www.elsevier.com / locate / livprodsci
Variance components of fertility in Spanish Landrace pigs
*
L. Varona , J.L. Noguera
´Area de Produccio Animal, Centre UdL-IRTA, C /Rovira Roure 177, 25198 Lleida, Spain
Received 31 December 1999; received in revised form 23 May 2000; accepted 23 May 2000
Abstract
Fertility is a discrete trait with two categories (1, successful mating, 0, unsuccessful mating). A Bayesian analysis with a binary threshold animal model has been performed with 18 695 AI mating records from 1987 to 1997, concerning 4085 sows and 187 boars. The pedigree included all individuals genetically linked with data. The binary response was modeled under a probit approach. The model for liability includes paternal and maternal genetic and permanent environmental effects, 54 herd-year–season and seven order of parity effects. Posterior mean (and standard deviation) for paternal heritability was 0.028 (0.014), for maternal heritability 0.038 (0.014), and 0.028 (0.009) and 0.072 (0.017) for ratios of paternal and maternal permanent environmental effects. Posterior mean (and standard deviation) of genetic correlation between paternal and maternal genetic effects was 20.513 (0.264). Differences between parities suggest that fertility is bigger in second parity than in the first one, and decrease in subsequent parities. 2001 Elsevier Science B.V. All rights reserved.
Keywords: Fertility; Threshold model; Bayesian analysis; Pigs
1. Introduction tion in sows has been systematically carried out by culling (Dagorn and Aumaitre, 1979; Dijkhuizen et In pig production, success in conception is a al., 1989).
crucial economic task. Delays in pregnancy or failure Evidence of genetic variation in conception rate to conceive lead to a substantial loss in efficiency of has been detected in cattle (Saloniemi et al., 1986; production (Legault, 1978; Jalvingh et al., 1992). In Mantysaari et al., 1993). However, Elbers et al. breeding schemes, for a long time, selection efforts (1996) found a very small risk of recurrence of have been concentrated on growth, feed conversion failure of conception along different parities in the ratio and carcass quality (Haley et al., 1988). More same sow, suggesting a small genetic component in recently, selection has also been focused on prolifica- female fertility.
cy (Bampton, 1992; Ducos et al., 1992; Estany et al., The conception rate depends on a great number of 1995). Success in conception, as a measure of factors. Apart from female fertility, it also depends fertility, has not been included as an objective in on male fertility. Boar selection according to their current selection programs. However, indirect selec- ability to fertilize sows in natural or artificial insemi-nation may have an economic interest. Moreover, genetic evaluation of boars in traits based on female
*Corresponding author. Tel.:134-973-702-637; fax:
134-973-fertility can provide a useful tool to select progeny.
238-101.
E-mail address: [email protected] (L. Varona). For that reason, knowledge of the genetic
ship between male and female fertility may be of with data. In all cases the reproduction is carried out substantial interest for breeding programs (Land, using double artificial insemination, always under the
1978). same technical conditions. Estrus detection was
Nevertheless, fertility is a complex trait, its ex- performed twice daily by boar presence. pression is discrete (1, successful mating, 0,
unsuc-cessful mating). Following Thompson (1979) and 2.2. The model Gianola (1982), methods for continuous data are not
appropriate for discrete data. In recent years, Markov The assumed model for the underlying distribution Chain Monte Carlo methods (Albert and Chib, 1993; of the liability (I ) was:f
Sorensen et al., 1995; Moreno et al., 1997) allow the
If5Xb1Z u1 m1Z u2 p1Z p3 m1Z p4 p1e
analysis of categorical traits with models that con-sider its particular structure of probability.
Further-where b are the systematic effects (54 herd-year– more, models with more than one genetic effect have
season and seven order of parity effects); um and up been also developed (Varona et al., 1999). In this
are the vectors of maternal and paternal genetic case, fertility is suspected of having genetic and
effects; pm and p are the vectors of maternal andp permanent boar and sow effects.
paternal permanent effects; e is the residual vector, The objective of this study is to determine the
and X, Z , Z , Z and Z are the incidence matrices1 2 3 4 sources of environmental and genetic variability of
that link liability with systematic, genetic and perma-fertility, measured as success of conception, allowing
nent environmental effects. its consideration for inclusion in selection programs.
