Accounting for lactation length and weaning-to-conception intervalin genetic evaluations for litter size in swine1

D. Marois2, J. R. Brisbane, and J.-P. Laforest3

Department of Animal Science and Centre de Recherche en Biologie de la Reproduction (CRBR),Laval University, Quebec City, Quebec, Canada G1K 7P4

ABSTRACT: Effects of lactation length and weaning-to-conception interval on the subsequent litter size ofpurebred sows were estimated using an animal model.Data on 2,847 Landrace sows with 7,125 litters bornbetween January 1989 and May 1997 and on 1,234Yorkshire sows with 2,999 litters born between January1990 and May 1997 were obtained from two Canadianselection herds. Sows having a lactation of less than 14d (MMEW) were usually not mated until their secondestrus, whereas sows weaned after at least 14 d of lacta-tion (later weaning) were usually mated on their firstestrus. Litter size included both number of pigs bornalive and those stillborn. Linear, quadratic, and loga-rithmic effects of lactation length were tested. The effectof weaning-to-conception interval on litter size wasmodeled using an approach based on threshold vari-ables and an approach using segmented polynomials.Results indicated linear and logarithmic effects of lacta-

Key Words: Early Weaning, Lactation Duration, Litter Size, Pigs, Postweaning Interval

2000 American Society of Animal Science. All rights reserved. J. Anim. Sci. 2000. 78:1796–1810

Introduction

Modified Medicated Early Weaning (MMEW) is amanagement technique that involves administeringmedication to the sow prior to farrowing, removing allpiglets from the sow at an early age, and transferringthem to separate nursery and fattening facilities. Al-though the main purpose of MMEW is to improve thehealth of growing piglets, it also leads to an increasedgrowth rate (Britt, 1995). However, it was found thatthe shorter lactation of the dam is associated with a

1Financial and technical support for this project was provided byGenetiporc Inc. and the Canadian Centre for Swine Improvement.

2Present address: Genetiporc Inc., 1312 Rue St-Georges, St-Ber-nard, Beauce, Quebec, Canada, G0S 2G0 (E-mail: dmarois@globetrotter.qc.ca).

3Correspondence: phone: 418-656-2131 ext. 2596; fax: 418-656-3766; E-mail: Jean-Paul.Laforest@san.ulaval.ca.

Received August 2, 1999.Accepted February 1, 2000.

1796

tion length on subsequent litter size for Yorkshire andLandrace breeds, respectively. Litter size decreased asweaning-to-conception interval increased up to 7 and10 d for Yorkshire and Landrace, respectively, thenincreased with further increases in weaning-to-concep-tion interval up to 35 and 30 d for the two breeds, andthen remained constant. The MMEW sows did not havelower subsequent litter sizes than later-weaned sowsbecause the negative effect of a shorter lactation wasoffset by the positive effect of a longer weaning-to-con-ception interval. However, average time spent open perparity was longer for MMEW sows than for later-weaned sows. Both lactation length and weaning-to-conception interval should be considered in models forthe genetic evaluation of litter size in purebred swine.Segmented polynomials can be used to predict littersize as a continuous function of weaning-to-conceptioninterval or to derive weaning-to-conception interval ad-justment factors for litter size.

smaller litter size at the subsequent farrowing (Xue etal., 1993; Dewey et al., 1994; Mabry et al., 1996), withlonger weaning-to-estrus intervals (Xue et al., 1993;Mabry et al., 1996), and with poorer first-service far-rowing rates (Mabry et al., 1996). Often, to improvesubsequent litter sizes, sows are not bred until theirsecond estrus after an early weaning, which increasesthe weaning-to-conception interval (WCI). Various au-thors have reported significant effects of WCI on thesubsequent litter size (Dewey et al., 1994; Vesseur et al.,1996; Koketsu and Dial, 1997). The effects commonlyincluded in statistical models for genetic evaluation oflitter size in swine are parity number, season of far-rowing, mating type (AI or natural mating), and num-ber of matings (Perez-Enciso and Gianola, 1992; Schaef-fer et al., 1993; Sullivan and Dean, 1994). It is proposedthat MMEW introduces additional effects of lactationlength and WCI that should be included in these mod-els. Therefore, the objective of this study was to esti-mate effects of lactation length and WCI on subsequentlitter size of the sow using a genetic evaluation model.

Genetic evaluation of litter size in swine 1797

Table 1. Summary statistics of the data for both breeds

Item Landrace Yorkshire

No. of records 7,125 2,999No. of animals 3,755 1,699No. of sows with records 2,847 1,234No. of sires 424 257No. of dams 1,463 664With records 1,233 470Without records 230 194

Mean litter size (SD) 10.55 (2.90) 10.80 (2.92)

The data for this analysis came from two Canadianpurebred herds, each with a mixture of MMEW andlater-weaned litters. This mixture rarely occurs in com-mercial practice but is useful for the purpose of thisstudy because it allows the effects of both treatmentsto be compared in sows within the same herd envi-ronment.

Materials and Methods

Data

Records came from purebred Landrace sows with lit-ters born between January 1989 and May 1997 andpurebred Yorkshire sows with litters born between Jan-uary 1990 and May 1997. All litters were from parities1 to 6. Data on each sow included birth date, age atfirst farrowing, and size and parity of the birth litter.Data on each litter included parity, age of the sow,farrowing date, type of mating (AI or natural), numberof services, previous lactation length, previous wean-ing-to-first-mating interval, previous WCI, and littersize. Litter size included both live and stillborn piglets.Only records with complete information on the birthlitter, farrowing date, parity number, age at farrowing,type of mating, number of services, previous lactationlength, previous weaning-to-first-mating interval, andWCI were used. Records with previous lactation lengthlonger than 35 d (less than 1% of all parity 2 to 6 litters)or previous WCI longer than 60 d (approximately 5%of all parity 2 to 6 litters) were deleted. As in Xue etal. (1998), only litters with at least four piglets wereincluded in analyses. A total of 7,125 litters from 2,847Landrace sows and 2,999 litters from 1,234 Yorkshiresows were used in the analyses. Pedigrees of sows weretraced back to five generations and used in the animalmodel. The oldest ancestors were born in 1979. A de-scription of the data for both breeds is given in Table 1.

