the number of individuals genotyped and marker resolutions increase, our ability to identify partial dominance and partial recessives will also increase (e.g.,
      • Jiang J.
      • Ma L.
      • Prakapenka D.
      • VanRaden P.M.
      • Cole J.B.
      • Da Y.
      A large-scale genome-wide association study in U.S. Holstein cattle.
      ). In the short term, heuristic approaches aimed at identifying haplotypes of negative effect (regardless of their mode of action), as proposed by
      • Howard J.T.
      • Tiezzi F.
      • Huang Y.
      • Gray K.A.
      • Maltecca C.
      A heuristic method to identify runs of homozygosity associated with reduced performance in livestock.
      , or, to a larger extent, methods to constrain homozygosity accumulation based on genome-wide measures of inbreeding will remain the most effective approaches.

       Global Measures of Inbreeding and Recessive Load

      Although estimates of genomic values have received a lot of attention in the past few years, estimates of inbreeding depression in dairy are less common in the literature.
      • Miglior F.
      • Burnside E.B.
      • Dekkers J.C.M.
      Nonadditive genetic effects and inbreeding depression for somatic cell counts of Holstein cattle.
      ,
      • Miglior F.
      • Burnside E.B.
      • Kennedy B.W.
      Production traits of Holstein cattle: Estimation of nonadditive genetic variance components and inbreeding depression.
      ) estimated the impact of inbreeding depression in health and production traits in Canadian dairy cattle using nonadditive genetic models. A 1% increase in inbreeding resulted in a 0.01 increase in lactation SCS (
      • Miglior F.
      • Burnside E.B.
      • Dekkers J.C.M.
      Nonadditive genetic effects and inbreeding depression for somatic cell counts of Holstein cattle.
      ), 25.1 kg less milk, 0.9 kg less fat, 0.8 kg less protein, and an increase in fat and protein percentage of 0.05% (
      • Miglior F.
      • Burnside E.B.
      • Kennedy B.W.
      Production traits of Holstein cattle: Estimation of nonadditive genetic variance components and inbreeding depression.
      ).
      • Smith L.A.
      • Cassell B.G.
      • Pearson R.E.
      The effects of inbreeding on the lifetime performance of dairy cattle.
      indicated that a 1% increase in the inbreeding coefficient of Holstein resulted in 37 kg less milk, 1.2 kg less fat, and 1.2 kg less protein per lactation, along with increases in first-calving age of 0.4 d and calving interval of 0.3 d, and a reduction in length of productive life of 13.1 d. More recent studies (
      • Pryce J.E.
      • Hayes B.J.
      • Goddard M.E.
      Novel strategies to minimize progeny inbreeding while maximizing genetic gain using genomic information.
      ;
      • Cole J.B.
      A simple strategy for managing many recessive disorders in a dairy cattle breeding program.
      ;
      • Doekes H.P.
      • Veerkamp R.F.
      • Bijma P.
      • De Jong G.
      • Hiemstra S.J.
      • Windig J.J.
      Inbreeding depression due to recent and ancient inbreeding in Dutch Holstein-Friesian dairy cattle.
      ) have substantially confirmed these figures. In Table 1 are reported the current estimates of inbreeding depression used by the Council of Dairy Cattle Breeding and their impact on the Net Merit index. Table 2 reports the −log10(P-values) and estimates of pedigree genomic inbreeding depression obtained from yield deviations of a sample of approximately 15,000 Holstein cows born between 2013 and 2015. Estimates of inbreeding depressions were higher for all traits compared with those currently used in PTA correction, but that may reflect the small sample size in the analysis, rather than actual differences in population values. Interestingly, in all cases, the significance of genomic inbreeding was higher than that of pedigree inbreeding, suggesting that genomic inbreeding might better capture the underlying true recessive load, in accordance with what was shown by
      • Forutan M.
      • Ansari Mahyari S.
      • Baes C.
      • Melzer N.
      • Schenkel F.S.
      • Sargolzaei M.
      Inbreeding and runs of homozygosity before and after genomic selection in North American Holstein cattle.
      .
      Table 1Inbreeding (F) depression and Net Merit value for US dairy
      TraitInbreeding depression (1%)Trait value in Net Merit, $Value, $ (1% F)
      Milk (lb)−63.90−0.0040.30
      Fat (lb)−2.373.56−8.40
      Protein (lb)−1.893.81−7.20
      Productive life (mo)−0.2621.00−5.50
      SCS0.004−117.00−0.50
      Daughter pregnancy rate−0.1311.00−1.40
      Cow conception rate−0.162.20−0.40
      Heifer conception rate−0.082.20−0.20
      Cow livability−0.0812.00−1.00
      Net Merit $−25.001.00−25.00
      Table 2Significance [−log10(P-value)] and regression coefficients for 1% increase in genomic or pedigree inbreeding (F)
      TraitPedigree FGenomic F
      −log10(P-value)Regression coefficient (1%)−log10(P-value)Regression coefficient (1%)
      Milk (lb)4.95−78.18.06−81.2
      Fat (lb)4.67−3.639.96−3.58
      Protein (lb)3.18−1.817.47−2.86
      Productive life (mo)0.33−0.561.5−0.85
      Daughter pregnancy rate0.57−0.120.8−0.02
      SCS0.11−0.080.14~0

