domain: sdv info shs

text:
Michel Doreau

Anne Ferlay

Linseed: a valuable feedstuff for ruminants

Keywords: Linseed, milk, beef, omega-3 fatty acids, methane Graine de lin, lait, viande bovine, acides gras oméga-3, méthane

Linseeds are used in ruminant feeding for a long time, but this feedstuff knows now increasing interest. Linseeds are rich in alpha-linolenic acid, a fatty acid from the omega-3 series. Despite an extensive biohydrogenation of dietary alpha-linolenic acid in the rumen, its concentration in milk and beef meat increases with linseed incorporation in diets; this increase is accompanied by that of other fatty acids produced during biohydrogenation, especially conjugated linoleic acids and trans 18:1 fatty acids. The increase in cow fertility due to omega-3 fatty acids has not been demonstrated. Furthermore, linseed incorporation in ruminant diets is one of the most efficient ways to decrease enteric methane emissions. In addition to a global mitigating effect of all lipid sources on methane, linseeds have a specific effect due to changes in rumen microbial ecosystem. The practical use of linseeds in ruminant feeding at a large scale requires the absence of negative effect at any step of the ruminant production system. An excessive supply of lipids from linseeds can have deleterious effects on digestive efficiency, milk fat and protein content, beef susceptibility to oxidation, milk and beef fatty acid composition, but when linseed incorporation in the diet does not exceed ca. 3% of additional fat, only positive effects are remaining. A challenge is the increase in linseed cropping to meet increased needs for animal feeding.

1 Introduction 1 Although linseed is not commonly used nowadays in rumi-2 nant feeding, this is an ancient feedstuff which has been used 3 from the nineteenth century, as crude seed or cake (Grandeau,4 1876). In the first part of the twentieth century, linseed ex-5 peller cake has been used especially for beef fattening, and 6 was used not really for nutritional benefits but for giving a 7 shiny coat, and also a tasty meat [START_REF] Dumont | Engraissement des vaches de réforme de race Charolaise. Effet d'un apport de tourteau de lin sur les performances d'engraissement et les propriétés physico-chimiques et sensorielles de la viande[END_REF]. The 8 Correspondence: michel.doreau@clermont.inra.fr development of the use of fat sources in ruminant feeding in the 1990s as a mean to increase energy density of the diet concerned first palm oil, animal fat derivatives, and commonly used seeds such as cottonseed, soybean and rapeseed. A significant use of linseed is very recent and due to its richness in alpha-linolenic acid (18:3 n-3, or cis-9, cis-12, cis-15 18:3), potentially allowing an increase in omega-3 fatty acids (FA) in milk and meat. However, the extent of increase in omega-3 FA in these products is limited because of the wide biohydrogenation of polyunsaturated FA in the rumen, prior to absorption. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

"ocl150022" -2015/8/7 -10:45 -page 2 -#2 i i i i i i i i M. Doreau and A. Ferlay: OCL 2015, 22(6) A few years ago, an additional interest for linseed has been put 1 forward: linseed FA have been shown to significantly decrease 2 enteric methane production by ruminants [START_REF] Martin | Methane mitigation in ruminants: from microbe to the farm scale[END_REF].

3 Methane mitigation is a major issue for decreasing greenhouse 4 gases emissions from livestock. The Bleu-Blanc-Coeur initia-5 tive, born in France and aiming to develop omega-3 FA in hu-6 man foods through promoting feeding animals with omega-3, 7 considers this double interest of linseeds. Linseeds are now 8 used essentially as an extruded mixture of 50-70% linseeds 9 and 30-50% other feeds such as bran, in order to obtain a prod-10 uct which is easy to handle and to incorporate in concentrates.

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This paper presents an overview of the interest of the incorpo-12 ration of linseed in diets for providing omega-3 FA to rumi-13 nants, then of the use of linseed for methane mitigation. In the 14 last part, the perspectives of increase in linseed use for animal 15 feeding are discussed.

16 2 Linseed, a provider of omega-3 17 for ruminants [START_REF] Glasser | a. Oilseed lipid supplements 19 and fatty acid composition of cow milk: a meta-analysis[END_REF] Linseeds varieties fed to animals contain a high level of 19 oil (40%) with 55% of 18:3 n-3 (Glasser et al., 2008a, Pe-20 tit, 2010). Adding linseeds to ruminant diets is susceptible reduce the risk of cardiovascular diseases [START_REF] Mills | Milk intelligence: mining milk for bioactive substances associated with human health[END_REF].

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Details on omega-3 FA effects on human health are reported in 30 a paper by Mourot (this issue).

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A specificity of digestive processes in ruminants is an ex-32 tensive biohydrogenation of dietary FA in the rumen, prior to 33 absorption which occurs in the small intestine. As a conse-34 quence, the amount of omega-3 FA reaching the small intestine 35 is much lower than the dietary intake of omega-3 FA, resulting 36 in a quantitatively low transfer of these FA in milk and meat, 37 compared to monogastric animals [START_REF] Doreau | Enhancing fatty acid composition of milk and meat through animal feeding[END_REF]. For- FA is found (Glasser et al., 2008c). The major one is vaccenic 54 acid (trans-11 18:1), but 12 other trans isomers and 5 cis iso-55 mers, mainly oleic acid (cis-9 18:1) reach the intestine and are 56 thus absorbed and available for transfer into milk and meat. Different attempts have been made to decrease biohydrogenation through protection of lipids. The only one which has been proved to be efficient is the encapsulation of lipids in a coat of proteins treated with formaldehyde [START_REF] Doreau | Enhancing fatty acid composition of milk and meat through animal feeding[END_REF]Fievez et al., 2007). However this technique is not used, in particular owing to its cost, to the use of formaldehyde, and to possible adverse effects of excessive amounts of polyunsaturated fats on animal health and product quality.

Concerning the FA metabolism, 18:3 n-3 represents on average 1.9% of 18-carbon FA reaching the duodenum because of its extensive biohydrogenation in the rumen. Nevertheless, the transfer rate from duodenum to milk is lower for 18:3 n-3 than that for other 18-carbon FA (Glasser et al., 2008b). In mammary gland and in muscle, an important de novo synthesis occurs from plasma acetate and butyrate, leading to a variety of short-and medium chain FA in milk fat. Moreover, the activity of a Δ9-desaturase leads to the formation of cis-9, trans-11 18:2 (rumenic acid) from vaccenic acid. In addition, a specific metabolic pathway occurs in the muscle, but not in the mammary gland: the elongation and desaturation of 18:3 n-3, leading to the formation of eicosapentaenoic acid (EPA, 20:5 n-3) and docosapentaenoic acid (DPA, 22:5 n-3) in muscle. However, the last step of desaturation towards docosahexaenoic acid (DHA, 22:6 n-3) is of very low extent in vertebrates [START_REF] Doreau | Enhancing fatty acid composition of milk and meat through animal feeding[END_REF].