Breeds were housed separately. In both breeds, ap-proximately 37, 25, 18, 11, 6, and 3% of litter recordswere from parities 1 to 6, respectively. Mean ages atfarrowing in parities 1 to 6 were approximately 362,510, 660, 807, 954, and 1,105 d with standard deviationsof 30 to 50 d. After 1992, two management practiceswere used in the herd with regard to weaning and re-breeding. In approximately half of the litters, the sowswere weaned between 7 and 14 d of lactation following

the method of MMEW described by Connor (1990).These sows were not mated until at least 18 d afterweaning (usually at their second estrus). In the remain-der of the litters, the sows were weaned after at least15 d of lactation and were mated on their first estrus.In this paper, the two management practices are re-ferred to as MMEW and “later weaning,” respectively.Before 1992, all litters used later weaning. Previouslactation length had a bimodal distribution; 33 and 25%of multiparous litters were born after MMEW in Lan-drace and Yorkshire, respectively. Mean weaning-to-first-mating intervals were 8 and 30 d for later-weanedsows and MMEW sows, respectively. In Landrace, 70%of later-weaned sows had a WCI of 6 d or less, and55% of MMEW sows had a WCI between 25 and 32 d.Corresponding proportions for Yorkshire were 77 and63%. In each breed, approximately 72% of matings weredone by AI and 28% by natural service. For both breeds,approximately 1, 58, and 41% of AI matings involvedone service, two services, and more than two services,respectively. For natural mating of Landrace sows, 43,15, and 42% involved one service, two services, andmore than two services, respectively. For Yorkshire,the corresponding proportions were 7, 36, and 57%.There were no matings involving both AI and naturalservice. Individual sows produced some litters byMMEW and some by later weaning. The allocation ofsows to weaning type at any given time was at random.

Statistical Analyses

The first mixed model fitted to the data was the fol-lowing:

y = Xb + Z1a + Z2p + Z3c + e [1]

where y is a vector of litter sizes, b is a vector of fixedeffects, a is a vector of random direct genetic effects ofanimals, p is a vector of uncorrelated random perma-nent environmental effects of sows, c is a vector of un-correlated random sow birth litter effects, e is a vectorof random residuals, and X, Z1, Z2, and Z3 are designmatrices relating records to the appropriate fixed orrandom effects. It is assumed that E(y) = Xb. The vari-ance-covariance structure of random effects is asfollows:

V

apce

=

Aσ2a 0 0 0

0 Iσ2p 0 0

0 0 Iσ2c 0

0 0 0 Iσ2e

where A is the numerator relationship matrix, I is anidentity matrix of appropriate order, and σ2

a, σ2p, σ2

c,and σ2

e are the genetic, permanent environment, birthlitter, and residual variances, respectively.

The two breeds were analyzed separately. Fixed ef-fects were contemporary group (sows were grouped by

Marois et al.1798

farrowing date with a 4-wk spread within each group,108 groups in Landrace, and 90 in Yorkshire), parity(six individual class effects from 1 to 6), mating type(AI or natural service), number of matings (three classeffects: 1, 2, or > 2), interaction of mating type andnumber of matings, age at farrowing fitted as a linearcovariate within each parity, age at first farrowing asa linear covariate, parity of the sow’s birth litter (sixindividual class effects from 1 to 6), size of the sow’sbirth litter (four discrete class effects, each having asimilar number of records: < 10, 10 to 11, 12 to 13, and> 13 pigs), previous lactation length fitted as a linearand a quadratic covariate, and the estrus number ofthe sow’s last mating (three discrete class effects codedas 1 if the sow conceived at her first estrus after weaningthe previous litter, 2 if she conceived at a later estrus,and 0 for first-parity litters). The estrus number ofMMEW sows (those weaned < 2 wk after farrowing)was not known with certainty because they were notclosely observed for signs of estrus until at least 18 dafter weaning. For these sows, the estrus number wascoded as 2 if the last mating was at least 18 d afterweaning; otherwise, it was coded as 1. Later-weanedsows were observed for estrus as soon as they wereweaned and mated as soon as they showed estrus. Forthese sows the estrus number was coded as 1 if theyconceived at the first mating and 2 otherwise. Bothfarms were on a weekly farrowing schedule. Using con-temporary groups covering 4 wk allowed grouping sowswith similar management and allowed the number ofsows per group to be large enough to accurately esti-mate group effects.

Variance components were estimated using the deriv-ative-free restricted maximum likelihood (DFREML)approach of Meyer (1988). A value of 10−8 for the vari-ance of (−2log L) was used as the iteration stoppingcriterion, where L is the likelihood. The iterations wererestarted using the previous estimates as starting val-ues, in order to check convergence to a global maximum.Asymptotic standard errors of the estimates were ob-tained from the inverse of the average information ma-trix. Estimates were also obtained for a model excludingrandom birth litter effects. A test statistic:

Λ = −2logL2

L1

was calculated, where L1 is the likelihood of the modelincluding birth litter effects and L2 is the likelihood ofthe model without those effects. The test statistic Λwascompared to the standard chi-square distribution withone degree of freedom to test significance of birth lit-ter effects.

The PEST software described by Groeneveld and Ko-vac (1990) was used to estimate the fixed effects ofthe model using variance components estimated withDFREML. An F-test based on an estimate of the errorvariance was performed to test the significance of the

fixed effects. For Model [1], that estimate is given bythe following:

σ2e = (y′ y − b′X′y − a′Z1′y − p′Z2′y − c′Z3′y)

n − r

where b is the generalized least squares solution for b,a, p, and c are BLUP of a, p, and c, respectively, n isthe number of observations, and r is the rank of matrixX. Nonsignificant fixed effects were sequentiallydropped from the model, in order of least significance,leaving only significant factors (P < .05).

Analyses of Weaning-to-Conception Interval Effects

To fit an effect as a covariate, one must make anassumption about the form (e.g., linear, quadratic, orcubic) of that effect. Litter records were put into classintervals of WCI with at least 100 records per class inorder to have a similar sampling variance associatedwith each class mean. Class means for litter size wereplotted against class means for WCI, and the plot isshown in Figure 1. Due to the curvilinear relationship oflitter size with WCI, it is unlikely that simple covariateswould fit the effect of WCI suitably. The following alter-native approaches were investigated using PEST.