      MANAGING INBREEDING GLOBALLY AND LOCALLY WITH THE USE OF GENOMIC INFORMATION

      Every breeding program aims at maintaining genetic diversity and limiting the inbreeding accumulation while maximizing the response to selection. This is achieved by maximizing the effective population size and minimizing the rate of inbreeding. Currently, inbreeding in the US dairy is controlled at the population level with the use of expected future inbreeding or genomic future inbreeding (
      • Sun C.
      • VanRaden P.M.
      • Cole J.B.
      • O'Connell J.R.
      Improvement of prediction ability for genomic selection of dairy cattle by including dominance effects.
      ). These quantities are the average (pedigree/genomic) inbreeding expected when a bull is mated to a random sample of cows in the population so that the higher the ratio of expected to genomic future inbreeding, the more related the bull is to the current population (
      • VanRaden P.M.
      • Olson K.M.
      • Wiggans G.R.
      • Cole J.B.
      • Tooker M.E.
      Genomic inbreeding and relationships among Holsteins, Jerseys, and Brown Swiss.
      ). Minimization of progeny inbreeding (
      • Pryce J.E.
      • Hayes B.J.
      • Goddard M.E.
      Novel strategies to minimize progeny inbreeding while maximizing genetic gain using genomic information.
      ), linear programming (
      • Weigel K.A.
      Controlling inbreeding in modern breeding programs.
      ), look-ahead mate selection (
      • Shepherd R.K.
      Implementing look ahead mate selection.
      ), selection against lethal alleles (
      • Van Eenennaam A.L.
      • Kinghorn B.P.
      Use of mate selection software to manage lethal recessive conditions in livestock populations.
      ;
      • Cole J.B.
      • Null D.J.
      • VanRaden P.M.
      Phenotypic and genetic effects of recessive haplotypes on yield, longevity, and fertility.
      ;
      • Upperman L.R.
      • Kinghorn B.P.
      • MacNeil M.D.
      • Van Eenennaam A.L.
      Management of lethal recessive alleles in beef cattle through the use of mate selection software.
      ), index selection including Mendelian variance (
      • Santos D.J.A.
      • Cole J.B.
      • Lawlor Jr., T.J.
      • VanRaden P.M.
      • Tonhati H.
      • Ma L.
      Variance of gametic diversity and its application in selection programs.
      ), and genomic selection including dominance (
      • Sun C.
      • VanRaden P.M.
      • Cole J.B.
      • O'Connell J.R.
      Improvement of prediction ability for genomic selection of dairy cattle by including dominance effects.
      ) have all been proposed as methods to controlling inbreeding.
      One of the most effective methods to manage genetic variability and inbreeding over the long term is optimum contribution selection (OCS;
      • Meuwissen T.H.
      Maximizing the response of selection with a predefined rate of inbreeding.
      ). Optimum contribution selection assigns the contributions from each potential parent by minimizing the global coancestry between prospective parents weighted by their contributions. Although OCS has been available since the 1990s, its practical use has been limited in dairy cattle populations. There are several reasons for its limited adoption, but probably the main limiting factor resides in the structure of dairy breeding. In vertically integrated industries, such as swine or poultry breeding, decisions are centralized at the nucleus level. However, the dairy industry remains fragmented, and breeding decisions ultimately rest with individual farmers. This makes the application of systemic approaches logistically challenging. With the adoption of genomics, though, the dairy genetic industry is slowly reshaping, moving toward scenarios more similar to those of other livestock where tighter control of the population size and structure is possible. Within this context, OCS is probably destined to regain momentum. To this extent, the availability of genomic data offers an opportunity to apply OCS with a broader range of options compared with pedigree information (