Response in fertility is modeled with a probit approach: 18 695 artificial insemination mating records, and
15 191 successful ( y51) and 3504 unsuccessful
2
f Iub, u , u , p , p ,s 5N Xb1Z u 1Z u
( y50), from 1987 to 1997, concerning 4085 sows
s
f m p m p ed
s
1 m 2 p and 187 boars, from two purebreed Landrace herds 21Z p3 m1Z p , I4 p se
d
were used. An artificial insemination was determined
as a success when the sow got pregnant (farrowing where t is the threshold that defines the categories of or abort). A more detailed description of data for response, n is the total number of data, b are the different orders of parity is presented in Table 1. The systematic effects (54 herd-year–season and seven pedigree included 5067 individuals genetically linked order of parity effects); u and u are the vectors of
m p
maternal and paternal genetic effects; pm and p arep the vectors of maternal and paternal permanent
Table 1 2
effects;s is the residual variance (set to 1), and X,
Summary of data e
Z , Z , Z and Z are the incidence matrices that1 2 3 4
Parity Records Successful %
link liability with systematic, genetic and permanent
1 4585 3677 80.02 environmental effects.
2 3547 3030 85.42
The following prior distributions were assumed:
and tery and Lewis (1992). All iterations of the analysis were used to compute posterior means and standard
2 2
f p
s
puspd
5N 0, Is
spd
deviations so that all the available information from the output of the Gibbs sampler could be considered. where A is the numerator relationship matrix and G2 2 Densities of marginal posterior distributions were is the matrix of (co)variance components,smandsp
calculated using the algorithms of Silverman (1986). are the permanent environmental variances for sows
and boars, respectively.
2 2
Moreover, prior distributions of G, sm and sp
3. Results and discussion
where the following vague proper distributions
f(G)5IW(SG,5) 3.1. Analysis of convergence of the Gibbs sampler
2 22
f(sm)5x ssm,5d
2 22 Convergence and effective sample size results for
f
s d
sp 5x ssp,5dheritabilities, ratios of permanent environmental where sm50.1, sp50.1 and effects and genetic correlation between male and female fertility are presented in Table 2. The number 0.1 0
SG5
F
G
of iterations to discard ranged from 2412 to 11 484 0 0.1and the effective sample size (EFS) ranged from 52.8 to 357.4.
2.3. The Gibbs sampler
The number of iterations discarded in this analysis (50 000) were substantially greater than every value Bayesian analysis of the univariate and bivariate
proposed by the algorithm of Raftery and Lewis models were carried out with the Gibbs sampler
(1992). The effective sample size computed by the algorithm (Geman and Geman, 1984; Gelfand and
algorithm proposed by Geyer (1992) was relatively Smith, 1990; Tanner, 1993) to obtain autocorrelated
high, with the exception of genetic correlation be-samples from the joint posterior density and
sub-tween maternal and paternal genetic effects. How-sequently from the marginal posterior densities of all
ever, summaries of marginal posterior distributions the unknowns in the model. The Gibbs sampler
can be estimated with a low Monte Carlo error. consists of an iterative sampling scheme of updated
full posterior conditional distributions. The full
pos-3.2. Heritabilities and correlations terior conditional distributions for the locations
parameters (herd-year–season; parity effects;
pater-A summary of marginal posterior distributions for nal and maternal breeding values and permanent
maternal and paternal heritabilities, ratios of perma-environmental effects) were univariate normal
dis-nent environmental effects and genetic correlation tributions, the posterior distribution of the genetic
between paternal and maternal effects is presented in (co)variance component is an inverted Wishart, and
Table 3. As can be observed in this table, posterior the posterior distributions of paternal and maternal
means of paternal heritability and ratio of environ-permanent environmental variances were inverted
mental permanent variation are low (0.028 and chi-squares. Moreover, the posterior conditional
dis-0.028). Posterior mean of maternal heritability was tributions of augmented underlying variables are
censored normal as described by Sorensen et al.
Table 2
(1995). A more detailed description of the
distribu-Analysis of convergence (burn in) and effective sample size (EFS)
tions involved can also be found in previous studies
Parameter Burn in EFS
(Wang et al., 1993, 1994; Sorensen et al., 1995).