Threshold Variable Approach. The effect of previousWCI was modeled using regression on threshold vari-ables (e.g., Dewey et al., 1994). For Yorkshire, ninethresholds (t1 = 5, t2 = 6, t3 = 7, t4 = 13, t5 = 25, t6 = 27,t7 = 29, t8 = 33, and t9 = 45 d) and nine correspondingthreshold variables (xj, j = 1, 2, ..., 9) were used. Formultiparous litters, xj = 1 if WCI ≥ tj, and xj = 0 other-wise. All parity-1 litters had xj = 0 (j = 1, 2, …, 9).Threshold values were chosen such that there were atleast 100 litter records between each consecutive pair.The model fitted included all the fixed and random ef-fects found significant in the previous analyses as wellas the threshold variables. The regression coefficientassociated with the threshold variable tk estimates themean difference between records having WCI ≥ tk−1 and< tk and records having WCI ≥ tk and < tk+1. For example,the regression coefficient associated with t1 estimatesthe mean difference between litters born after a WCIof 0 to 4 d and litters born after a 5-d WCI. For Landrace,the same procedure was repeated, but because of thelarger data set, 19 thresholds could be used insteadof nine. Estrus number was dropped from the modelbecause the effect was not significant after adding thethreshold variables. Litters between each consecutivepair of thresholds were grouped and the group meansfor observed and predicted litter size from that modelwere plotted against the group mean WCI. Predictedlitter size at tk ≤ WCI < tk+1 was calculated as follows:

LStk= 1

ni∑ni

i=1

contgri + 15 ∑

6

j=2

parityj + b lactat + ∑m≤k

m=1

cm,

where contgri are parityj are model solutions for contem-porary group i and for parity j, respectively, ni is the

Genetic evaluation of litter size in swine 1799

Figure 1. Relationship between mean litter size and mean weaning-to-conception interval for 2,018 Landrace sows(4,554 multiparous litter records) and 845 Yorkshire sows (1,841 multiparous litter records). Means are for classintervals of weaning-to-conception interval that have at least 100 observations per class. Classes are 0 to 4, 5, 6, 7, 8,9 to 12, 13 to 14, 15 to 19, 20 to 24, 25 to 27, 28, 29, 30, 31, 32, 33 to 34, 35 to 37, 38 to 44, 45 to 52, and 53 to 60 d forLandrace and 0 to 4, 5, 6, 7 to 12, 13 to 24, 25 to 26, 27 to 28, 29 to 32, 33 to 44, and 45 to 60 d for Yorkshire.

number of contemporary groups (108 for Landrace and90 for Yorkshire), lactat is the mean lactation length,and b and cm are the estimated regression coefficientsfor the previous lactation length and threshold variablem, respectively. Predicted litter size for WCI < 5 d was:

LS0 = 1ni

∑ni

i=1

contgri + 15 ∑

6

j=2

parityj + b lactat.

The threshold variable approach is more accurate thanthe approach of coding WCI as discrete class intervaleffects, because it makes use of the knowledge that WCIis a continuous variable.

Segmented Polynomial Approach. The thresholds usedabove were dropped from the model, and three newthresholds (w1, w2, w3) were used. Then, four new vari-ables describing WCI were defined as:

WCI1 =

WCI if WCI ≤ wi

w1 if WCI > w1;

WCI2 =

0 if WCI ≤ w1

WCI − W1 if WCI > w1 and WCI ≤ w2

w2 − w1 if WCI > w2; [2]

WCI3 =

0 if WCI ≤ w2

WCI − w2 if WCI > w2 and WCI ≤ w3

w3 − w2 if WCI > w3;

WCI4 =

0 if WCI ≤ w3

WCI − w3 if WCI > w3.

All parity-1 litters had WCI1 = WCI2 = WCI3 = WCI4= 0. The model included the linear and quadratic effectsof the four variables as well as all significant fixed andrandom effects of Model [1]. The objective was to obtainpredicted values of litter size that are a continuousfunction of previous WCI and that have a form consis-tent with the predicted values from the model based onthreshold variables. Models with two or four thresholdswere also investigated, but results were less successfuland are not presented here. Model predictions werestudied for many different values of w1, w2, and w3 inorder to obtain a function that was as smooth as possible(i.e., a function with minimum changes in the slope atthe thresholds), and at the same time consistent withthe solutions from the previous model. Variables thatwere not statistically significant were dropped only ifthat did not have a deleterious effect on the smoothnessof the predicted function. Records were grouped by WCI(with the same grouping as in the threshold variablemodel), and group mean observed and predicted littersize were plotted against group mean WCI. The sameprocedure was repeated after splitting the data into twosubsets based on type of weaning (i.e., later weaning orMMEW).

Alternative Model for Lactation Length Effects

An alternative model was studied in which the linearregression on lactation length (LACT) was replacedwith a regression on LNLACT = ln(LACT + 1), whereln is the natural logarithm function. The functionln(LACT + 1) was used instead of ln(LACT) because of

Marois et al.1800

the presence of records with LACT = 0. This type ofregression was used by Aumaıtre (1978) and Te Brake(1978) to model the effect of previous lactation lengthon litter size. Litter records were ranked and groupedby previous lactation length with at least 100 recordsper group. Group means for observed litter size andlitter size predicted from the linear regression and logregression models were plotted against the group meanlactation length. The model best describing the effectof previous lactation length on litter size was the onewith the smallest estimated error variance and withmean predicted litter sizes nearest to the observedmeans. The final model used to describe litter size forLandrace was as follows:

LSijk = CGi + PARj + b1jAFijk + b2LNLACTijk

+ d1WCI 12ijk + d2WCI 2ijk + d3WCI 22

ijk [3]+ d4WCI 3ijk + d5WCI 32

ijk + pk + ak + eijk

and, for Yorkshire:

LSijk = CGi + PARj + b1jAFijk + b2 LACTijk

+ d1WCI 12ijk + d2WCI 2ijk + d3WCI 22

ijk [4]+ d4WCI 3ijk + d5WCI 32

ijk + pk + ak + eijk

where CGi is the fixed effect of contemporary group i;PARj is the fixed effect of parity j; AFijk is the age atfarrowing of sow m at parity j; b1j is the partial regres-sion of litter size on age at farrowing in parity j;LNLACTijk is the natural logarithm of previous lacta-tion length; LACTijk is the previous lactation length; b2is the partial regression of litter size on natural loga-rithm of previous lactation length for Landrace or thepartial regression on previous lactation length for York-shire; WCI1ijk, WCI2ijk, and WCI3ijk are the segmentedpolynomial variables defined as in Eq. [2] with (w1, w2,