The general responses of milk FA composition to linseeds feeding concern saturated FA, trans-18:1, conjugated and nonconjugated isomers of 18:2 and 18:3 n-3. The extent of change in milk FA concentration is generally proportional to the level of inclusion of linseeds in the diet (Ferlay et al., 2013;Glasser et al., 2008a). The effects of increasing amounts of extruded linseeds in the diet have been studied by different authors [START_REF] Barton | L'apport de 49 lin dans la ration des vaches laitières : effets sur la production, 50 la composition du lait et des produits laitiers, les émissions de 51 méthane et les performances de reproduction[END_REF]Ferlay et al., 2013;[START_REF] Hurtaud | Linear rela-52 tionship between increasing amounts of extruded linseed in dairy 53 cow diet and milk fatty acid composition and butter properties[END_REF]. The major changes concern increases in trans-18:1 and total conjugated linoleic acid (CLA) concentrations in milk. Feeding linseeds increases the milk concentrations of different isomers of 2) [START_REF] Chilliard | Diet, rumen biohydrogenation and nutritional quality of cow and goat milk fat[END_REF], Lerch et al., 2012c). These FA concentrations increased linearly with increasing amounts of linseeds whereas 18:3 n-3 concentration increased slightly (Ferlay et al., 2013), confirming that this FA was highly biohydrogenated in the rumen. The relationship between 18:3 n-3 intake and 18:3 n-3 as a proportion of milk FA is linear (Fig. 1). The transfer of 18:3 n-3 from diet to milk is close to 4.5%. Only [START_REF] Kennelly | The fatty acid composition of milk fat as influ-60 enced by feeding oilseeds[END_REF] reported a higher transfer when cows fed a protected linseed oil, with a milk concentration higher than 20% of total FA. Moreover, the milk saturated FA decreased linearly with increasing amounts of linseed. For the same level of cis-9, trans-11 18:2 in the milk fat, linseed supplementation increased the milk concentration of trans FA other than trans-11 18:1 and cis-9, trans-11 18:2 more than grazed grass (Ferlay et al., 2008(Ferlay et al., , 2013)). Significant increases were observed for cis-9, trans-13 and trans-11, cis-15 18:2 with linseed or linseed oils because these FA are main intermediates of ruminal biohydrogenation of 18:3n-3 [START_REF] Chilliard | Milk fatty acids in dairy cows fed whole crude linseed, extruded linseed or linseed oil, and their relationship with methane output[END_REF]Ferlay et al., 2013;Glasser et al., 2008c;Lerch et al., 2012b). Lerch et al. (2012c) studied the effects of long-term supplementation ???, page 2 of 9 "ocl150022" -2015/8/7 -10:45 -page 3 -#3 Doreau and A. Ferlay: OCL 2015, 22(6) Fig. 1. Effect of increasing amounts of 18:3 n-3 intake from linseeds on milk 18:3 n-3 proportion (from [START_REF] Chilliard | Milk fatty acids in dairy cows fed whole crude linseed, extruded linseed or linseed oil, and their relationship with methane output[END_REF]Ferlay et al., 2013;[START_REF] Hurtaud | Linear rela-52 tionship between increasing amounts of extruded linseed in dairy 53 cow diet and milk fatty acid composition and butter properties[END_REF]. Equation of linear regression is: Y = 0.0018X + 0.38 (R 2 = 0.59), where Y is milk 18:3 n-3 proportion (g/100 g of total FA) and X is 18:3 n-3 intake (g/d).

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(2.5 to 3% of oil in DM) with extruded linseed over 2 consecu-1 tive lactations, successively on a grass silage-based diet and at [START_REF] Corazzin | Effect of whole linseed addition on meat production and quality of Italian Simmental and Holstein young bulls[END_REF]Scollan et al., 2005). Due to ru-11 minal biohydrogenation, the proportion of 18:3 n-3 in per-12 centage of total FA remains low. For example in Longissimus 13 thoracis, it increases from 0.5 to 0.9-1.6% (Normand et al.,14 2005, 5 trials), from 0.4 to 1.9% [START_REF] Mach | Increasing the amount of n-3 fatty acid in meat from young Holstein bulls through nutrition[END_REF], from 15 0.4 to 0.8% [START_REF] Barton | L'apport de 49 lin dans la ration des vaches laitières : effets sur la production, 50 la composition du lait et des produits laitiers, les émissions de 51 méthane et les performances de reproduction[END_REF], from 0.6 to 2.0% (Herdmann 16 et al., 2010), from 1.2 to 1.6% [START_REF] Corazzin | Effect of whole linseed addition on meat production and quality of Italian Simmental and Holstein young bulls[END_REF], from 0.4 17 to 0.6% [START_REF] Habeanu | Extruded linseed and 39 rapeseed both influenced fatty acid composition of total lipids 40 and their polar and neutral fractions in longissimus thoracis and 41 semitendinosus muscles of finishing Normand cows[END_REF], from 0.9 to 1.4% (Mialon 18 et al., 2015). Differences in the extent of the increase depend 19 more on the amount of added fat and their processing than 20 on the duration of distribution before slaughter. It can also be 21 noted that pasture feeding, which is another source of 18:3 n-3, 22 increases 18:3 n-3 in meat, although generally to a lower extent 23 (Scollan et al., 2005). The increase in muscle 18:3 n-3 concen-24 tration is significantly higher with extruded linseeds than with 25 rolled linseeds [START_REF] Normand | Produire de la viande bovine enrichie en acides gras polyinsaturés oméga 3 à partir de graines de lin : quelles modalités d'apport du lin, quelles conséquences sur la qualité de la viande ? Renc[END_REF], and higher in ground 26 or rolled linseeds than with whole linseeds (Maddock et al., 27 2006). The increase in 18:3 n-3 was higher in Longissimus tho-28 racis than in Rectus abdominis and Semitendinosus in a trial by 29 Mialon et al. (2015), but this difference was not observed in tri-30 als by [START_REF] Normand | Produire de la viande bovine enrichie en acides gras polyinsaturés oméga 3 à partir de graines de lin : quelles modalités d'apport du lin, quelles conséquences sur la qualité de la viande ? Renc[END_REF] and by [START_REF] Habeanu | Extruded linseed and 39 rapeseed both influenced fatty acid composition of total lipids 40 and their polar and neutral fractions in longissimus thoracis and 41 semitendinosus muscles of finishing Normand cows[END_REF].

Despite elongation process, very long-chain FA are present 32 in muscle in low proportions whatever the diet: less than 0.7 33 and 0.4% of total FA for DPA and EPA, respectively, and 34 this proportion is either unchanged or moderately increased 35 by linseed supply [START_REF] Barton | L'apport de 49 lin dans la ration des vaches laitières : effets sur la production, 50 la composition du lait et des produits laitiers, les émissions de 51 méthane et les performances de reproduction[END_REF][START_REF] Corazzin | Effect of whole linseed addition on meat production and quality of Italian Simmental and Holstein young bulls[END_REF] 36 [START_REF] Habeanu | Extruded linseed and 39 rapeseed both influenced fatty acid composition of total lipids 40 and their polar and neutral fractions in longissimus thoracis and 41 semitendinosus muscles of finishing Normand cows[END_REF][START_REF] Herdmann | Effect of dietary n-3 and n-6 PUFA on lipid composi-45 tion of different tissues of German Holstein bulls and the fate of 46 bioactive fatty acids during processing[END_REF]Mialon et al., 37 2015). These three latter authors also observed an increase in

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CLA, but the two former authors did not. In any case, the CLA concentration in beef is too low for a possible effect on human health. Beef trans-18:1 FA comprise a significant amount of isomers other than trans-11, but few studies are available about the effect of linseeds on this pattern. With diets based on 30% straw and 70% concentrates, extruded linseed did not change the proportion of trans-11 (33%) but trans-12, -13, -14 and -15 increased at the expense of trans-9 and -10 [START_REF] Habeanu | Extruded linseed and 39 rapeseed both influenced fatty acid composition of total lipids 40 and their polar and neutral fractions in longissimus thoracis and 41 semitendinosus muscles of finishing Normand cows[END_REF].

