Selection for increased number of piglets at d 5 after farrowing has increased litter size and reduced piglet mortality 1

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1 Publishe November 25, 2014 Selection for increase number of piglets at 5 after farrowing has increase litter size an reuce piglet mortality 1 B. Nielsen,* 2 G. Su, M. S. Lun, an P. Masen *Pig Research Centre, Danish Agriculture an Foo Council, DK-1609 Axeltorv, Denmark; an Department of Molecular Biology an Genetics, Aarhus University, DK-8830 Tjele, Denmark ABSTRACT: Selection for litter size at 5 after farrowing (LS5) was introuce in 2004 to increase the number of piglets weane an to reuce piglet mortality in Danish Lanrace an Yorkshire. The objective of this stuy was to investigate selection responses for LS5, total number born (TNB), an mortality [MORT, efine as (TNB LS5)/TNB] when selection for increasing LS5 was a part of the breeing goal. Data were collecte from nucleus hers recore from 2004 to 2010, incluing first litters of 42,807 Lanrace sows an 33,225 Yorkshire sows. The ata were analyze using a 3-trait animal moel of TNB, MORT, an LS5. Significant (co) variances were estimate between the 3 traits in both populations. The heritabilities of TNB, MORT, an LS5 were 0.10, 0.09, an 0.09 in Lanrace an 0.12, 0.10, an 0.10 in Yorkshire. The genetic correlations were 0.28 an 0.22 between TNB an MORT, 0.74 an 0.68 between TNB an LS5, an an between MORT an LS5 in Lanrace an Yorkshire, respectively. The results show that the genetic improvement of LS5 was a combination of increase TNB an reuce MORT. During the observation perio, the genetic improvement was 1.7 piglets per litter for LS5, 1.3 piglets per litter for TNB, an 4.7% for MORT in Lanrace an 2.2 piglets per litter, 1.9 piglets per litter, an 5.9% in Yorkshire. Phenotypic improvement was 1.4 piglets per litter for LS5, 0.3 piglets per litter for TNB, an 7.9% for MORT in Lanrace an 2.1 piglets per litter, 1.3 piglets per litter, an 7.6% in Yorkshire. In aition, genetic gain was evaluate in 3 phenotypic groups of TNB, representing the 25% smallest litters, the 50% meium litters, an the 25% largest litters. In all 3 groups, the genetic an phenotypic gains of TNB an LS5 increase, whereas MORT reuce in both populations. Key wors: breeing, fertility, litter size, piglet mortality 2013 American Society of Animal Science. All rights reserve. J. Anim. Sci : oi: /jas INTRODUCTION 1 This work was partly fune by the Danish Ministry of Foo, Agriculture an Fisheries (grant number ). The authors gratefully acknowlege Peer Berg (Aarhus University, Denmark) for valuable iscussions uring the initial phase of the project. 2 Corresponing author: bni@lf.k Receive October 15, Accepte February 19, In commercial pig prouction, the number of weane pigs is a key factor to increases prouctivity, an litter size has been one of the most important traits in pig prouction. Therefore, selection for large litter size has been a part of the Danish pig breeing program since 1992, an the selection strategy has resulte in a consierable increase in total number born (TNB; Sorensen et al., 2000; Su et al., 2007). It has been reporte that the genetic correlation between TNB an mortality is positive but unfavorable (Lun et al., 2002; Damgaar et al., 2003; Su et al., 2007). Consequently, selection for increasing TNB will increase the number of stillborn as well as the preweaning mortality. Previous stuies have showe that there is a substantial potential for genetic improvement of piglet survival, especially when piglet mortality is high as uner outoor prouction systems (Roehe et al., 2010). It was observe that most cases of eath occurre at farrowing an uring the first 5 after farrowing in Danish Lanrace an Yorkshire (Su et al., 2007, 2008). To avoi an aitional increase in the number of stillborn an to reuce the mortality of the piglets in the early nursing perio, the breeing goal in the Danish bree- 2575