      • Clark S.A.
      • Kinghorn B.P.
      • Hickey J.M.
      • van der Werf J.H.J.
      The effect of genomic information on optimal contribution selection in livestock breeding programs.
      ). Genomic-derived breeding value estimates can explain a portion of Mendelian sampling variation and, therefore, can explain more than the parent-average EBV. Previous research has shown that using genomic relationships to control inbreeding, as an alternative to pedigree relationships, resulted in no additional genetic gain, except in the case of very large full-sib families (
      • Clark S.A.
      • Kinghorn B.P.
      • Hickey J.M.
      • van der Werf J.H.J.
      The effect of genomic information on optimal contribution selection in livestock breeding programs.
      ).
      • Engelsma K.A.
      • Veerkamp R.F.
      • Calus M.P.L.
      • Windig J.J.
      Consequences for diversity when prioritizing animals for conservation with pedigree or genomic information.
      showed that the benefits of using either the pedigree or the genomic relationship in OCS algorithms vary across the genome. Still, on average, the difference between the two is small. In all of these cases, though, little was done to track the actual recessive load of individuals. Recent inbreeding produces long stretches of DNA shared by individuals. These, in turn, will be enriched with deleterious variants that have been exposed to purging opportunities for less time. Runs of homozygosity (ROH) have been proposed as a measure to track recent autozygosity and better capture recent inbreeding that is more related to the actual recessive load of individuals (
      • Doekes H.P.
      • Veerkamp R.F.
      • Bijma P.
      • De Jong G.
      • Hiemstra S.J.
      • Windig J.J.
      Inbreeding depression due to recent and ancient inbreeding in Dutch Holstein-Friesian dairy cattle.
      ).
      • Howard J.T.
      • Pryce J.E.
      • Baes C.
      • Maltecca C.
      Invited review: Inbreeding in the genomics era: Inbreeding, inbreeding depression, and management of genomic variability.
      , among others, have discussed the use of alternative metrics to measure inbreeding, yet little is known about the long-term impact of using pedigree, genomic, or ROH measures on genetic gains, or about the accumulation of harmful mutations in a population.

      CASE STUDIES

       Case Study 1: Simulation Study on the Optimal Contribution

      In this section, we present a case study in which we have investigated the use of alternative metrics of ancestry in OCS for simulated scenarios using genomic information. A production trait and a fitness trait were generated with GenoDiver (
      • Howard J.T.
      • Tiezzi F.
      • Pryce J.E.
      • Maltecca C.
      Geno-Diver: A combined coalescence and forward-in-time simulator for populations undergoing selection for complex traits.
      ) software following typical genetic architectures of dairy populations. We simulated a polygenic yield trait (h2 = 0.45; 1,000 QTL). A fitness trait was simulated under partial dominance, with a proportion of lethal loci of 5% of the total number of fitness trait loci (FTL); then, OCS was simulated for 30 generations. At each generation, genomic information was used to obtain breeding values of individuals, whereas different measures were used for the optimal contribution portion; namely, relationships based on pedigree, genomic, and 2 different types of ROH (5 and 10 Mb). Selection was performed only on the production trait. Genetic progress for all scenarios was measured at the end of the 30 generations, along with fitness parameters, which included homozygosity and segregating sublethal alleles.