There has been a steady decline of fertility in major dairy cow breeds associated with the improvement of genetic merit for milk production [START_REF] Barbat | Female fertility in 35 French dairy breeds: current situation and strategies for improve-36 ment[END_REF][START_REF] Butler | Energy balance relationships with follicular development, ovulation and fertility in postpartum dairy cows[END_REF]. Part of this decline is due also to extended period of negative energy balance and intense mobilisation of body reserves during early lactation. The relationships among energy balance, body condition score and reproductive function are well documented (e.g. infrequent LH pulses, delayed ovarian activity, abnormal estrous cycles, poor follicular response to gonadotropins, reduction of oocyte quality and embryo survival [START_REF] Butler | Energy balance relationships with follicular development, ovulation and fertility in postpartum dairy cows[END_REF][START_REF] Chagas | Invited review: New perspectives on the roles of nutrition and metabolic priorities in the subfertility of high-producing dairy cows[END_REF]. Recent interest on lipid feeding to cows has focused on reproduction because of their high energy density and a supply of specific FA. Lipid supplementation could influence reproduction by altering the size of the dominant follicle, shortening the interval between calving and the first postpartum ovulation, increasing progesterone concentration during the luteal phase of the oestrous cycle, modulating uterine prostaglandin synthesis, and improving oocyte and embryo quality and maintenance of pregnancy (Santos et al., 2008). The omega-6 and omega-3 polyunsaturated FA seem to have the major effects on reproductive responses. Nevertheless, results from feeding linseeds on reproductive variables are inconsistent. Some authors reported an improved increased follicular and corpus luteum growth (Santos et al., 2008), oocyte [START_REF] Moallem | Dietary α-linolenic acid from flaxseed oil improved folliculogenesis and IVF performance in dairy cows, similar to eicosapentaenoic and docosahexaenoic acids from fish oil[END_REF]Zachut et al., 2010) and embryo quality (Thangavelu et al., 2007), decreased pregnancy loss [START_REF] Ambrose | Lower pregnancy 32 losses in lactating dairy cows fed a diet enriched in alpha-33 linolenic acid[END_REF], reduced plasma prostaglandin (Petit et al., 2002), and increased serum progesterone concentration [START_REF] Jahani-Moghadam | Effect of lin-56 seed feeding on blood metabolites, incidence of cystic follicles, 57 and productive and reproductive performance in fresh Holstein 58 dairy cows[END_REF], reduced interval from calving to ovulation [START_REF] Colazo | Reproductive performance of dairy cows is influenced by prepartum feed restriction and dietary fatty acid source[END_REF]. In contrast, others noted no changes in milk progesterone concentration or corpus luteum activity (Ponter et al., 2006), or oocyte quality (Bilby et al., 2006[START_REF] Fouladi-Nashta | 16 Oocyte quality in lactating dairy cows fed on high levels of n-17 3 and n-6 fatty acids[END_REF]. The inconsistencies among these studies could be due to differences in the amounts of lipid supplements, duration of supplementation, and season. The global effect on cow fertility has not been evidenced: no effect of linseed feeding has been reported on conception rate [START_REF] Ambrose | Lower pregnancy 32 losses in lactating dairy cows fed a diet enriched in alpha-33 linolenic acid[END_REF]Bork et al., 2010;[START_REF] Petit | Conception rate and reproductive function of dairy cows fed different fat sources[END_REF]Petit et al., 2008), or pregnancy rate [START_REF] Jahani-Moghadam | Effect of lin-56 seed feeding on blood metabolites, incidence of cystic follicles, 57 and productive and reproductive performance in fresh Holstein 58 dairy cows[END_REF]. Further studies with a larger number of animals are necessary to be conducted in order to confirm these results.

3 Linseed, a way to mitigate methane emissions by ruminants Among greenhouse gases, which are responsible of global warming, methane is the major contributor for livestock activities: more than 40% of greenhouse gases, when they are expressed as carbon dioxide-equivalents. The major part of ???, page 3 of 9 "ocl150022" -2015/8/7 -10:45 -page 4 -#4 Doreau and A. Ferlay: OCL 2015, 22(6) methane is produced in the digestive tract of ruminants, especially in the rumen, which is the main site of digestion. In the rumen, dietary carbohydrates are fermented by bacteria and protozoa in volatile fatty acids, which are the main energy source for ruminants. During fermentation, hydrogen is produced, then is converted in methane by the action of another type of microbes, archaea methanogens. The abatement of methane emissions is a challenge for scientists.

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Dietary lipids are considered now by the scientific community as the best way for enteric methane mitigation (reviews by [START_REF] Hristov | Mitigation from methane and 49 nitrous oxide emissions from animal operations. I. A review of 50 enteric methane mitigation options[END_REF][START_REF] Martin | Methane mitigation in ruminants: from microbe to the farm scale[END_REF]. Although their effect on methane emission is not systematic, lipids present advantages compared to other dietary options: chemicals and additives such as nitrates raise the issue of acceptability by consumers, tannins often reduce animal performances, highcereal diets question about the use of large amounts of cereals in ruminant feeding. When lipids are given in substitution to carbohydrates, methane is reduced because it is produced from carbohydrates, but not from lipids. In addition, some lipid sources decrease rumen protozoa which are important producers of hydrogen, which is the precursor of methane. The strongest decrease in rumen protozoa is obtained with linseeds on one hand, and coconut and palm kernel oil on the other hand. These latter lipid sources have the drawback to be rich in medium-chain saturated FA (12:0 and 14:0), which are considered as deleterious for human health. As a consequence, linseeds could be the best choice for methane mitigation. Review of experimental data show that on average linseeds reduce more methane emission than saturated sources (calcium salts of palm oil, tallow), and unsaturated sources containing oleic acid (rapeseed) or linoleic acid (sunflower, cottonseed) [START_REF] Martin | Methane mitigation in ruminants: from microbe to the farm scale[END_REF]. However, between-experiments variability of response is high, so that some authors do not distinguish fat sources for their effect on methane emission [START_REF] Grainger | Can enteric methane emissions 33 from ruminants be lowered without lowering their production? 34[END_REF]. It has been shown that the effect of linseeds remains at least for one year after starting their distribution to cows [START_REF] Martin | Methane output and rumen microbiota in dairy cows in response to long-term supplementation with linseed or rapeseed of grass silage-or pasture-based diets[END_REF]. This long-term effect is especially interesting because products which decrease methane often have a short-term effect, due to the adaptation of rumen microbes to dietary changes. Increasing the proportion of linseeds in the diet until 5% additional fat results in a strong decrease in methane (Fig. 2). In practical conditions, a lower addition of linseeds is recommended, to avoid any risk of disturbances of fibre digestibility, which often occurs for high linseed supply, and any risk of excessive increase in some trans FA in products which may have a negative effect of human health. Although most results evidence the effect of linseed for methane mitigation, for an unknown reason, linseeds did not decrease methane emission in some experiments (Van Zijderveld et al., 2011).