Table 2. Estimated variance components (± SE) and the log likelihood for models withand without a random birth litter effect for litter size in Landrace and Yorkshire sows.Estimates are genetic (σ2

a), permanent environment (σ2p), birth litter (σ2

c), residual (σ2e),

and phenotypic (σ2phen) variances, and heritability (h2), permanent environment (p2),

and birth litter (c2) variance expressed as percentage of the phenotypic variance

Landrace Yorkshire

Model with Model without Model with Model withoutItem birth litter birth litter birth litter birth litter

σ2a .858 ± .080 .887 ± .158 1.628 ± .176 1.685 ± .331

σ2p .535 ± .042 .631 ± .143 .366 ± .053 .490 ± .247

σ2c .158 ± .102 — .181 ± .176 —

σ2e 6.503 ± .138 6.536 ± .138 5.681 ± .191 5.693 ± .191

σ2phen 8.056 ± .147 8.053 ± .150 7.856 ± .223 7.867 ± .251

h2 .107 ± .010 .110 ± .019 .207 ± .022 .214 ± .038p2 .067 ± .006 .078 ± .018 .047 ± .007 .062 ± .032c2 .020 ± .012 — .023 ± .022 —log L −10,940 −10,942 −4,520 −4,521Λa 2.81, P = 0.94 1.15, P = .283

aMinus two times the logarithm of the likelihood ratio for testing H0:σ2c = 0.

w3) equal to (6, 13, 36) for Landrace and (5, 14, 39) forYorkshire, d1, d2, d3, d4, and d5 are the partial regres-sion coefficients on segmented polynomial variables; pk

is the random permanent environmental effect of sowk; ak is the random genetic effect of the sow k; and eijk

is the random residual effect. Least squares means forparities were calculated by adding the appropriate par-ity solution to the average solution for the levels of eachof the other effects in the model. For multiparous litters,calculations were carried out separately for MMEW andlater-weaned sows using average lactation length andWCI for each type of weaning. A previous lactation doesnot exist for parity-1 observations. Therefore, the leastsquares means for parity 1 were calculated as the sumof the average solution for contemporary group, theaverage age at first farrowing effect, and the parity1 solution.

Results and Discussion

In both breeds, random birth litter effects in Model[1] were not statistically significant based on the loglikelihood ratio test shown in Table 2. This result couldbe due to the fact that there were few littermate sowsin the data. Over 60% of the records were on sows withno littermate, and the average number of sows per litterwas only 1.5. Random birth litter effects were droppedfrom the model. Estimated heritability and repeatabil-ity for Landrace are 11 and 19%, respectively. Corres-ponding values for Yorkshire are 21 and 28%. Theseestimates are close to those found in the literature (Ha-ley et al., 1988; Schaeffer et al., 1993; Estany and Sore-nsen, 1994).

Among all fixed effects included in Model [1], onlycontemporary group, parity, estrus number, the lineareffect of previous lactation length, and the age of the

Genetic evaluation of litter size in swine 1801

Figure 2. Relationship of mean litter size and mean weaning-to-conception interval with mean previous lactationlength for 2,018 Landrace sows (2a; 4,554 multiparous litter records) and 845 Yorkshire sows (2b; 1,841 multiparouslitter records). Means are for class intervals of previous lactation length that have at least 100 observations per class.Classes are 0 to 6, 7, 8, 9, 10, 11 to 16, 17 to 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, and 28 to 35 d for Landrace and 0 to7, 8, 9 to 10, 11 to 14, 15 to 18, 19 to 20, 21, 22, 23, 24, 25 to 26, 27, 28, and 29 to 35 d for Yorkshire.

sow at farrowing were significant for both breeds (re-sults not shown). Litter size increased by .60 ± .09 and.24 ± .13 pigs/litter for every 10-d increase of the previ-ous lactation length for Landrace and Yorkshire, re-

spectively. Sows mated at the second estrus gave 1.05± .14 and .95 ± .23 extra piglets at their subsequentlitter compared to sows mated at the first estrus forLandrace and Yorkshire, respectively. Because mean

Marois et al.1802

lactation length for Landrace sows that conceived at thesecond estrus was 11.9 d shorter than mean lactationlength for Landrace sows that conceived at the firstestrus, the real increase in subsequent litter size forsows that conceived at the second estrus was only .34pigs/litter (+1.05 pigs/litter + [−11.9 d × .06 pigs/litter]).For Yorkshire, mean lactation length for sows that con-ceived at the second estrus was 13.5 d shorter thanmean lactation length for sows that conceived at thefirst estrus, resulting in a real increase of .62 pigs/litterin subsequent litter size for sows that conceived at thesecond estrus.

After adding the threshold variables describing WCIeffects to the model, the effect of estrus number wasmuch smaller and was not statistically significant ineither breed (P = .125 and .062 for Landrace and York-shire, respectively). This is due to the positive correla-tion between estrus number and WCI. After dropping

Table 3. Estimates of fixed effects for the model fitting weaning-to-conception intervalwith threshold variables in Landrace and Yorkshire sows

with mixed MMEW and later weaning

Landrace Yorkshire

Effect Solution SE P Solution SE P

Contemporary group (Not shown) (Not shown)

Parity1 .65 .31 .034 −1.22 .42 .0042 −.28 .21 .186 −1.11 .31 <.0013 .36 .21 .081 −.30 .31 .3434 .48 .21 .026 .08 .32 .8115 .10 .23 .647 .19 .34 .5716 0 — — 0 — —

Age at farrowing, dParity 1 .0017 .0021 .417 .0123 .0027 <.001Parity 2 .0087 .0024 <.001 .0055 .0033 .091Parity 3 −.0025 .0021 .239 .0018 .0035 .603Parity 4 −.0016 .0024 .493 −.0023 .0043 .590Parity 5 −.0081 .0028 .004 −.0004 .0052 .933Parity 6 −.0033 .0039 .403 .0058 .0063 .354