2
The Gibbs sampler analysis was carried out h 8426 139.7
p 2
through a simple chain of 700 000 iterations, after hm 11 187 163.4
2
p 2412 289.8
discarding the first 50 000. The analysis of conver- p 2
pm 4920 357.4
gence and the calculation of effective sample size
rg 11 484 52.8
Raf-Table 3
Summary of marginal posterior distributions of heritabilities, percentage of permanent environmental variation and genetic correlation [mean, mode, posterior standard deviation (PSD), and percentiles at 1, 5, 50, 95 and 99%]
Mean Mode PSD 1% 5% 50% 95% 99%
2
hp 0.028 0.025 0.014 0.005 0.007 0.025 0.053 0.069
2
hm 0.038 0.036 0.014 0.007 0.016 0.036 0.064 0.074
2
pp 0.028 0.026 0.009 0.010 0.013 0.026 0.043 0.053
2
pm 0.072 0.071 0.017 0.026 0.050 0.071 0.099 0.112
rg 20.513 20.560 0.264 20.917 20.867 20.560 20.010 0.261
Table 4
also low (0.038), but the ratio of maternal permanent
Summary of marginal posterior distributions of differences with
effects was slightly higher (0.072). These results
first parity
show that 17% of variation of liability assuming a
Parity Mean Mode Median PSD
probit threshold model are determined by paternal
and maternal sources of variation. Another 83% of 2 0.193 0.196 0.192 0.037
3 0.083 0.080 0.082 0.041
variation in the underlying variable can be attributed
4 0.107 0.108 0.107 0.045
to unknown sources of variation. As previously
5 0.049 0.048 0.048 0.049
shown by Elbers et al. (1996), the female-based 6 20.009 20.009 20.010 0.054 source of variation was small, and most of the causes .6 20.033 20.035 20.033 0.048
for failure in AI can be attributed to external factor not based on the sow. These results are also in
agreement with the ones obtained by Boichard and Moreover, a non-presented simulation study confirms Manfredi (1994) in conception rate of dairy cattle. A the ability of the statistical procedure to recover the non-reported analysis of sensibility show minor simulated parameters. Further research will be neces-changes when different priors were assumed, as sary to investigate the source of the strong estimated expected from the size of the database and the low genetic correlation.
amount of information provided by the selected Results for order of parity in the underlying scale
priors. are presented in Table 4. Differences between
A high negative genetic correlation between ma- parities suggest that fertility is greater in second ternal and paternal genetic effects is obtained (poste- parity than the first one, and decrease in subsequent rior mean of 20.513) with 95.24% of posterior ones. These results are in complete agreement with probability of genetic correlation smaller than 0. This the direct observation of data (Table 1). Aging result is surprising, because several studies in dairy effects of the sire were not considered, because sires cattle suggest very low genetic correlation (Hansen, was kept in the insemination center for only about 8 1979; Boichard and Manfredi, 1994). As pointed out to 10 months.
by Boichard and Manfredi (1994), the estimate of As a major consequence, the low heritability this genetic correlation is very sensitive to extreme implies that efficiency of selection for these traits males. It must be noticed that, due to semen quality will be small. Genetic correlation with other traits of control, extreme sterile sires are not included. More- economic importance must be carried out to de-over, it must be considered that only 187 boars are termine some alternatives for indirect selection. included in the analysis. However, this strong
nega-tive genetic correlation resembles the ones obtained
by the maternal animal model (Meyer, 1992; Robin- Acknowledgements
son, 1996), which also includes two genetic effects
camp, E.W., 1992. An economic comparison of management References
strategies on reproduction and replacement in sow herds using dynamic probabilistic model. Livest. Prod. Sci. 32, 331–350. Albert, J.H., Chib, S., 1993. Bayesian analysis of binary and
Land, R.B., 1978. Genetic improvement of mammalian fertility: a polychotomous response data. J. Am. Stat. Assoc. 88, 669–
review of opportunities. Anim. Reprod. Sci. 1, 109–135. 679.