For any option aiming to decrease methane emission by animals, it is mandatory to check that the decrease is not compensated for by an increase in the other greenhouse gases, carbon dioxide and nitrous oxide. For linseeds, there is a compensation for a minor part, due to the higher carbon footprint for linseed than for cereals that they replace. The effect of introducing linseeds in the diet has been calculated by life cycle assessment for the whole farming system, for beef cattle [START_REF] Nguyen | Effect of type of ration and allocation methods on the environmental impacts of beef-production systems[END_REF] and for dairy cattle (Nguyen et trates could be fed lipids all year long, in order to provide 3.5% 71 additional fat. In this case, lipid supply can reduce total green-72 house gases emissions from cattle by 6%. However, this option 73 is expensive at present due to the higher cost of oleagineous 74 seeds compared to cereals [START_REF] Doreau | Mitigation of enteric methane for French cattle: Potential extent and cost of selected actions[END_REF]. Use of linseed in ruminant feeding could be developed if 78 linseed crops are developed. In several countries, the use of lin-79 seed in crop rotations is limited by a lower yield per ha than ce-80 reals, and by the relative price of cereals and linseeds. Among 81 crops which are frequently used in rotations in Europe, rape-82 seed is competitive, and grain legumes allow the decrease in 83 N fertilisation in the multiannual system. This is not the case 84 of linseed, for which average yield stagnates at 20 q/ha. For 85 France, national linseed production covers one half of present 86 needs for animal nutrition. The potential of increase in surfaces 87 is high, but a significant rise requires a strong coordination of 88 actors of the food chain [START_REF] Charrier | Alimentation animale et organisation des filières: une comparaison pois protéagineux-lin oléagineux pour comprendre les facteurs freinant ou favorisant les cultures de diversification[END_REF]. Ways of im-89 provement which may lead in the short-term to tripling French 90 surfaces (30 000 ha instead of 10 000 ha now) have been pro-91 posed by [START_REF] Labalette | 62 La filière lin oléagineux française : panorama et perspectives[END_REF], and include a larger choice 92 of varieties, better rotation choices and higher prices relative 93 to cereals. This latter can be achieved by feed industry, but the 94 price of milk and meat enriched in omega-3 should also be 95 higher. This is possible by a selective milk collection, which is 96 already organised in some dairy factories, by the development 97 of dairy and beef brands for niche markets, and by the pro-98 motion and lobbying such as the Bleu-Blanc-Coeur initiative, 99 ???, page 4 of 9 "ocl150022" -2015/8/7 -10:45 -page 5 -#5 Doreau and A. Ferlay: OCL 2015, 22(6) which is positively received by consumers. Incentives related 1 to public policies can be thought, owing to the environmental 2 interest on linseed use for the abatement of methane emission 3 by ruminants.

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The positive effect of linseeds on omega-3 FA in milk and 5 beef, and the methane abatement, are two arguments for using 6 linseeds at a large scale. However, this practice will increase does not exceed 5% of dry matter; this corresponds to 3.5% 14 added FA from linseeds in diet DM. Higher proportion some-15 times decreases digestibility [START_REF] Petit | Review: Feed intake, milk production and milk composition of dairy cows fed flaxseed[END_REF]. rumen and then a decrease in milk fat content (Chilliard et al., 32 2009). A decrease in milk fat yield with linseed oil feeding is 33 often reported (Glasser et al., 2008a). Generally, feeding diets 34 with whole or crushed or micronized linseed had no effect on 35 the milk protein content in mid lactation [START_REF] Petit | Review: Feed intake, milk production and milk composition of dairy cows fed flaxseed[END_REF] whereas 36 a decrease in protein content (0.5 g/kg) was observed with ex-37 truded linseed [START_REF] Barton | L'apport de 49 lin dans la ration des vaches laitières : effets sur la production, 50 la composition du lait et des produits laitiers, les émissions de 51 méthane et les performances de reproduction[END_REF]. Concerning the longterm linseed supplementation, during the first year of experi-39 mentation, linseed diet had no effect on the milk and fat yields 40 compared to the control diet. Linseed supplement decreased 41 the milk protein content, without changing protein yield. Thus, 42 long-term effects of supplementation with linseeds were similar to those observed during short-term (1 to 3 months) studies 44 (Lerch et al., 2012a). With a moderate linseed incorporation in (2005): differences are very low (Tab. 2). Whole linseeds have been used by [START_REF] Maddock | Effect of processing flax in beef feedlot diets on performance, carcass characteristics, and trained sensory panel ratings[END_REF] and [START_REF] Corazzin | Effect of whole linseed addition on meat production and quality of Italian Simmental and Holstein young bulls[END_REF]. Results suggest that linseed hull does not limit a normal digestion of the seed. It can be concluded that the incorporation of linseeds for finishing cattle has no effect or a slightly positive effect on performances. Although it has been shown that lipid supply in fattening diets generally increases carcass fat proportion [START_REF] Clinquart | Utilisation des matières grasses chez les bovins à l'engraissement[END_REF], available data for linseed supply do not fully support this statement: linseeds may increase [START_REF] Dufrasne | Effets de l'incorporation de graines de lin floconnées sur support d'orge chez le taurillon à l'engraissement[END_REF] or not [START_REF] Maddock | Effect of processing flax in beef feedlot diets on performance, carcass characteristics, and trained sensory panel ratings[END_REF][START_REF] Normand | Produire de la viande bovine enrichie en acides gras polyinsaturés oméga 3 à partir de graines de lin : quelles modalités d'apport du lin, quelles conséquences sur la qualité de la viande ? Renc[END_REF]Razminowicz et al., 2008) carcass fatness. The reality of a difference between linseed and other lipid sources needs further research.

It is sometimes argued that linseeds contain cyanogenic compounds which could be toxic for animals. They are present as glycosides, and are likely to vary more with cultivar than with location or year [START_REF] Oomah | Cyanogenic compounds in flaxseed[END_REF]. Seed treatments can decrease cyanides. Pelleting decreases total cyanides, especially at high and prolonged temperatures [START_REF] Feng | Effectiveness of different processing methods in reducing hydrogen cyanide content of flaxseed[END_REF]. Extrusion divided cyanhydric acid by 4, whereas rolling divided them by 2 (one comparison, [START_REF] Normand | Incidence d'un apport alimentaire d'acides gras polyinsaturés en cours d'engraissement sur les performances zootechniques et les qualités des viandes de gros bovins[END_REF]; a very pronounced decrease in cyanhydric acid was observed with another extrusion technology: 10 mg/kg for extruded linseeds vs. 165 to 240 mg/kg for rolled linseeds (6 comparisons, [START_REF] Normand | Produire de la viande bovine enrichie en acides gras polyinsaturés oméga 3 à partir de graines de lin : quelles modalités d'apport du lin, quelles conséquences sur la qualité de la viande ? Renc[END_REF]. However, cyanhydric acid content in plasma is not increased by rolled or extruded linseed inclusion in the diet, suggesting a possible detoxification in the rumen [START_REF] Normand | Incidence d'un apport alimentaire d'acides gras polyinsaturés en cours d'engraissement sur les performances zootechniques et les qualités des viandes de gros bovins[END_REF]. Nevertheless, cyanogenic compounds are transferred to a low extent in milk, but according to [START_REF] Petit | Review: Feed intake, milk production and milk composition of dairy cows fed flaxseed[END_REF], milk concentrations are too much low to result in a toxic effect for humans, if taking account the daily doses which are considered as safe by health authorities.

Due to their high amount of polyunsaturated FA, linseeds may be subject to oxidation. During a 120-day conservation, peroxide value and vitamin E content are stable for rolled linseeds, whereas the former increases and the latter decreases for extruded linseeds [START_REF] Normand | Produire de la viande bovine enrichie en acides gras polyinsaturés oméga 3 à partir de graines de lin : quelles modalités d'apport du lin, quelles conséquences sur la qualité de la viande ? Renc[END_REF]. It is recommended to use new batches of extruded linseeds every 2 months if there is no incorporation of antioxidant, in order to prevent a possible decrease in intake by animals. A concern related to the use of polyunsaturated FA is the susceptibility of lipids to oxidation [START_REF] Durand | High-fat rations and lipid peroxidation in ruminants: consequences on the health of animals and quality of their products[END_REF]. Milk and beef lipid oxidation may occur, when linseeds are incorporated in diets, but often there is no increased susceptibility to oxidation, for example when rolled or extruded linseeds are fed to fattening cattle in moderate amounts (750 g/day) [START_REF] Normand | Produire de la viande bovine enrichie en acides gras polyinsaturés oméga 3 à partir de graines de lin : quelles modalités d'apport du lin, quelles conséquences sur la qualité de la viande ? Renc[END_REF]. However, lipid oxidation may occur when animals have been submitted to oxidative stress during their lifetime, after inflammatory or infectious events, or in the pre-slaughter period, after an emotional or physical stress [START_REF] Durand | Le stress oxydant chez les animaux de rente: principes généraux[END_REF]. For this reason, an additional supply of vitamin E or of vegetal antioxidants in the diet may reduce milk susceptibility to oxidation (Focant et al., 1998) and in beef meat after carcass ageing and meat display on shelfs [START_REF] Gobert | Plant extracts combined with vitamin E in PUFA-rich diets 30 of cull cows protect processed beef against lipid oxidation[END_REF].