2 2576 Nielsen et al. ing program was change in 2004 to focus on the litter size at 5 after farrowing (LS5). The trait LS5 is a composite trait as it combines TNB an mortality until 5 after farrowing. It is expecte that selection for LS5 will lea to an increase of TNB an a reuction of piglet mortality. The objective of this stuy was to investigate the realize genetic improvement of TNB an piglet mortality (recore as the ratio between the sum of stillborn an ea piglets up to 5 after farrowing an TNB) after selection for increasing LS5 was introuce as a part of the breeing goal in Danish Lanrace an Yorkshire populations. MATERIALS AND METHODS Animal Care an Use Committee approval was not obtaine for this stuy because the ata were obtaine from an existing atabase of performance recors. Data All ata were supplie by the Danish Agriculture an Foo Council, Pig Research Centre, Axeltorv, Denmark. The ata were collecte from Danish Lanrace an Yorkshire nucleus hers uring the perio from January 2004 to December During the recoring perio, the populations were selecte on the basis of a selection inex in which LS5 was a main component trait. Sows were kept uner commercial conitions, an all matings were by AI. There were no protocols for assisting the sows uring the birthing process. At farrowing, TNB was recore as the total number of fully forme piglets born, incluing the number of stillbirths. The ata recoring system oes not account for the piglets that ie in utero. At birth, the piglets were earmarke, an cross-fostering was permitte uring the whole suckling perio to ensure animal welfare. During the assignment of cross-fostering, piglets might be exchange between litters. Different hers might have ifferent strategies for cross-fostering to use the nursing capacity of sows efficiently. During the first 5 after farrowing, the ea piglets in each litter were recore an were assigne to the biological litters accoring to their earmarks. Litter size at 5 after farrowing in each litter was calculate as the TNB minus the number of stillborn an ea piglets up to 5 after farrowing. The mortality (MORT) was calculate as (TNB LS5)/TNB in each litter. Survival status of the piglets that because of cross-fostering were transferre to another litter was recore to the litter of the biological mother. To avoi possible bias in estimation of genetic parameters an preiction of breeing values ue to phenotypic selection of sows after first litter, only the first litter recors of each sow were inclue in the ata. Thus, Table 1. Number of farms, year-week, an sows (litters) 1 Bree Farms Year-week Sows (Litters) Lanrace ,807 Yorkshire ,225 1 Only first parity was consiere. the ata in the analysis comprise recors of first parity from 42,807 Lanrace sows (gilts) an 33,225 Yorkshire sows (gilts; Table 1). Statistical Analysis Litter size an mortality up to 5 after farrowing were analyze using a 3-trait animal moel. Su et al. (2007) claime that the nursing sow ha a small effect on piglet survival rate uring the first 5 after birth. Knol et al. (2002) reporte that incluing the nurse sow effect in a moel for piglet survival gave erratic results. In the current stuy all 3 traits were consiere as the traits of biological sows, ignoring the cross-fostering effect. The basic moel to escribe the observations was y= Xb+ Z u+ Z + e, u where y is the vector of observations for the 3 traits (TNB, LS5 an MORT); b is the vector of fixe effects, incluing effects of year-month an litter genotype (purebre or crossbre), as well as effects of age at first parity (regressions on the first an secon orers of age covariables); u is a vector of ranom her-year-month effects; is a vector of ranom sow genetic effects; e is a vector of ranom resiuals; an X, Z u, an Z are incience matrices associating b, u, an with y. Assumptions for ranom effects were u 0 I Σ 0 0 u u ~ N 0 0 A 0, Σ e, I Σ e e where Σ, u Σ, an Σ e are covariance matrixes for her-year-month effects, aitive genetic effects of sow, an resiuals, respectively; I u an I e are the ientity matrices of imension equal to the number of her-yearmonth classes an the number of observations, respectively; an A is the matrix of aitive genetic relationships among animals in the peigree. The peigree was trace back 4 generations an inclue 49,800 Lanraces an 39,674 Yorkshires. The numbers of base animals were 441 an 422 in the Lanrace an Yorkshire populations, respectively. The parameters in the moels were