       Genome Architecture

      A total of 54,240 biallelic markers (minor allele frequency = 0.10) were generated distributed over 29 autosomes using GenoDiver v. 3.0. Parameters were chosen to obtain a base population and effective population size of approximately 100. A population of 400 males and 1,000 females was then created and retained as a base for the remaining of the simulations.

       Yield Trait Architecture

      One thousand QTL with additive effects were generated randomly across the 29 autosomes. All QTL were generated from a gamma distribution with shape and scale of 0.4 and 1.66, respectively. A minor allele frequency of 0.05 was adopted for QTL in the base populations. Genetic architecture was completely determined by the QTL with an h2 of 0.45.

       Fitness Trait Architecture

      The generation of FTL was split among lethal and sublethal recessives. For both categories, fitness was defined as relative fitness and parameterized in terms of selection coefficient (s) and dominance coefficient (h) (
      • Wright S.
      Evolution in Mendelian populations.
      ). Selection coefficients were generated from a gamma distribution with different parameters for lethal and sublethal variants. As a result, sublethal loci had a mean frequency 0.03 with a mean selection coefficient of 0.013 and a mean degree of dominance of 0.296. An upper threshold on sublethal loci frequency in the base population was placed at 0.08. Conversely, lethal alleles had a mean frequency of 0.013, a mean selection coefficient of 0.72, and mean degree of dominance of 0.001. An upper threshold on lethal loci frequency was placed at 0.05. One thousand FTL were generated for the fitness trait.

       Covariance Between Fitness and Quantitative Traits

      A pleiotropic covariance between the quantitative and fitness trait of 0.2 was simulated using a trivariate reduction algorithm.

       Selection and OCS

      At each generation, 50 males and 200 females were selected and mated based on their genomic breeding values obtained through genomic BLUP (
      • VanRaden P.M.
      Efficient methods to compute genomic predictions.
      ). The replacement rate for each generation was 0.8 for sires and 0.3 for females. Each mating resulted in 3 progenies (this was done to ensure that enough individuals were available for replacement at each generation). At each generation, optimal contribution selection was performed using the software “eva” (

      Berg, P., J. Nielsen, and M. K. Sørensen. 2006. EVA: Realized and predicted optimal genetic contributions. Book of Abstracts: CD Commun. 27-09. WCGALP, s. 246, World Congress on Genetics Applied to Livestock Production, Belo Horizonte, Brazil.

      ). Four different metrics were used for the OCS portion of the simulation. Relationships were constrained based on pedigree; a realized genomic relationship obtained using the VanRaden algorithm number 2 (
      • VanRaden P.M.
      Efficient methods to compute genomic predictions.
      ), with allele frequencies obtained from the base population after the random mate stage; or ROH relationship matrices (
      • Luan T.
      • Yu X.
      • Dolezal M.
      • Bagnato A.
      • Meuwissen T.H.
      Genomic prediction based on runs of homozygosity.
      ) for ROH of 5 and 10 Mb, respectively. Details on how these were obtained can be found in
      • Howard J.T.
      • Tiezzi F.
      • Huang Y.
      • Gray K.A.
      • Maltecca C.
      Characterization and management of long runs of homozygosity in parental nucleus lines and their associated crossbred progeny.
      . Each scenario was replicated 10 times. A pictorial schematic of the overall simulation is reported in Figure 1.
      Figure thumbnail gr1
      Figure 1Simulation architecture of case study of alternative metrics of ancestry in optimum contribution selection (OCS) using genomic information. Each simulation was repeated 10 times. ROH = runs of homozygosity.