Published literature does not mention flavour problems of milk from cows fed linseeds. When linseeds are given as formaldehyde-treated seeds, protecting them from rumen degradation and resulting in high 18:3 n-3 absorption, a fish taste in meat, an increase in rancidity and in a decrease in ???, page 5 of 9 "ocl150022" -2015/8/7 -10:45 -page 6 -#6 i Doreau and A. Ferlay: OCL 2015, 22(6) (2004) and [START_REF] Normand | Produire de la viande bovine enrichie en acides gras polyinsaturés oméga 3 à partir de graines de lin : quelles modalités d'apport du lin, quelles conséquences sur la qualité de la viande ? Renc[END_REF] feed intake was not determined so that additional fat supply is not known. In the experiment by [START_REF] Maddock | Effect of processing flax in beef feedlot diets on performance, carcass characteristics, and trained sensory panel ratings[END_REF] fat content of diets was not specified. ???, page 6 of 9 "ocl150022" -2015/8/7 -10:45 -page 7 -#7 i Doreau and A. Ferlay: OCL 2015, 22(6) overall liking are observed (Scollan et al., 2005). Rancidity 1 is due to oxidation, and fishy taste is likely due to components 2 related to 20-and 22-carbon FA produced by FA elongation.

i i i i i i i M.
i i i i i i i M.
3 This negative judging is not observed when linseeds are un-4 protected (Wood et al., 2003[START_REF] Normand | Produire de la viande bovine enrichie en acides gras polyinsaturés oméga 3 à partir de graines de lin : quelles modalités d'apport du lin, quelles conséquences sur la qualité de la viande ? Renc[END_REF], i.e. when OCL 2015, 22(6).

???, page 9 of 9

21 to

 21 increase the concentration of polyunsaturated FA in dairy 22 products and beef. Ruminant products contain a variety of FA. 23 Some of them may be of potential benefits to human health, 24 including polyunsaturated FA of the omega-3 FA series. The 25 main omega-3 FA in milk fat is 18:3 n-3. In beef, omega-3 FA 26 are composed of both 18:3 n-3 and 20-and 22-carbon FA. The 27 omega-3 FA, and more particularly 20-and 22-carbon FA, can 28

38 age

 38 FA are in the form of galactolipids, and to a lesser extent, 39 of phospholipids, glycerides and free FA. In concentrates, FA 40 are in the form of phospholipids and cholesterol esters in mem-41 branes, and of glycerides as storage lipids; oilseeds are thus 42 rich in triglycerides. In addition, additives providing fats and 43 oils are sometimes given as triglycerides or as calcium salts. In 44 the rumen, which is the first digestive compartment where feed 45 fermentation and metabolism occur, lipids are first hydrolysed 46 by microbial enzymes. Free FA are then hydrogenated and 47 isomerised by other microbial enzymes, to a large extent in 48 the case of polyunsaturated FA, incompletely in the case of 49 monounsaturated FA. These processes are detailed in Doreau 50 et al. (2012). Disappearance of 18:3 n-3 is close to 90%. Few

51 18 :

 18 2 FA reach the intestine, but, besides significant amounts 52 of stearic acid (18:0), a very large panel of cis-and trans-18:1 53

2

  pasture. Compared to control diet, linseeds resulted in the en-3 richment of different isomers of CLA and conjugated linolenic 4 acids, particularly cis-9, trans-11, trans-13 18:3, identified for 5 the first time in bovine milk fat. 6 Supplying linseeds for beef production has the same global 7 consequences on FA meat composition as on milk, but with 8 some particularities. The increase in 18:3 n-3, EPA and DPA 9 has been demonstrated in all trials where linseeds were used 10 (e.g.

7

  only if animal performances (milk yield and composition for 8 dairy cows, liveweight gain and carcass characteristics) are 9 unchanged or improved. Lipid incorporation in diets may de-10 crease fibre digestibility, due to possible disturbances in rumen 11 microbial ecosystem and fermentation. However, most scien-12 tists agree that this risk is negligible when FA content of diets 13

16A

  range of experiments has been carried out in dairy cows, 17 using linseeds in different forms and amounts. During most 18 short-term studies, feeding up to 15% linseed in diet dry mat-19 ter (DM) did not change DM intake (Ferlay et al., 2013; Petit, 20 2010). In early lactation, discrepancies among experiments on 21 the effect of whole or processed linseed supplementation on 22 milk yield could result from differences in diet composition 23 and length of experiment (Petit, 2010). The whole linseed sup-24 plementation did not modify milk yield and milk fat content 25 and yield in mid-or late lactation (Petit, 2010). Nevertheless, 26 linseed micronisation or extrusion results in variable effects 27 on milk fat concentration, with a possible decrease. One ex-28 planation could be the possible increasing rate of oil release 29 from extruded seeds into the rumen compared to whole seeds, 30 which could result in an increased production of trans FA in 31

5

  biohydrogenation normally occurs. It can be concluded that at 6 normal levels of incorporation, linseeds do not affect milk or 7 beef taste.

9

  The major interest of linseeds in ruminant nutrition is the 10 increase in omega-3 FA in milk and beef with a moderate 11 supply in cattle diet. Although this increase in quantitatively 12 slight, due to rumen biohydrogenation, it contributes to en-13 hance milk and beef nutritional quality, and the image of these 14 products for the consumer. This positive role of linseeds in ru-15 minant nutrition is reinforced by their role for enteric methane 16 mitigation. However, an excessive incorporation in diets may 17 increase some trans FA in products or decrease milk fat and 18 protein contents, and feed efficiency of the diet. It could be 19 recommended to limit linseed incorporation to ca. 3% addi-20 tional fat in the diet. However, a large increase in the use of 21 linseeds for feeding ruminant is limited by the possibilities of 22 increase in linseed cropping. 23 Highlight 24 Linseed use in ruminant nutrition can be developed in the 25 future owing to interest in improving fatty acid composition 26 of milk and meat, and also in decreasing methane emissions. 27 Incorporation in diets up to 3% is possible without side effects 28 on animal performance. An increase in linseed use requires an 29 increase in areas devoted to linseed crops. and A. Ferlay: OCL 2015, 22(6) Ferlay A, Agabriel C, Sibra C, Journal C, Martin B, Chilliard Y. 2008. 1 Tanker milk variability of fatty acids according to farm feeding 2 and husbandry practices in a French semi-mountain area. Dairy 3 Sci. Technol. 88: 193-215. 4 Ferlay A, Doreau M, Martin C, Chilliard Y. 2013. Effects of incre-5 mental amounts of extruded linseed on milk fatty acid composi-6 tion in dairy cows receiving hay or corn silage. J. Dairy Sci. 96: Vlaeminck B, Jenkins T, Enjalbert F, Doreau M. 2007. 9 Assessing rumen biohydrogenation and its manipulation in vivo, 10 in vitro and in situ. Eur. J. Lipid Sci. Technol. 109: 740-756. 11 Focant M, Mignolet E, Marique M, et al. 1998. The effect of vitamin 12 E supplementation of cow diets containing rapeseed and linseed 13 on the prevention of milk fat oxidation. J. Dairy Sci. 81: 1095-and A. Ferlay: OCL 2015, 22(6) Petit HV, Dewhurst RJ, Scollan ND, et al. 2002. Milk production 1 and composition, ovarian function, and prostaglandin secretion 2 of dairy cows fed omega-3 fats. J Dairy Sci. 85: 889-899. 3 Petit HV, Cavalieri FB, Santos GT, Morgan J, Sharpe P. 2008. Quality 4 of embryos produced from dairy cows fed whole flaxseed and the 5 success of embryo transfer. J. Dairy Sci. 91: 1786-1790. 6 Ponter AA, Parsy AE, Saadé M, et al. 2006. Effect of a supplement 7 rich in linolenic acid added to the diet of post partum dairy cows 8 on ovarian follicle growth, and milk and plasma fatty acid com-9 positions. Reprod. Nutr. Dev. 46: 19-29. 10 Raes K, Haak L, Balcaen A, Claeys E, Demeyer D, De Smet S. 2004. 11 Effect of linseed feeding at similar linoleic acid levels on the fatty 12 acid composition of double-muscled Belgian Blue young bulls. 13 Meat Sci. 64: 307-315. 14 Razminowicz RH, Kreuzer M, Leuenberger H, Scheeder MRL. 2008. 15 Efficiency of extruded linseed for the finishing of grass-fed steers 16 to counteract a decline of omega-3 fatty acids in the beef. Livest.