Lactation length, d .0470 .0090 <.001 .015 .012 .219WCI ≥ 5 d .18 .14 .203 −.34 .18 .057WCI ≥ 6 d −.32 .15 .030 .10 .26 .719WCI ≥ 7 d −.36 .22 .107 −.18 .35 .603WCI ≥ 8 d −.71 .32 .028 — — —WCI ≥ 9 d .26 .36 .475 — — —WCI ≥ 13 d .72 .38 .055 .68 .38 .071WCI ≥ 15 d .10 .39 .807 — — —WCI ≥ 20 d .67 .38 .077 — — —WCI ≥ 25 d −.35 .34 .301 .11 .36 .753WCI ≥ 27 d — — — .22 .32 .482WCI ≥ 28 d 1.02 .33 .002 — — —WCI ≥ 29 d −.39 .32 .227 .25 .34 .467WCI ≥ 30 d .27 .29 .351 — — —WCI ≥ 31 d −.22 .27 .406 — — —WCI ≥ 32 d −.08 .30 .791 — — —WCI ≥ 33 d −.03 .33 .924 .33 .38 .390WCI ≥ 35 d .11 .35 .764 — — —WCI ≥ 38 d −.58 .36 .115 — — —WCI ≥ 45 d .79 .35 .024 −.79 .38 .038WCI ≥ 53 d −.14 .33 .663 — — —

σ2e = 6.48, 6,986 df σ2

e = 5.67, 2,888 df

estrus number from the model, the effect of previouslactation length for Yorkshire became much smallerand was not statistically significant (P = .219). This isbecause in the data conception at the second estrusgave larger litter size than conception at the first estrus,but conception at the second estrus was associated withshorter lactation length than conception at the firstestrus. Shorter lactations gave smaller litter size.Hence, when the nonsignificant estrus number effectwas removed from the model, the lactation length effectwas unadjusted for estrus number and was smallerthan it was previously. Litter records were put intoclass intervals of previous lactation length with at least100 records per class in order to have similar samplingvariance associated with all class means. Class meansfor litter size and for WCI were plotted against classmeans for previous lactation length, and the plots areshown in Figure 2. For Yorkshire, the trend in litter

Genetic evaluation of litter size in swine 1803

Figure 3. Predicted effect of weaning-to-conception interval on litter size using five segmented polynomials forLandrace and Yorkshire sows. Curves presented for Landrace (3a) were fitted across the segments 1) { 0 to 6, 7 to 14,15 to 30, 31 to 60} , 2) { 0 to 6, 7 to 12, 13 to 30, 31 to 60} , 3) { 0 to 5, 6 to 14, 15 to 30, 31 to 60} , 4) { 0 to 6, 7 to 17, 18to 36, 37 to 60} , and 5) { 0 to 6, 7 to 13, 14 to 36, 37 to 60} . Curves presented for Yorkshire (3b) were fitted across thesegments 1) { 0 to 6, 7 to 17, 18 to 32, 33 to 57} , 2) { 0 to 6, 7 to 14, 15 to 32, 33 to 57} , 3) { 0 to 5, 6 to 14, 15 to 32, 33to 57} , 4) { 0 to 5, 6 to 14, 15 to 39, 40 to 57} , and 5) { 0 to 5, 6 to 14, 15 to 44, 45 to 57} . Different starting values(—1, −.5, 0, .5, and 1 piglet at WCI = 0) were used to separate the curves to allow comparison of their shapes.

Marois et al.1804

size follows the trend of WCI, except for lactationslonger than 25 d. For Landrace, however, this is notthe case. For Landrace, 93 and 7% of later-weaned sowsconceived at first and second estrus, respectively. ForMMEW sows, 10 and 90% conceived at first and second

Figure 4. Mean observed litter size, mean predicted litter size from the threshold variable model, and mean predictedlitter size from the segmented polynomial model, plotted against weaning-to-conception interval. Means are for classintervals of weaning-to-conception interval that have at least 100 observations per class. Classes are 0 to 4, 5, 6, 7, 8,9 to 12, 13 to 14, 15 to 19, 20 to 24, 25 to 27, 28, 29, 30, 31, 32, 33 to 34, 35 to 37, 38 to 44, 45 to 52, and 53 to 60 d forLandrace (4a) and 0 to 4, 5, 6, 7 to 12, 13 to 24, 25 to 26, 27 to 28, 29 to 32, 33 to 44, and 45 to 60 d for Yorkshire (4b).

estrus, respectively. The corresponding proportions forYorkshire are 96 and 4% for later-weaned sows and 2and 98% for MMEW sows. Age at farrowing effects alsotended to be smaller for both breeds when WCI effectswere included in the model, particularly for parity 2

Genetic evaluation of litter size in swine 1805

Table 4. Estimates of fixed effects for models with segmented polynomials inmultiparous Landrace and Yorkshire sows with mixed

MMEW and later weaning

Landrace Yorkshire

Effect Solution SE P Solution SE P

Contemporary group (Not shown) (Not shown)

Parity1 1.03 .45 .021 −1.67 .56 .0032 −0.25 .21 .233 −1.08 .31 .0013 .39 .21 .063 −.28 .31 .3714 .50 .21 .019 .10 .32 .7405 .12 .23 .603 .23 .34 .5026 0 —

Age at farrowing, dParity 1 .0018 .0021 .383 .0122 .0027 <.001Parity 2 .0094 .0024 <.001 .0054 .0033 .097Parity 3 −.0024 .0021 .252 .0014 .0035 .699Parity 4 −.0016 .0024 .507 −.0024 .0043 .572Parity 5 −.0083 .0028 .003 −.0007 .0052 .888Parity 6 −.0033 .0039 .396 .0058 .0063 .360

Lactation length, d — — — .016 .012 .186

ln(lactation length + 1) .53 .11 <.001 — — —WCI12 −.0081 .0081 .319 −.033 .018 .073WCI2 −.62 .13 <.001 −.03 .15 .823WCI22 .079 .020 <.001 .007 .019 .699WCI3 .124 .036 .001 .063 .066 .343WCI32 −.0030 .0014 .027 −.0012 .0021 .554

σ2e = 6.48, 7,000 df σ2

e = 5.67, 2,892 df

litters. This is because age at farrowing was moderatelypositively correlated to previous WCI (r = .36 and .27for Landrace and Yorkshire, respectively) and both ef-fects are positively correlated to litter size. The esti-mated fixed effects for the model fitting WCI effectswith thresholds are shown in Table 3.