       Results

      In all cases, performing no OCS resulted in higher inbreeding, with homozygosity levels approximately 10% higher for “no OCS” scenarios compared with all other scenarios (Figure 2). As expected, when comparing the different inbreeding metrics used in OCS, genomic information obtained from the diagonal of the genomic relationship matrix was best at constraining the increase of homozygosity, whereas pedigree information was the worst. The ROH measures were intermediate between pedigree and the GRM. Again, this was expected because ROH minimizes only the portion of homozygosity that resides in long, contiguous stretches of the genome, not the overall homozygosity.
      Figure thumbnail gr2
      Figure 2Increase in overall population homozygosity in the simulated scenarios. Without OC = no optimal contribution selection (OCS); pedigree OC = pedigree OCS; genomic OC = genomic OCS; short ROH OC = 5-Mb runs of homozygosity (ROH) OCS. Long ROH OC = 10-Mb ROH OCS.
      Overall homozygosity measures do not truly reflect the recessive load of the populations under different scenarios. Figure 3 reports the average percentages of sublethal alleles carried at homozygous state. In this case No_OCS resulted in a higher accumulation of recessive load. All OCS methods constrained the accumulation of sublethal homozygous effectively. The ROH measures were intermediate between pedigree and genomic. Genetic progress for the simulated scenarios is reported in Figure 4. No OCS resulted in the highest genetic gain, followed by ROH, genomic OCS, and pedigree OCS. It should be noted that in this respect the simulation is simplistic because it assumes that no new additive (or dominance) variation is generated and that genomic architecture remains constant over time. This might not be the case in real scenarios and results need to be interpreted with caution. Furthermore, as a consequence of this simplification, the exhaustion of current genetic variability reflects the “success” in selection.
      Figure thumbnail gr3
      Figure 3Increase in homozygous sublethal over generations in the simulated scenarios. Without OC = no optimal contribution selection (OCS); pedigree OC = pedigree OCS; genomic OC = genomic OCS; short ROH OC = 5-Mb runs of homozygosity (ROH) OCS. Long ROH OC = 10-Mb ROH OCS.
      Figure thumbnail gr4
      Figure 4Genetic progress (in yield units) in the simulated scenarios. Without OC = no optimal contribution selection (OCS); pedigree OC = pedigree OCS; genomic OC = genomic OCS; short ROH OC = 5-Mb runs of homozygosity (ROH) OCS. Long ROH OC = 10-Mb ROH OCS.

       Case Study 2: Characterization of the Age of Inbreeding

      The premise of using ROH as a measure of inbreeding is related to the need to control recent inbreeding, the one for which deleterious variants had a relatively short purging opportunity. Among the disadvantages of ROH measures of inbreeding is the need to establish an arbitrary cutoff delimiting the ROH (and, therefore, the time considered). Often, this threshold is based on the a priori expectation of the investigator.
      • Druet T.
      • Gautier M.
      A model-based approach to characterize individual inbreeding at both global and local genomic scales.
      presented an alternative, elegant, and self-contained approach to this problem. In their work, they aimed at identifying segments of the genome that are homozygous by descent (HBD). These segments occur when individuals inherit copies of an ancestral chromosome. As for ROH, the length of the HBD depends on the number of generations and the population's structure. But unlike ROH, HBD are explicitly modeled through a hidden Markov model. The result is that the overall inbreeding can then be divided into different age classes, and these classes can then be related to the total depression load based on their age. In Figure 5, the HBD distribution of the 15,000 Holsteins described in previous sections is reported. Individuals had genotypes available for 67,904 SNP markers. For this analysis, the R package “RZooRoH” (
      • Bertrand A.R.
      • Kadri N.K.
      • Flori L.
      • Gautier M.
      • Druet T.
      RZooRoH: An R package to characterize individual genomic autozygosity and identify homozygous-by-descent segments.
      ) was used, which implements the method of
      • Druet T.
      • Gautier M.
      A model-based approach to characterize individual inbreeding at both global and local genomic scales.
      described above. Partial homozygosity was obtained for a power of 2 series, including inbreeding from approximately 1 to 256 generations ago. In Figure 5, it can be seen that most of the inbreeding in the individuals is concentrated between 4 and 16 generations ago. It is also evident that considerable variability in class distribution is present among individuals. This can be better observed in Figure 6, in which a random sample of individual partial inbreeding coefficients are depicted based on their age of inbreeding. It is evident that for different individuals with similar overall inbreeding, the contribution of partial inbreeding of different age can vary dramatically. To explore the potential effect of age of inbreeding on inbreeding depression, we regressed these partial coefficients on yield deviations, as outlined in the previous section. In Table 3 we report the partial regression coefficients for inbreeding grouped from 1 to 4 generations ago and from 4 to 64 generations. The grouping was, in this case, done arbitrarily to explore old versus new inbreeding; inbreeding of >64 generations ago was excluded under the assumption that it would need to be mostly free of deleterious variants and in recognition of the small sample of individuals used. More in-depth analysis with a larger collection of individuals, possibly across breeds, would need to account explicitly for all partial inbreeding coefficients. In all cases, inbreeding depression estimates were higher for more recent inbreeding than for older inbreeding. Estimates were also higher than those obtained by both pedigree and genomic information, possibly highlighting that partial inbreeding estimates tend to overestimate real inbreeding depression because they are likely not independent. In addition, a scaling effect might result in different levels of inbreeding depression, given that partial inbreeding estimates might have different variances. Finally, as inbreeding in different classes is also a function of marker density, it is possible that denser marker density would be needed to capture smaller segments (and their associate effects). More research in this area is needed to highlight the possible use of age-related HBD partial inbreeding coefficients.
      Figure thumbnail gr5
      Figure 5Distribution of partial inbreeding coefficients (F) for age of inbreeding; gen = generation; HBD = homozygous by descent; RK = no. of generations threshold.
      Figure thumbnail gr6
      Figure 6Distribution of class of inbreeding, based on age for a sample of Holstein cows. Age class represent age of inbreeding.
      Table 3Regression coefficients for a 1% increase in genomic homozygous-by-descent inbreeding classes for generations 1 to 4 and 4 to 8
      TraitPartial inbreeding regression coefficient
      Generations 1–4Generations 4–8
      Milk (lb)−118.3
      P < 0.01,
      −78.3
      P < 0.01,
      Fat (lb)−4.4
      P < 0.01,
      −3.82
      P < 0.01,
      Protein (lb)−3.38
      P < 0.05.
      −2.60
      P < 0.05.
      Productive life (mo)−0.83
      P < 0.05.
      −0.32
      P < 0.05.
      Daughter pregnancy rate−0.14
      P < 0.05.
      −0.04
      SCS0.0030.002
      ** P < 0.01,
      * P < 0.05.