  17

  al., In these studies, linseed supply was of limited extent 60 and given to high-producing animals (2% additional fat to lac-61 tating cows in winter for dairy, 3% of additional fat to the bull 62 fattening herd for beef), corresponding to present practices in 63 France for farmers who use linseeds. In both types of farms, 64 the use of linseeds slightly decreases greenhouse gases emis-65 sions, and slightly increases other environmental impacts as 66 energy use, due to extrusion process, and land use, because 67 crop yield per hectare is lower for linseeds than for cereals that 68 linseeds replace. If strong public policies for decreasing green-69 house gases are implemented, all ruminants receiving concen-70

	CH 4 (g/kg DMI)
		-7%	-15%		Hay-based diet
	20	-4%	-8%		Maize silage-based
					diet
	15			-38%	-35%
	10
	Control	EL	EL	EL
		1.8% fat	3.6% fat	5.2% fat
	Fig. 2. Effect of increasing amounts of extruded linseeds (EL) on
	methane emission in two different diets (from Martin et al., 2009).
	2013).

Table 1 .

 1 Effect of linseed supply on beef liveweight gain.

	Type

18

  Santos JEP, Bilby TR, Thatcher WW, Staples CR, Silvestre FT. 2008. Long-chain fatty acids of diet as factors influencing reproduction 20 in cattle. Reprod. Dom. Anim. 43: 23-30. Scollan ND, Richardson I, De Smet S, et al. 2005. Enhancing the content of beneficial fatty acids in beef and consequences for meat quality. In: Hocquette JF, Gigli S, Indicators of milk and beef quality. Wageningen, The Netherlands: Wageningen Academic Publishers, pp. 151-162. Thangavelu G, Colazo MG, Ambrose DJ, Oba M, Okine EK, Dyck MK. 2007. Diets enriched in unsaturated fatty acids enhance early embryonic development in lactating Holstein cows. Theriogenology 68: 949-957. Van Zijderveld SM, Dijkstra J, Perdok HB, Newbold JR, Gerrits WWJ. 2011. Dietary inclusion of diallyl disulfide, yucca powder, calcium fumarate, an extruded linseed product, or medium-chain fatty acids does not affect methane production in lactating dairy cows. J. Dairy Sci. 94: 3094-3104. Wood JD, Richardson RI, Nute GR, et al. 2003. Effects of fatty acids on meat quality: a review. Meat Sci. 66: 21-32. Zachut M, Arieli A, Lehrer H, Livshitz L, Yakoby S, Moallem U. 2010. Effects of increased supplementation of n-3 fatty acids to transition dairy cows on performance and fatty acid profile in plasma, adipose tissue, and milk fat. J. Dairy Sci. 93: 5877-5889. Cite this article as: Michel Doreau, Anne Ferlay. Linseed: a valuable feedstuff for ruminants.

19 21

Bilby TR, Sozzi A,Lopez MM, et al. 2006. Pregnancy, bovine so-

the diet (less than 3% additional fat), milk yield is unchanged 46 and the risk of decrease in milk fat or protein yield is low.

47

Linseed supply to diets has also been studied in fattening 48 cattle. Table 1 summarizes 20 comparisons between control 49 and supplemented diets. On average, animal liveweight gain is 50 higher by 9% with linseed-supplemented diets than with con-51 trol diet, differences ranging between +25% and -15%. Within 52 experiment, differences are often non-significant. Difference


N Li

& R Richoux

M Boutinaud

P Martin

Gagnaire

V Gagnaire
email: valerie.gagnaire@rennes.inra.fr

: V Gagnaire

R Richoux

Erratum to: Role of somatic cells on dairy processes and products: a review

In addition, there is an error in the text, page 529, the last sentence of the second paragraph in Section 4.1.2, which should read as follows: Nevertheless, the desirable but weak lipolysis observed in Swiss-type cheeses is mainly due to the ripening flora Propionibacterium freudenreichii rather than to the lipoprotein lipase being rapidly inactivated during heat treatment of cheese making (Dherbécourt et al. 2010).

Everything else in the paper remains correct.

We are grateful to Mary Bret for the English correction of this paper and to Anne-Laure Jacquet for her Caseolis" for their scientific support.


domain: sdv info

text:
B O Fragomeni
email: fragomen@uga.edu

D A L Lourenco

Shogo Tsuruta

Yutaka Masuda

Ignacio Aguilar

Andres Legarra

T J Lawlor

Ignacy Misztal

Hot topic: Use of genomic recursions in single-step genomic best linear unbiased predictor (BLUP) with a large number of genotypes

Keywords: single-step method, genomic selection, genomic recursion Hot topic: Use

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Single-step genomic BLUP (ssGBLUP; [START_REF] Aguilar | Hot topic: A unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score[END_REF][START_REF] Christensen | Genomic predictions when some animals are not genotyped[END_REF] has emerged as a simple yet accurate tool for genetic evaluations. Its main advantages over multistep methods are simplicity, no double counting, and resistance to preselection bias [START_REF] Vitezica | Bias in genomic predictions for populations under selection[END_REF][START_REF] Vanraden | Measuring genomic pre-selection bias in theory and in practice[END_REF][START_REF] Legarra | Single Step, a general approach for genomic selection[END_REF]. As originally defined, ssGBLUP uses classical BLUP mixed equations extended with the inverse of the genomic (G) and pedigree (A 22 ) relationship matrices for genotyped animals. With algorithms as described in [START_REF] Aguilar | Efficient computation of the genomic relationship matrix and other matrices used in single-step evaluation[END_REF], the cost of obtaining these matrices is cubic, and currently there is a soft limit of about 150k genotyped animals in the model; however, >600k genotyped animals are available for US Holsteins (https://www.cdcb.us/Genotype/cur_density.html). Several approaches have been proposed to overcome such a limit [START_REF] Legarra | Computational strategies for national integration of phenotypic, genomic, and pedigree data in single-step best linear unbiased prediction[END_REF][START_REF] Fernando | A class of Bayesian methods to combine large numbers of genotyped and non-genotyped animals for whole-genome analyses[END_REF][START_REF] Liu | A singlestep genomic model with direct estimation of marker effects[END_REF] but either they have convergence problems or are expensive and hard to program and use with data and a variety of models such as multiple trait or random regressions. [START_REF] Faux | A recursive algorithm for decomposition and creation of the inverse of the genomic relationship matrix[END_REF] attempted to extend the rules used in creation of the numerator relationship matrix to approximate the inverse of G. Their method was based on incomplete Cholesky factorization, where only genomic relationships between close relatives were considered. However, the approximation was not accurate enough, and steps proposed to increase that accuracy were expensive.