3 Litter size an piglet mortality 2577 estimate by REML using the software package DMU (Masen an Jensen, 2010). 2 Phenotypic variance ( σ ) was efine as p σ p = σ u + σ + σ for TNB an LS5 as well as MORT, e 2 2 where σ is the variance of her-year-month effects, u σ 2 is the variance of sow aitive genetic effects, an σ is e the resiual variance. All 3 traits, TNB, LS5 an MORT, were consiere as traits of the sow. Therefore, heritability was calculate as the ratio of sow aitive genetic variance to phenotypic variance, i.e., h =σ / σ. p The asymptotic (co)variances for the estimates of (co)variance components were obtaine from the approximate observe information matrix, an approximate SE for functions of estimate (co)variances were estimate using Taylor series expansion (Su et al., 2007). Genetic trens were calculate as the year mean of EBV, an phenotypic tren was calculate as year mean of observations of sows on the basis of the birth year of the sows. Chen et al. (2010) reporte that there was a nonlinear relationship between the aitive genetic effect of the number of stillbirths an the environmental eviation of litter size an suggeste that selection for increasing survival at birth for a large litter might not simultaneously reuce mortality for a small litter. It can be argue that the reuction in MORT might be ifferent in large litters compare with small litters in the present populations. Therefore, it coul be important to investigate whether the expecte reuctions of piglet mortality ue to selection for LS5 were realize in ifferent sizes of litters. For this purpose, the sows were ivie into 3 phenotypic groups base on the phenotypic litter size (TNB) within each year, representing the 25% smallest litters, the 50% meium litters, an the 25% largest litters. The genetic an phenotypic gains of LS5, TNB, an MORT were calculate within each group. RESULTS Lanrace sows ha slightly larger litter size an slightly lower mortality rate than Yorkshire sows (Table 2). The mean TNB an the mean LS5 were 13.7 an 11.1 in Lanrace an 13.5 an 10.8 in Yorkshire, respectively. The mean mortality was 0.18 in Lanrace an 0.20 in Yorkshire. The mean mortality was calculate as the mean of the mortality obtaine in each litter. The withinyear SD of TNB an LS5 range from 3.6 to 3.9 in the 2 populations, an the within-year SD of MORT was 0.18 in Lanrace an 0.20 in Yorkshire. The sow genetic (co)variances between TNB, MORT, an LS5 were all significantly ifferent from 0 in the 2 populations (Table 3). The genetic variances of TNB, MORT, an LS5 were 1.48, 0.003, an 1.07 in Lanrace an 1.65, 0.004, an 1.34 in Yorkshire. Table 2. Total number of litters, mean an SD within years for total number born (TNB), piglet mortality (incluing stillborn an number of ea piglets until 5 after farrowing), an litter size at 5 after farrowing (LS5) Item No. of litters Mean SD Lanrace TNB 42, Mortality 42, LS5 42, Yorkshire TNB 33, Mortality 33, LS5 33, The environmental variances in the moel were escribe by her-year-month effects an resiual effects. The resiual variance escribe a significant part of total variation in Lanrace as well as in Yorkshire (Table 3). Resiual covariances between TNB, MORT, an LS5 were all significantly ifferent from 0 in the 2 populations. The variances of her-year-month effects were small an less than the genetic variances for all 3 traits in both populations because the moel alreay inclue year-month as fixe effect. Table 3. Covariance matrices of her-year-week effect, maternal genetic effect, an resiuals relate to the total number born (TNB), piglet mortality incluing stillborn (MORT), an litter size at 5 (LS5) in Lanrace an Yorkshire 1 Variance component Lanrace Her-year-week effect Σ Trait (Co)variances an SE TNB MORT LS5 TNB 0.17 (0.03) (0.001) 0.09 (0.02) u MORT (0.0001) (0.001) LS (0.02) Genetic, sow Σ TNB 1.48 (0.13) (0.004) 0.93 (0.10) MORT (0.0002) (0.004) LS (0.10) Resiual Σe TNB (0.13) (0.004) 9.41 (0.10) MORT (0.0002) (0.004) LS (0.10) Yorkshire Her-year-week TNB 0.25 (0.03) (0.001) 0.15 (0.03) effect Σu MORT (0.0001) (0.002) LS (0.03) Genetic, sow Σ TNB 1.65 (0.15) (0.006) 1.01 (0.12) Resiual MORT (0.0004) (0.006) LS (0.14) Σe TNB (0.14) (0.005) 8.48 (0.12) MORT (0.0004) (0.006) LS (0.13) 1 Asymptotic SE are shown in brackets.