Figure 3 shows the predicted values from some mod-els fitting WCI effects as segmented polynomials. Thebest curve was obtained with the set of intervals 0 to6, 7 to 13, 14 to 36, 37 to 60} for Landrace and with { 0to 5, 6 to 14, 15 to 39, 40 to 57} for Yorkshire. Theseare identified as curve 5 in Figure 3a and as curve 4 inFigure 3b. Figure 4 shows the mean litter sizes observedand predicted from the threshold variable approach andfrom the segmented polynomial approach plottedagainst WCI. Both predicted curves show similar trendswith WCI, but the segmented polynomial approachgives a smoother curve of predicted values. Both ap-proaches show good agreement with the observed curve;the closest agreement is at 0 to 7 d and 27 to 35 d WCIbecause most of the data were within those intervals.When these plots were repeated separating litters bornafter MMEW from those born after a later weaning,the plots were similar to the original plots, withoutseparating the data, for each of the two subsets of thedata (results not shown). Estimated fixed effects for thecurve 5 in Figure 3a for Landrace and for the curve 4in Figure 3b for Yorkshire are given in Table 4. Themodel for these curves was fitted with a linear regres-sion on the natural logarithm of lactation length for

Landrace and with a linear regression on lactationlength for Yorkshire. For Yorkshire, none of the polyno-mial regression coefficients was significantly differentfrom zero. An F-ratio test comparing the residual sumsof squares of the model fitting WCI with five polynomialvariables (the model of Table 4) to the residual sumsof squares of the model fitting no effect of WCI indicateda significant effect of WCI on multiparous litter size (F= 4.77 with 5 and 2,892 df, P < .001). The small numberof litters could explain the nonsignificance of the polyno-mial regression coefficients. The mean observed andpredicted litter sizes are plotted against previous lacta-tion length in Figure 5. For both breeds, predicted val-ues from the linear regression and log regression mod-els were similar, except at lactation lengths below 7 dfor Landrace, for which the log regression predicted alower mean litter size, which was closer to the observedmean. Because the log regression better fits the data forshort lactations for Landrace and the estimated errorvariance is smaller with the log regression on previouslactation length (6.48 vs 6.49 for the model with thelinear regression on previous lactation length), themodel of Table 4 was chosen as the final model to de-scribe the litter sizes for that breed. For Yorkshire,neither the linear nor the log regression on previouslactation length was significant, but the model fittinga linear regression had a slightly smaller estimate oferror variance (5.67 vs 5.68 for the model with the logregression on previous lactation length) and was themodel chosen as the final model for Yorkshire.

Marois et al.1806

Figure 5. Mean observed litter size and mean litter size predicted using a model with a linear effect of lactationlength and using a model with a logarithmic effect of lactation length, plotted against mean previous lactation length.The data in 5a are for 2,018 Landrace sows with 4,554 multiparous litter records, and the data in 5b are for 845Yorkshire sows with 1,841 multiparous litter records. Means are for class intervals of previous lactation length thathave at least 100 observations per class. Classes are 0 to 6, 7, 8, 9, 10, 11 to 16, 17 to 18, 19, 20, 21, 22, 23, 24, 25, 26,27, and 28 to 35 d for Landrace and 0 to 7, 8, 9 to 10, 11 to 14, 15 to 18, 19 to 20, 21, 22, 23, 24, 25 to 26, 27, 28, and29 to 35 d for Yorkshire.

Genetic evaluation of litter size in swine 1807

Figure 6. Mean residuals from the model fitting an effect of weaning-to-conception interval using five segmentedpolynomials and mean residuals from the model fitting an effect of estrus number, plotted against mean weaning-to-conception interval. Means are for class intervals of weaning-to-conception interval that have at least 100 observationsper class. Classes are 0 to 4, 5, 6, 7, 8, 9 to 12, 13 to 14, 15 to 19, 20 to 24, 25 to 27, 28, 29, 30, 31, 32, 33 to 34, 35 to37, 38 to 44, 45 to 52, and 53 to 60 d for Landrace (6a) and 0 to 4, 5, 6, 7 to 12, 13 to 24, 25 to 26, 27 to 28, 29 to 32,33 to 44, and 45 to 60 d for Yorkshire (6b).

The final models are described by Eq. [3] and [4] forLandrace and Yorkshire, respectively. A model fittingonly the estrus number without any polynomial orthreshold effects of WCI was sub-optimal, as shown by

Figure 6, which plots the mean residuals from the modelfitting the effect of estrus number and from the modelfitting the effect of WCI using segmented polynomials,against mean WCI. The model using the estrus number

Marois et al.1808

Figure 7. Estimated effects of previous lactation length on litter size for 2,018 Landrace sows (4,554 multiparouslitter records) and 845 Yorkshire sows (1,841 multiparous litter records).

does not differentiate between first-estrus sows thatconceived litters within 6 d of weaning and first-estrussows that conceived 6 to 12 d after weaning. This iswhy there are very large negative residuals for WCIbetween 6 to 12 d in Figure 6, particularly for Landracesows. The model fitting WCI effects also had smallerestimated error variance than the model fitting the es-trus number effect (6.48 with 7,000 df compared to 6.52with 7,004 df for Landrace and 5.67 with 2,892 df com-pared to 5.68 with 2,896 df for Yorkshire). Finally, WCIis much easier to record than estrus number because

Figure 8. Effects of weaning-to-conception interval on litter size estimated using segmented polynomials for 2,018Landrace sows (4,554 multiparous litter records) and 845 Yorkshire sows (1,841 multiparous litter records).

only the mating dates have to be known. Knowing allestrus dates precisely may allow the fitting of a bettermodel for the genetic evaluation of litter size. However,because early weaning introduces variations in the abil-ity of sows to express estrus and to cycle again (Britt,1995), it could be difficult to record first estrus preciselyin routine practice for MMEW sows. Weaning-to-con-ception interval is an important trait with a geneticbasis (e.g., Ten Napel et al., 1995a). In adjusting littersize for previous WCI, we are assuming that the effect ismainly environmental. The genetic correlation between