Recently, [START_REF] Misztal | Using recursion to compute the inverse of the genomic relationship matrix[END_REF] proposed a method based on genomic recursion, where genomic breeding value (GBV) of a new genotyped animal is conditioned on GBV of all the previous genotyped animals. One of their proposed algorithms was called "algorithm for proven andyoung animals" (APY). This algorithm conditioned "young" animals on a small subset of "proven" animals. The APY algorithm has a cubic cost with the number of animals treated as proven and a linear cost with the animals treated as young; direct inversion is required for only a small portion of G composed of relationships among animals treated as proven. This algorithm was tested with simulated data and with US Holstein data [START_REF] Fragomeni | Use of genomic recursions and algorithm for proven and young animals for single-step genomic BLUP analyses with a large number of genotypes[END_REF]. In simulations, accuracies with APY were close to those with direct inverted G even when some animals with records were treated as young. This suggests that the definition of "proven" is not critical and this subset may not need to be composed of parents or animals with records, or possess any other special requirement. In US Holsteins with genotypes on 15k proven bulls and 60k young bulls, the correlations of genomic EBV (GEBV) obtained through APY and regular method were >0.99.

In real data sets, genotyped animals include bulls and cows. Although the number of proven bulls is limited and increases slowly (~2,000/yr for US Holsteins), the number of cows with genotypes can be very high. The purpose of this study was to evaluate the accuracy of GEBV with APY for US Holsteins, considering genotypes of bulls and cows and treating various groups of animals as proven and young.

MATERIALS AND METHODS

Genomic Recursions

The recursion for the additive genetic effect of animal i (u i ) can be written as [START_REF] Misztal | Using recursion to compute the inverse of the genomic relationship matrix[END_REF]

u u u p u i i i j j i j i | ... , 1 1 1 1 - = - = + ∑ ε
where u is an additive genetic effect, p relates animals to all previous j individuals, and ε is the error term. Calculations can proceed as

p g G M p i i i i i i i i i i i i i m g , : , : : , : , , , , var 1 1 1 1 1 11 1 1 - - - - - = ( ) = = ( ) = - ε 1 1 1 1 1 : ,:
' ,

i i i - - g
where M is a diagonal matrix of genomic Mendelian sampling, and G = {g ij } is a genomic relationship matrix, g is a vector of G, and p is a vector that contains p. Then, the inverse of G can be created using a formula as in [START_REF] Henderson | A simple method for computing the inverse of a numerator relationship matrix used in prediction of breeding values[END_REF] and [START_REF] Quaas | Additive genetic model with groups and relationships[END_REF]:

G I P M I P TM T - - - = - ( ) - ( )= 1 1 1 ' ' ,
where T is a triangular matrix, P = {p ij }, and I is an identity matrix; if many of its elements are very small, they can be set to 0 and G -1 may be computed at a low cost.

The APY Algorithm

In genomic recursions, contributions from proven and young animals can be separated as

u u u u p u p u i i i jj j proven ij j j young i | , ,..., . " " " " 1 2 1 - ∈ ∈ = + + ∑ ∑ ε
However, the contribution of information from young animals to other genotyped animals is 0 in GBLUP because young animals do not get information from data. Then, neglecting these contributions,

u u u u p u i i i jj j proven i | , ,..., . " " 1 2 1 - ∈ = + ∑ ε
As shown in [START_REF] Misztal | Using recursion to compute the inverse of the genomic relationship matrix[END_REF], the simplified recursions lead to a new formula for an approximate inverse of G called APY:

G G G G M G G G G M M G G M - - - - - - - - - = + - - 1 1 1 1 1 1 1 1 1 pp pp py g yp pp pp py g g yp pp g -- ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ 1 , m g g i ii ip pp pi , , = - - G G G 1
where G pp is a subset of G relating proven animals, G py relates proven and young animals, G ip relates the ith young animal with all proven animals, and M g is a diagonal matrix. Although this algorithm results in the same GEBV for GBLUP as the regular inversion of G -1 , for ssGBLUP, the APY algorithm leads to an approximation, as a young genotyped animal may provide ties to ungenotyped ancestors. This happens if at least one of its parents is not genotyped. The APY G -1 is a sparse matrix with nonzero elements forming an L shape, with only a diagonal for the submatrix due to young animals; the only direct inversion required is for G pp . Whereas the regular G -1 requires quadratic storage and cubic computations, the APY G -1 requires quadratic storage and cubic computations only for animals treated as proven and linear storage and computations for animals treated as young. When the number of animals treated as proven is a small fraction of all animals, the APY G -1 has approximately a linear cost and can provide large savings in memory and especially in computing time.

Field Data

To check the quality of this approximation for G -1 , we tested it using real data. Phenotypic data included 11,626,576 records for final score on 7,093,380 cows, with 10,709,878 animals in the pedigree provided by Holstein Association USA Inc. (Brattleboro, VT). Final score is a weighted linear combination of 5 major breakdown score for type traits in dairy cattle, and was chosen for this study because of availability of records. Genotypes on 42,503 SNP markers were available for 569,404 animals. However, to have comparisons with the regular ssGBLUP where direct inversion of G is used, analyses involved only 100,000 of the genotyped animals, which is the limitation of ssGBLUP for the available computer. Thus, genotypes were considered for all 23,174 bulls with progeny information, all 27,215 cows with records (hereafter termed "cows"), and additionally 49,611 young animals.

Analyses

Initially, GEBV were calculated using the regular ssGBLUP, which applies direct inversion for G. Second, GEBV were calculated using APY to obtain G -1 recursively (G -1 APY ) with several different definitions for proven animals: only sires; sires and cows; only cows; and sires with >5 progeny including sons and daughters. Third, previous analyses were repeated with "proven" animals randomly sampled from the group of all 100k genotyped animals in sets of 2k, 5k, 10k, 15k, and 20k animals; the sampling was replicated 4 times. Evaluations for final score were done using a single trait model as described in [START_REF] Tsuruta | Analysis of age specific predicted transmitting abilities for final scores in Holsteins with a random regression model[END_REF]. All analyses were conducted with blup90iod2 (http:// nce.ads.uga.edu/wiki/BLUPmanual) program with modifications as in [START_REF] Aguilar | Efficient computation of the genomic relationship matrix and other matrices used in single-step evaluation[END_REF]. The quality of approximations was assessed by correlations between GEBV for the almost 50k young animals obtained from ssGBLUP using direct inversion of full G (regular ss-GBLUP) and ssGBLUP using approximated G -1 from the APY algorithm.

RESULTS AND DISCUSSION

Table 1 summarizes runs with regular and APY ssG-BLUP when the subset of animals treated as "proven" were sires, sires + cows, cows, and sires with >5 daughters. For all subsets, the correlations of GEBV obtained with a regular and APY algorithms are >0.99. In all cases except when cows were treated as proven, the convergence rate was close to a regular run, indicating good computing properties. The smallest set of proven animals with good predictive ability was sires with >5 daughters (16,434 animals). Treating more animals as proven-that is, including sires with <5 progeny-only marginally affected the correlations. Computing an inverse for 16k animals (assuming cubic algorithm for inversion) cost about 200-fold less than for 100k animals and would cost 4,000-fold less for 600k animals.