4 2578 Nielsen et al. Table 4. Heritability (on the iagonal), phenotypic correlation (below the iagonal), an genetic correlation (above the iagonal) for total number born (TNB), piglet mortality incluing stillborn (MORT), an litter size at 5 (LS5) in Lanrace an Yorkshire 1 Lanrace Yorkshire Item TNB MORT LS5 TNB MORT LS5 TNB 0.10 (0.008) 0.28 (0.06) 0.74 (0.03) 0.12 (0.01) 0.22 (0.07) 0.68 (0.04) MORT 0.14 (0.005) 0.09 (0.008) (0.05) 0.09 (0.06) 0.10 (0.01) (0.05) LS (0.002) (0.004) 0.09 (0.008) 0.71 (0.003) (0.004) 0.10 (0.01) 1 Approximate SE are given in parentheses. The heritabilities of TNB, MORT, an LS5 were 0.10, 0.09, an 0.09 in Lanrace an 0.12, 0.10, an 0.10 in Yorkshire (Table 4). The genetic correlation between TNB an MORT were 0.28 an 0.22 for the Lanrace an Yorkshire, respectively. The genetic correlations between TNB an LS5 were 0.74 an 0.68, an the genetic correlations between MORT an LS5 were an for Lanrace an Yorkshire, respectively. The phenotypic correlations between TNB an MORT were 0.14 an 0.09 for Lanrace an Yorkshire, respectively. The phenotypic correlations between TNB an LS5 were 0.77 an 0.71 an between MORT an LS5 were an for Lanrace an Yorkshire, respectively. The phenotypic correlations between the 3 traits were on the same level as the genetic correlations except for the phenotypic correlations between TNB an MORT, which were less than the genetic correlations. The genetic correlations inicate that selection for large TNB woul increase both LS5 an MORT, whereas selection for large LS5 woul increase TNB but ecrease MORT. As shown in Figs. 1 an 2, there was a clear phenotypic tren an a clear genetic tren that LS5 an TNB increase, whereas MORT ecrease over the years in both populations. During the perio from 2003 to 2009, the genetic improvement was 1.7 piglets for LS5, 1.3 piglets for TNB, an 4.7% for MORT in Lanrace an 2.2 piglets, 1.9 piglets, an 5.9% in Yorkshire. The phenotypic improvement was 1.4 piglets for LS5, 0.3 piglets for TNB, an 7.9% for MORT in Lanrace an 2.1 piglets, 1.3 piglets, an 7.6% in Yorkshire. These improvements confirme that selection for LS5 ha resulte in a consierable irect response for LS5 itself an a consierable correlate response for TNB an MORT. Figure 3 shows the changes of year means of EBV for 3 groups of litters with small, meium, an large TNB, an Fig. 4 shows the year means of phenotypes for the 3 groups. It was observe that MORT was slightly greater in the group with large TNB compare with the groups with small an meium TNB. However, the trens for both phenotypic an genetic changes over the years were almost the same for each trait in the 3 groups. Clearly, selection for LS5 reuce piglet mortality not only for small an meium litters but also for large litters. The expecte response to selection for LS5 was calculate approximately. In both brees, the selection proportion was about 1:150 for males an 1:3 for females. This gave a theoretical selection intensity i = 0.5( ) = 2. However, some animals were not available for selection because of various reasons (e.g., poor health, fertility problems, an restriction on inbreeing), an thereby, the real selection intensity was assume to be i = 1.5. The breeing values of LS5 were preicte Figure 1. Phenotypic means by sow year of birth for total number born (TNB), mortality (MORT), an litter size at 5 after farrowing (LS5) in the first parity (gilt results) of Lanrace (line with circles) an Yorkshire (line with triangles) populations.

5 Litter size an piglet mortality 2579 Figure 2. Mean EBV by sow year of birth for total number born (TNB), mortality (MORT), an litter size at 5 after farrowing (LS5) in Lanrace (line with circles) an Yorkshire (line with triangles) populations. The EBV were ajuste so that sows with birth year at 2003 have a mean EBV equal to 0. Figure 3. Mean EBV by sow year of birth for total number born (TNB), mortality (MORT), an litter size at 5 after farrowing (LS5) in 3 phenotypic levels of total number born: the 25% small litters (line with circles), the 50% meium litters (line with triangles), an the 25% largest litters (line with crosses) in first litter of Lanrace (L-sows) an Yorkshire (Y-sows). The EBV were ajuste so that sows with birth year at 2003 have a mean EBV equal to 0 in the 50% meium litters.