Genetic evaluation of litter size in swine 1809

WCI and litter size is reported to be small (Adamec andJohnson, 1997; Ten Napel et al., 1998). If WCI has animportant genetic correlation with litter size, then thecorrect procedure would be to use a multivariate modelto produce EBV for both litter size and WCI. The meth-ods used to estimate the WCI effects in this studycaused the models to be more complicated than thoseused in typical routine evaluations of litter size. How-ever, after the WCI effects have been estimated, theycan be used to preadjust the data to a standard WCIof 5 d, and the preadjusted data can then be used in aroutine genetic evaluation model that does not includeWCI effects. The more complicated models may be usedonly on occasions to check that the preadjustments arecorrect. This is the approach being adopted by the Cana-dian Centre for Swine Improvement in genetic evalua-tions of purebred Canadian swine. Analyses omittedlitters with fewer than four piglets born. This approachwas also used by Xue et al. (1998). The omission proba-bly had little effect on the results, because fewer than2% of all litters were omitted, and the omitted litterswere evenly distributed across levels of the fixed effects.

From the final model, least squares mean litter sizesin Landrace were 10.06, 10.27, 10.91, 11.02, 10.64, and10.52 pigs for parities 1 to 6, respectively. In Yorkshire,they were 10.16, 10.67, 11.47, 11.85, 11.97, and 11.75pigs for parities 1 to 6, respectively. Parity-1 litter sizeincreased significantly by .12 pigs for every 10-d in-crease in age at farrowing in Yorkshire. In Landrace,there was no significant effect of age at farrowing forparity-1 litters. Parity-2 litter size increased by .09 and.05 pigs for every 10-d increase in age at farrowing forLandrace and Yorkshire, respectively. In Yorkshire, theincrease is not significant due to the smaller amountof data for that breed. Southwood and Kennedy (1991)and Culbertson et al. (1997) have found similar effectsof age at farrowing for parities 1 and 2.

Figure 7 shows the estimated effect of previous lacta-tion length on litter size using the final models. ForLandrace, the log regression best described the effectof previous lactation length on litter size as found byCole et al. (1975), Aumaıtre (1978), and Te Brake

Table 5. Predicted effects of different lactation lengths and weaning-to-conceptionintervals on subsequent litter size in multiparous Landrace and Yorkshire sows.

Effects are expressed relative to a lactation length of 21 dand a weaning-to-conception interval of 5 d

Weaning-to-conception interval, d

Landrace Yorkshire

Lactation length, d 2 5 15 25 30 2 5 15 25 30

5 −.51 −.68 −1.02 −.21 −.02 +.43 −.25 +.09 +.58 +.738 −.30 −.47 −.81 +.01 +.19 +.48 −.21 +.14 +.62 +.77

10 −.19 −.36 −.70 +.11 +.30 +.51 −.17 +.17 +.66 +.8115 +.00 −.17 −.51 +.31 +.49 +.59 −.10 +.25 +.73 +.8821 +.17 0 −.34 +.48 +.66 +.69 0 +.35 +.83 +.9825 +.26 +.09 −.25 +.56 +.75 +.75 +.06 +.41 +.89 +1.04

(1978). For Yorkshire, the effect of previous lactationlength was best described by a linear regression (.02pigs/d) as found by Xue et al. (1993) and Mabry et al.(1996), who obtained estimates of .04 and .06 pigs/d,respectively. Aherne and Kirkwood (1998) reported asignificant increase in litter size between 12 and 18 dof lactation length but no further increase for lactationlengths longer than 18 d. From Figure 7, it seems thata linear regression on previous lactation length couldpredict litter size well for Landrace, except when lacta-tion length is less than 7 d.

Figure 8 shows the estimated effect of WCI on littersize. The curves could be explained by the followinghypothesis. Sows with the shortest WCI are those thatshow estrus most quickly after weaning because theyare in a good nutritional and physiological state (Reeseet al., 1982; Mullan and Williams, 1989; Ten Napel etal., 1995b). Because of this good state, they have a largerlitter size than sows conceiving later (due to a largernumber of embryos produced and[or] to a higher embry-onic survival). At still longer WCI, the larger litter sizescould be explained by conception at the second estrus,which is generally recognized to give larger litter sizesthan conception at the first estrus (Clowes et al., 1994).Delaying breeding beyond the second estrus does notimprove litter size, as shown by the flattening out overthe last part of the curve. Changes in litter size withWCI were more important for Landrace than for York-shire. Dewey et al. (1994) found a similar U-shapedcurve with litter sizes at a minimum for sows conceivingat 7 to 10 d after weaning. Vesseur et al. (1994) foundthat litter sizes decreased as WCI increased from 0 to8 to 12 d and then increased with further increasesin WCI.

Table 5 shows the predicted effect of different lacta-tion lengths and WCI on the subsequent litter size.Numbers in the table are expressed as deviations fromthe predicted litter size for a lactation length of 21 dand a WCI of 5 d. For a given WCI, Table 5 indicatesa decrease of .47 pigs/litter for a Landrace sow lactatingfor 8 d compared to another one lactating for 21 d. Thecorresponding decrease for Yorkshire is .21 pigs/litter.

Marois et al.1810

In the data, the average WCI was 5 d for later-weanedsows and 30 d for MMEW sows. Table 5 shows that aLandrace sow weaned at 8 d with a WCI of 30 d produces.19 more pigs in the subsequent farrowing than a Lan-drace sow weaned at 21 d with a WCI of 5 d. For York-shire, the corresponding value is .77 extra pigs. Early-weaned sows gave larger litter sizes in this data becausethe negative effect of a shorter lactation was offset bythe positive effect of a longer WCI. However, MMEWsows spent an average of 38 d nonpregnant per parity,compared to only 26 d for later-weaned sows.

Implications

The analysis showed important effects of previouslactation length of up to .8 pigs and effects of weaning-to-conception interval of up to one pig. Effects of previ-ous lactation length and weaning-to-conception inter-val on litter size were more important in Landrace thanin Yorkshire. In order to avoid bias, both effects shouldbe included in models for genetic evaluation of littersize. The previous weaning-to-conception effect is curvi-linear with lowest litter size for previous weaning-to-conception interval of 7 to 10 d. This could be becausethese litters arise from late estrus in sows in a poorerphysiological state. The curvilinear shape of the wean-ing-to-conception interval effect cannot be accomodatedby linear or quadratic regressions but can be fitted us-ing segmented polynomials. Estimated weaning-to-con-ception interval effects can also be used to preadjustthe data to a standard weaning-to-conception intervalto keep the routine genetic evaluation model simpler.