Surprisingly good correlations were observed with only cows treated as proven although the convergence rate was affected, but was still much better than with ssGBLUP with unsymmetric equations constructed to avoid the inverse of G. [START_REF] Aguilar | Genetic evaluation using unsymmetric single step genomic methodology with large number of genotypes[END_REF]. This means that the original definition of animals as young and proven is not necessarily important for accuracy of GEBV; only the number of animals in G pp matters. To test this hypothesis, 2k, 5k, 10k, 15k, and 20k animals were chosen randomly from all bulls and cows and treated as proven in the APY algorithm. Rounds to convergence increased with subset size but were lower than with the regular algorithm. This suggest that G -1 by APY is well numerically conditioned. The correlations of GEBV with the regular and APY algorithms ranged from >0.94 for 2k animals to >0.99 for 20k animals, with very small variations among the replicates (Table 2). This means that the choice of animals in G pp is mostly arbitrary.

Initially, the last statement seems hard to believe; however, recursions generate very similar inverses regardless of the order of animals. The single step modi- To test whether the presence of sires and cows is crucial for good properties of APY, an extra set included 20k animals selected randomly only from young animals. The correlations of GEBV for this set were slightly lower than with complete random 20k choice and similar to a 15k random sample. Also, the convergence rate was slightly worse. In general, we expect better properties of APY when animals treated as "proven" are well related to animals treated as "young." Although proven sires are well related to the general population, cows and young animals may be less so.

The Henderson's algorithm for creating the inverse of the numerator relationship matrix (A -1 ) is based on younger animals conditioned on older animals [START_REF] Henderson | A simple method for computing the inverse of a numerator relationship matrix used in prediction of breeding values[END_REF]. In such a case, each recursion has at most 2 nonzero elements, each with a value of 0.5 and due to a parent. However, an identical A -1 can be derived with animals in the reverse order (see Appendix in [START_REF] Misztal | Using recursion to compute the inverse of the genomic relationship matrix[END_REF]. In such a case, the number of nonzero elements in each recursion can be greater than 2 and they can take different values. Assume the following genomic recursion, where the additive genetic effect of an animal i is conditioned on the first m animals:

u u u p u i i i j j i m j i | , , (m)
, min( , )

1 1 1 1 … - = - = ∑ + ε
where ε i (m) is the error term; although the error term should be smaller with larger m, apparently the reduction of ε i (m) for m >10k is small. In an alternate interpretation, the inverse of G created with APY is becoming more accurate as m increases, with small improvements beyond m > 10k.

The limited number of animals required in the recursion (<20k) suggests that the genomic information for a population has a limited dimensionality (<20k). Nearly all genomic information from a reference population is usually assumed to be accounted for by SNP solutions with a medium-size chip (~50,000 SNP markers). However, many SNP are correlated. [START_REF] Pintus | Use of different statistical models to predict direct genomic values for productive and functional traits in Italian Holsteins[END_REF] found that 15,207 principal components extracted from matrices based on 39,555 SNP markers explained 99% of the genetic variation. Thus, the real dimensionality of the SNP information may be ~15k. Alternately, when the number of QTL is high, the accuracy of GBLUP depends on the number of independent chromosome segments, with the number of the segments usually <10k [START_REF] Daetwyler | The impact of genetic architecture on genome-wide evaluation methods[END_REF]. Further research will determine whether the limits based on the recur-sion, eigenvalues, and chromosome segments are related through equivalent models.

The US Holstein population is very homogeneous. In other species, populations may be more diverse and a larger subset may be needed. [START_REF] Lourenco | Genomic evaluation by single-step GBLUP in Angus[END_REF] applied APY to genetic evaluation of US Angus for 3 traits with 52k genotyped animals. Using 4k and 8k subsets generated 84 and 97% of gains in accuracy, respectively, over BLUP compared with a regular ssG-BLUP. A detailed analysis on the number and choices of animals treated as proven in APY will be a topic for a separate study. Further investigations will also look at whether specific subgroups of animals are invariant to the selection of the subset of animals defined as proven.

The original derivation of the APY algorithm was based on labeling animals in the recursion as proven. Because the algorithm works with any sufficiently large subset of animals in the recursion, the designation of proven or young may no longer be relevant. In particular, the animals can be decomposed into a base genomic relationship group (b) and a conditional genomic relationship group (c); for example, with relevant matrices G bb and G bc .

In this paper, we focused on accuracy of ssGBLUP with G -1 calculated by APY. In practical implementations, important issues will be memory requirements and computing costs for a large number of genotyped animals. Assume a total of n = 500k genotyped animals, recursion on m = 20k animals, and double precision half-storage. The amount of memory necessary for APY G -1 is approximately 80 gigabytes (n × m × 8 = 20k × 500k × 8 bytes) or 8% of 1 terabyte (n 2 /2 × 8 = 500k × 500k × 8 bytes/2) required for a regular halfstored G -1 . As current servers have memory capacity in the order of terabytes, the memory requirements will not limit the APY algorithm. Computing APY G -1 would require approximately m 3 + 2m 2 (n -p) operations, or about 0.3% operations (n 3 ) for a regular G -1 . Another issue is efficient computations of A 22 1 -. In separate analyses (results not provided), computing this matrix using formulas similar to that of [START_REF] Stranden | Comparison of some equivalent equations to solve single-step GBLUP[END_REF] took negligible time and memory.

CONCLUSIONS

Inverse of a genomic relationship matrix can be approximated with the APY algorithm where actual inversion is applied only to a small subset of genotyped "proven" animals and an approximate inversion by recursion is applied on "young" animals. The approximation is very accurate when the number of animals in the subset is 10k or greater, and storage and computing costs can be dramatically lower. The choice of animals in the subset is arbitrary, as various definitions, including random choices, provide similar accuracy. The convergence rate is superior to that of conventional inversion. Costs of APY inversions with a larger number of animals are approximately linear, making the algorithm potentially suitable for any number of genotypes. Single-step GBLUP with APY may be suitable for models with any number of genotyped animals.

Table 1 .

 1 Correlations between genomic EBV with regular and APY (algorithm for proven and young) single-step genomic BLUP for young genotyped animals and rounds to convergence for different subset of animals used in recursions

	Definition	Animals		Rounds to
	of subset	in subset	Correlation	convergence
	All	100,000	1.000	567
	Sires	23,174	0.994	432
	Sires + cows	50,389	0.995	428
	Cows	27,215	0.992	797
	Sires >5 progeny	16,434	0.992	415

Table 2 .

 2 Ranges of correlations between genomic EBV with regular and APY (algorithm for proven and young) single-step genomic BLUP for young genotyped animals and rounds to convergence when different numbers of randomly sampled animals were used in the subset for recursions

	Number of		Rounds to
	proven animals	Correlation	convergence
	2,000	0.943-0.944	351-357
	5,000	0.971-0.972	354-367
	10,000	0.985	391-403
	15,000	0.989-0.990	411-480
	20,000 20,000 1	0.992-0.993 0.989-0.990	416-425 552-556

1

Proven were randomly sampled from the group of young animals.

Journal of Dairy Science Vol. 98 No. 6, 2015

ACKNOWLEDGMENTS

We gratefully acknowledge the very helpful comments by the two anonymous reviewers and insightful suggestions by section editor Jennie Pryce. This research was supported by grants from Zoetis (Florham Park, NJ), Cobb-Vantress Inc. (Siloam Springs, AR), Smithfield Premium Genetics (Rose Hill, NC), American Angus Association (St. Joseph, MO), Holstein Association USA (Brattleboro, VT), Pig Improvement Company (Hendersonville, TN), and by Agriculture and Food Research Initiative Competitive Grants no. 2015-67015-22936 from the US Department of Agriculture's National Institute of Food and Agriculture (Washington, DC). A. L. thanks INRA metaprogram SelGen and projects X-Gen and GenSSeq.