6 2580 Nielsen et al. Figure 4. Phenotypic means by sow year of birth for total number born (TNB), mortality (MORT), an litter size at 5 after farrowing (LS5) in 3 phenotypic levels of total number born: the 25% small litters (line with circles), the 50% meium litters (line with triangles), an the 25% largest litters (line with pluses) in first litter (gilt results) of Lanrace (L-sows) an Yorkshire (Y-sows). using a multitrait BLUP moel base on the ata consisting of recors from both nucleus hers an multiplier hers. The stanar eviation in EBV of LS5 was σ EBV = 0.35 for the animals without LS5 recors (most animals i not have their own LS5 recor at the time of selection), an the correlation between EBV of LS5 an selection inex was r = Assuming 1 generation per year, the expecte genetic gain of LS5 was about i r σ EBV = = 0.34 piglets per litter per year, which was consistent with the observe gain of LS5. DISCUSSION This stuy showe that selection for LS5 has le to genetic an phenotypic increases in TNB an LS5 an reuction in MORT. The results were consistent with the estimate genetic parameters of the 3 female traits for which the estimates of heritabilities for the 3 traits range from 0.09 to 0.12, an LS5 ha a strong positive genetic correlation with TNB an a strong negative correlation with piglet mortality. The heritabilities of TNB an LS5 range from 0.09 to 0.12 in Lanrace an Yorkshire, which is similar to the average of 0.10 reporte by Haley et al. (1988). However, the estimates were greater than those previously reporte for the same brees (Su et al., 2007). There were 2 possible reasons: 1) the stuy by Su et al. (2007) was base on a smaller number of litters (9,310 in Lanrace an 6,861 in Yorkshire) for a perio of 2 yr an therefore ha larger SE of the estimates, an 2) the ata in their stuy inclue recors from various parities, an the mixture of various parities together with phenotypic selection of sows (mainly for litter size) after first parity in practice coul have an influence on estimates of heritabilities. The heritability of mortality was foun to be 0.09 an 0.10 in Lanrace an Yorkshire, which for Lanrace was in accor with the results of Su et al. (2007); however, for Yorkshire it was a bit greater. In the literature there is rather large variation among heritabilities of mortality. In a review by Rothschil an Bianel (1998), the mean heritability was foun to be 0.05, covering a

7 Litter size an piglet mortality 2581 large variation, whereas Lamberson an Johnson (1984) reporte a heritability for preweaning survival at Ferguson et al. (1985) reporte a value of 0.14 in Yorkshire an 0.18 in Duroc. Damgaar et al. (2003) reporte a heritability of 0.13 for the proportion of stillbirths in Sweish Yorkshire. The positive but unfavorable genetic correlations at 0.28 an 0.22 between TNB an MORT in Lanrace an Yorkshire, respectively, coul explain why in the years between 1992 an 2004 breeing for increase TNB increase the piglet mortality. Lun et al. (2002) also foun an unfavorable genetic correlation between TNB an piglet mortality. In Lanrace they foun a negative correlation of between maternal genetic effects on total number born an proportion surviving from birth until 3 wk. Furthermore, an unfavorable positive genetic correlation between the number of live-born piglets an the proportion of ea piglets uring suckling was also foun by Damgaar et al. (2003). Similarly, Su et al. (2007) reporte a negative genetic correlation of TNB with piglet survival at birth an survival uring suckling. Other stuies ha reporte that selection base on ovulation rate an embryonic survival ha an unfavorable effect on number of stillborn piglets (Johnson et al., 1999; Petry an Johnson, 2004). The results of the present stuy as well as previous reports in the literature inicate that breeing only for TNB will increase piglet mortality. The negative but favorable genetic correlations of an between LS5 an MORT in Lanrace an Yorkshire show that breeing for LS5 can reuce the mortality at the same time as it increases the number of live piglets at 5 after farrowing. Su et al. (2007) reporte that genetic correlations between LS5 an number of piglets born alive were 0.84 an 0.82 an genetic correlations of LS5 with piglet survival at birth an survival from birth to 5 range from 0.38 to 0.58 in Lanrace an Yorkshire, respectively. Therefore, selection for high LS5 is expecte to reuce both mortality at farrowing an mortality uring the early suckling perio. The genetic correlations between LS5 an TNB at 0.74 an 0.68 in Lanrace an Yorkshire were greater than those reporte by Su et al. (2007). The positive an high genetic correlation shows that even if TNB is not part of the breeing goal, selection for LS5 will increase TNB per litter an the favorable correlation to mortality will ecreases the mortality rate in litters. However, if selection is base on TNB, LS5 will still increase, but the unfavorable genetic