Literature Cited

Adamec, V., and R. K. Johnson. 1997. Genetic analysis of rebreedingintervals, litter traits, and production traits in sows of the Na-tional Czech nucleus. Livest. Prod. Sci. 48:13–22.

Aherne, F., and R. Kirkwood. 1998. Factors affecting litter size. In:Revealing Research for the Alberta Pork Research Center. Al-berta Pork Research Centre, Edmonton, Alberta, Canada.

Aumaıtre, A. 1978. Les consequences zootechniques du sevrage pre-coce du porcelet. J. Rech. Porcine Fr. 251–274.

Britt, J. H. 1995. Pitfalls of early weaning, why it may not work onyour farm. In: Proc. North Carolina Healthy Hogs Seminar,Greenville, NC. pp 34–40.

Clowes, E. J., F. X. Aherne, and G. R. Foxcroft. 1994. Effect of delayedbreeding on the endocrinology and fecundity of sows. J. Anim.Sci. 72:283–291.

Cole, D. J. A., M. A. Varley, and P. E. Hughes. 1975. Studies in sowreproduction. 2. The effect of lactation length on the subsequentreproductive performance of the sow. Anim. Prod. 2:401–406.

Connor, J. F. 1990. Modified medicated early weaning. Proc. Am.Assoc. Swine Pract. pp 333–335.

Culbertson, M. S., J. W. Mabry, J. K. Bertrand, and A. H. Nelson.1997. Breed specific adjustment factors for reproductive traitsin Duroc, Hampshire, Landrace, and Yorkshire swine. J. Anim.Sci. 75:2362–2367.

Dewey, C. E., S. W. Martin, R. M. Friendship, and M. R. Wilson.1994. The effects on litter size of previous lactation length and

previous weaning-to-conception interval in Ontario swine. Prev.Vet. Med. 18:213–223.

Estany, J., and D. Sorensen. 1994. Comparison of alternative modelsfor selection for litter size in Danish Landrace and Yorkshirebreeds. Proc. 5th World Congr. Genet. Appl. Livest. Prod.17:323–326.

Groeneveld, E., and Kovac. M. 1990. A generalized computing proce-dure for setting up and solving mixed linear models. J. DairySci. 73:513–531.

Haley, C. S., E. Avalos, and C. Smith. 1988. Selection for litter sizein the pig. Anim. Breed. Abstr. 56:317–332.

Koketsu, Y., and G. D. Dial. 1997. Quantitative relationships betweenreproductive performance in sows and its risk factors. Pig NewsInfo. 18:47–51.

Mabry, J. W., M. S. Culbertson, and D. Reeves. 1996. Effects oflactation length on weaning-to-first service interval, first-servicefarrowing rate, and subsequent litter size. Swine Health Prod.4:185–188.

Meyer, K. 1988. DFREML—a set of programs to estimate variancecomponents under an Individual Animal Model. J. Dairy Sci.71(Suppl. 2):33–34 (Abstr.).

Mullan, B. P., and I. H. Williams. 1989. The effect of body reservesat farrowing on the reproductive performance of first-litter sows.Anim. Prod. 48:449–457.

Perez-Enciso, M., and D. Gianola. 1992. Estimates of genetic parame-ters for litter size in six strains of Iberian pigs. Livest. Prod.Sci. 32:283–293.

Reese, D. E., B. D. Moser, E. R. Peo, Jr., A. J. Lewis, D. R. Zimmerman,J. E. Kinder, and W. W. Stroup. 1982. Influence of energy intakeduring lactation on the interval from weaning to first estrus insows. J. Anim. Sci. 55:590–598.

Schaeffer, L. R., B. W. Kennedy, and R. A. Kemp. 1993. Within-herd evaluation of sow reproductive traits. Can. J. Anim. Sci.73:223–230.

Southwood, O. I., and B. W. Kennedy. 1991. Genetic, and environmen-tal trends for litter size in swine. J. Anim. Sci. 69:3177–3182.

Sullivan, B. P., and R. Dean. 1994. National genetic evaluations forswine in Canada. Proc. 5th World Congr. Genet. Appl. Livest.Prod. 17:382–385.

Te Brake, J. H. A. 1978. An assessment of the most profitable lengthof lactation for producing piglets of 20 kg body weight. Livest.Prod. Sci. 5:81–94.

Ten Napel, J., A. G. de Vries, G. A. J. Buiting, P. Luiting, J. W. M.Merks, and E. W. Brascamp. 1995a. Genetics of the Intervalfrom weaning to estrus in first-litter sows: distribution of data,direct response of selection, and heritability. J. Anim. Sci.73:2193–2203.

Ten Napel, J., B. Kemp, P. Luiting, and A. G. de Vries. 1995b. Abiological approach to examine genetic variation in weaning-to-oestrus interval in first-litter sows. Livest. Prod. Sci. 41:81–93.

Ten Napel, J., T. H. E. Meuwissen, R. K. Johnson, and E. W. Bras-camp. 1998. Genetics of the interval from weaning to estrus infirst-litter sows: correlated responses. J. Anim. Sci. 76:937–947.

Vesseur, P. C., B. Kemp, and L. R. den Hartog. 1994. The effect ofthe weaning-to-estrus interval on litter size, live born piglets,and farrowing rate in sows. J. Anim. Physiol. Anim. Nutr.71:30–38.

Vesseur, P. C., B. Kemp, and L. R. den Hartog. 1996. Reproductiveperformance of the primiparous sows—the key to improve farmproduction. Pig News Info. 17:35–40.

Xue, J. L., G. D. Dial, W. E. Marsh, P. R. Davies, and H. W. Momont.1993. Influence of lactation length on sow productivity. Livest.Prod. Sci. 34:253–265.

Xue, J., G. D. Dial, T. Trigg, P. Davies, and V. L. King. 1998. Influenceof mating frequency on sow reproductive performance. J. Anim.Sci. 76:2962–2966.