´ Legault, C., 1978. Analyse des composantes de la productivite Bampton, P.R., 1992. Best linear unbiased prediction for pigs –
´
numerique des truies. Ann. Zootech. 27 (4), 457–470. the commercial experience. Pig News Information 13 (No. 3),
Mantysaari, E.A., Grohn, Y.T., Quaas, R.L., 1993. Repeatability 125–129.
and heritability of lactational occurrence of reproductive dis-Boichard, D., Manfredi, E., 1994. Genetic analysis of conception
orders in dairy cows. Acta Vet. Scand. 32, 107. rate in French Holstein cattle. Acta Agric. Scand. Sect. A,
Meyer, K., 1992. Variance components due to direct and maternal Anim. Sci. 44, 138–145.
effects for growth traits in Australian beef cattle. Livest. Prod. Dagorn, J., Aumaitre, A., 1979. Sow culling: reasons for and
Sci. 31, 179–204. effect on productivity. Livest. Prod. Sci. 6, 167–177.
´
Moreno, C., Sorensen, D., Garcıa Cortes, L.A., Varona, L., Dijkhuizen, A.A., Krabbenborg, R.R.M., Huirne, R.B.M., 1989.
Altarriba, J., 1997. On biased inference about variance com-Sow replacement: a comparison of farmers actual decisions and
ponents in the binary threshold model. Genet. Sel. Evol. 29, model recommendations. Livest. Prod. Sci. 23, 207.
145–160. Ducos A., Bidanel, J.P., Ducrocq, V., Groeneveld, E., 1992. Use of
Raftery, A.E., Lewis, S.M., 1992. How many iterations in the multiple trait individual animal model for the prediction of
Gibbs sampler. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., breeding values of station tested pigs in France. Proceedings of
Smith, A.F.M. (Eds.), Bayesian Statistics IV. Oxford University the 43rd Annual Meeting of the E.A.A.P.
Press, Oxford, pp. 763–774. Elbers, A.R.W., Vernoy, J.C.M., Van den Broek, J., Verheijden,
Robinson, D.L., 1996. Estimation and interpretation of direct and J.H.M., 1996. Risk of recurrence of repeat breeding in sows
maternal genetic parameters for weights of Australian Angus with a repeat breeding in the first parity. J. Anim. Sci. 74,
cattle. Livest. Prod. Sci. 45, 1–11. 2327–2330.
Estany, J., Alfonso, L., Babot, D., Noguera, J.L., 1995. Genetic Saloniemi, H., Grohn, Y., Syvajarvi, J., 1986. An epidemiological evaluation of production and reproduction traits from field pig and genetic study on registered diseases in Finnish Ayrshire. data in Spain. In: Groeneveld, E. (Ed.), Application of Mixed Acta Vet. Scand. 27, 196.
Linear Models in the Prediction of Genetic Merit in Pigs. Proc. Silverman, B.W., 1986. Density Estimation For Statistics and Data Symposium, Germany. Commission of the European Com- Analysis. Chapman and Hall.
munities, pp. 26–31. Sorensen, D.S., Andersen, S., Gianola, D., Korsgaard, I., 1995. Gelfand, A., Smith, A.F.M., 1990. Sampling based approaches to Bayesian inference in threshold models using Gibbs sampling.
calculating marginal densities. J. Am. Stat. Assoc. 85, 398– Genet. Sel. Evol. 27, 229–249.
409. Tanner, M.A., 1993. Tools for Statistical Inference.
Springer-Geman, S., Springer-Geman, D., 1984. Stochastistic relaxation, Gibbs Verlag, New York.
distributions and the Bayesian restoration of images. IEEE Thompson, R., 1979. Sire evaluations. Biometrics 35, 339–353. Trans. Pattern Anal. Machine Intell. 6, 721–741. Varona, L., Misztal, I., Bertrand, J.K., 1999. Threshold–linear vs. Geyer, C.J., 1992. Practical Markov Chain Monte Carlo. Stat. Sci. linear–linear analysis of birth weight and calving ease using an 7, 473–483. animal model. I. Variance component estimation. J. Anim. Sci. Gianola, D., 1982. Theory and analysis of threshold characters. J. 77, 1994–2002.
Anim. Sci. 54, 1079–1096. Wang, C.S., Rutledge, J.J., Gianola, D., 1993. Marginal Inferences Haley, C.S., Avalos, E., Smith, C., 1988. Selection for litter size in about variance components in a mixed linear model using
the pig. Anim. Breed. Abstr. 56, 317–332. Gibbs sampling. Genet. Sel. Evol. 25, 41–62.