correlation between TNB an mortality will lea to increase mortality in litters. The favorable genetic correlation between LS5 an mortality an between LS5 an TNB was well emonstrate by the genetic gains ue to selection for high LS5 from The genetic gain increase in TNB an LS5, an at the same time a genetic ecrease in mortality, was foun regarless of whether the am was categorize as having a low, meium, or high litter size. For the phenotypic group of the 25% largest litters, which ha the greatest mortality, the ecrease in piglet mortality was about 6% uring the perio from 2003 to 2010 (birth years of sows). Similarly, ecreases in piglet mortality were also foun in the groups of small an meium litters. Similar patterns were observe in the change of phenotypic means. The simultaneous reuction of mortality in small, meium, an large litters is in contrast to the results of Chen et al. (2010), who foun that selection for increasing survival at birth for large litter size might not simultaneously reuce mortality for small litter size. Thus, these authors suggeste that the genetic sensitivity of the number of stillbirths to litter size shoul be consiere as a selection criterion to improve piglet survival. On the basis of our results this oes not seem necessary, possibly because the mean litter size is relatively high for Danish Lanrace an Yorkshire. The trait of LS5 can be consiere a composite of 2 traits relate to fertility (TNB) an mortality (MORT), an response to selection for LS5 will be a combination of the 2 traits. Let us assume a mean litter has a total of 13 piglets born an the genetic reuction in mortality is 6%. Then over the perio from 2003 to 2009 the mean number of live piglets at 5 after farrowing was increase by 0.78 piglets because of the reuction of mortality. However, at the same time the genetic gains of LS5 for Lanrace an Yorkshire were 1.7 an 2.2 piglets, respectively, inicating that 35% to 45% of the selection response for LS5 was allocate to piglet welfare by reuce mortality, whereas the remaining selection response was allocate to increase fertility escribe by TNB. The results show that breeing can be a useful tool to increase animal welfare (Kanis et al., 2004). Breeing against mortality to reuce the number of ea piglets in the litter is just one example. The same tools that are use successfully to increase prouction can also be use to improve animal welfare. However, translation of welfare aspects into a clear breeing goal is not always straightforwar. The presente results of the MORT trait provie an explanation of what has occurre, but the selection for TNB an LS5 seems to be the riving factor. Traits such as LS5 evaluate in this paper will help to efficiently bree pigs for welfare-frienly husbanry. A further selection for reuction in piglet mortality might be achieve in the future by using more sophisticate moels that allow for selection for the maternal an the irect genetic components jointly (Knol et al., 2002; Ibáñez-Escriche et al., 2009; Roehe et al., 2009, 2010). In those moels the observations are binary responses at the piglet level score as a live or ea piglet. However, in the present stuy, a preliminary analysis was conucte

8 2582 Nielsen et al. for mortality using a generalize linear mixe moel consiering mortality as a binary istribute trait. The inferences from the moels clearly inicate an overispersion, as the observe number of litters with zero mortality was greater than that preicte by the moel. Varona an Sorensen (2010) suggest a hierarchical zero-inflate negative binomial moel for the trait of stillbirth. To allow for preicting maternal an irect components jointly an using information from correlate traits, the hierarchical 0-inflate negative binomial moel calls for an extension to a generalize linear multitrait moel that can hanle the covariance structure of irect aitive an maternal aitive genetic effects for mortality as well as aitive genetic effects for other traits. On the other han, many stuies (e.g., Gunsett, 1984; Mather et al., 1988) have reporte that a ratio trait is not a goo selection criterion because the istribution of ata for a ratio trait is unefine an have suggeste improving a ratio trait by selection for a linear inex that maximizes the correlation between the inex an the breeing value of the ratio trait. Conclusions The results of this stuy show that LS5 is a combine trait that has favorable genetic correlations with TNB an piglet survival. Selection for LS5 since 2004 has le to an increase of TNB an a reuction in mortality rate at farrowing an the first 5 after farrowing in Danish Lanrace an Yorkshire nucleus hers. LITERATURE CITED Chen, C. Y., I. Misztal, S. Tsuruta, W. O. Herring, J. Holl, an M. Culbertson Genetic analyses of stillbirth in relation to litter size using ranom regression moels. J. Anim. Sci. 88: Damgaar, L. H., L. Ryhmer, P. Løvenahl, an K. 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