      FINAL REMARKS

      The adoption of genomic information as standard practice in dairy breeding has facilitated considerably increased genetic progress, yet it poses a challenge for the maintenance of long-term variability and the accumulation of harmful mutations. Average losses due to known recessives affecting fertility are currently estimated at $5.77, $3.65, $0.94, and $2.96 in Ayrshire, Brown Swiss, Holstein, and Jersey, respectively (
      • Cole J.B.
      • Null D.J.
      • VanRaden P.M.
      Phenotypic and genetic effects of recessive haplotypes on yield, longevity, and fertility.
      ). Although management of lethal mutations has become more effective in recent years, a large proportion of these economic losses is tied to partial recessives of small effect. The incredible amount of information accumulated in recent years, with more than 2 million cows genotyped, offers a unique opportunity to investigate partial recessive load and functional inbreeding depression, thus discriminating homozygosity on the basis of its potential detrimental effect. The identification of true deleterious partial recessives remains a long-term challenge. To this point, an important contribution to the understanding of the basic mechanisms of inbreeding depression and heterosis in the dairy population will be made by the growing number of crossbred individuals that are currently being genotyped. In the short term, measures of overall inbreeding more closely related to the overall recessive load could be used, either through the use of ROH or age-related partial inbreeding coefficients.

      ACKNOWLEDGMENTS

      Christian Maltecca and Francesco Tiezzi were supported by a grant provided by the Holstein Association USA (Brattleboro, VT). Christine Baes gratefully acknowledges grants provided by the DairyGen Council of Canadian Dairy Network (Guelph), as well as financial support from the Natural Sciences and Engineering Research Council (NSERC) of Canada (Ottawa). John Cole was supported by appropriated project 8042-31000-002-00-D, “Improving Dairy Animals by Increasing Accuracy of Genomic Prediction, Evaluating New Traits, and Redefining Selection Goals” of the Agricultural Research Service (ARS) of the USDA (Washington, DC). Mention of trade names or commercial products in this article is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the US Department of Agriculture. The USDA is an equal opportunity provider and employer. The authors have not stated any conflicts of interest.

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