Role of genetic markers in the prediction of classification of Czech Large White gilts to a hyperprolific line

The objective of statistical evaluation (discriminant analysis) was to find out whether the genetic endowment the gilt was born with is a high-quality discriminator for prediction of its future classification to a hyperprolific line (HPL). Based on the results a conclusion is drawn that the gilt with genotype CC of ESR gene will be classified to HPL in high probability – if the effect of this gene is not reduced by an interaction with other genes. The statistical analysis did not reveal a significant effect of FSHB gene in Czech Large White sows on their future classification to HPL. On the contrary, PRLR gene is a highquality discriminator. Obviously, it is highly probable that the gilt with genotype BB will be classified to HPL. It is to state from the analysis of pairs of the studied genes that the adult gilt with genotype CC of ESR gene and genotype BB of FSHB gene and/or PRLR gene will be classified to HPL in all probability. PRLR gene has a dominant effect in the pair ESR and PRLR. Genotype BB of PRLR gene (the most beneficial of the genotypes from the aspect of future classification of gilts to HPL) markedly increases posterior probability of alleles of ESR gene. If the classification of a gilt to HPL is predicted from the analysis of all three genes, the results of partial analyses are confirmed in most cases. The results of the experiment indicate a possible prediction of gilts on the basis of their genotype for classification to HPL but it cannot be confirmed that the identified »beneficial« genotype will always be expressed in different populations by an increase in reproductive traits.


Introduction
In France the method of hyperprolific lines (HPL) contributed to an increase in the genetic potential of pigs to a high level.BIDANEL and DUCOS (1994) reported that HPL of daughters of HPL boars of Large White breed exhibited a genetic improvement of the litter size by 0.9 piglet per litter.A need to increase the level of prolificacy in dam breeds resulted in development of methodology for the production of HPL also in the Czech Republic.
Oestrogen receptor gene is one of the best-known genes studied in relation with sow prolificacy.According to ROTHSCHILD (1996) the preferred allele D of ESR gene was associated with an increase in the number of piglets in the Large White breed by 0.4-0.5 piglet per litter.A significant effect of ESR locus on the number of weaned piglets (P≤0.01) in Large White breed was reported by OMELKA et al. (2006).However, they observed a negative effect of DD genotype on this trait.The influence of the ESR gene as a quantitative trait locus (QTL) for litter size in a German Landrace population was analysed by DRÖGEMÜLLER et al. (1999).They did not find any Pvu II polymorphism.The associations of ESR genotypes with reproduction traits of hybrid sows were studied by DEPUYDT et al. (1999).The assumed effect of ESR genotypes on fertility was not confirmed.BUSKE et al. (2006) investigated if the genotype of the gene ESR2 was associated with litter size in a commercial pig cross population.Sows were divided into two extreme performance groups, with large (≥14.3)and with small litter size (≤11.3).No association was found between different ESR2.
The results of ZHANG et al. (2004) showed that the polymorphism of FSHB locus was significantly associated with litter size.Total number born and number born alive of sows with genotype BB were higher, with the additive effect 1.02-1.42and 1.04-1.27piglets per litter, respectively.LINVILLE et al. (2001) did not prove any significant associations between polymorphic markers and studied genotypes of FSHB gene.Nevertheless, they admitted that other genetic changes within candidate genes influenced the studied traits (linear model).HUMPOLICEK et al. (2006) examined the effects of FSHB on the performance of Large White sows in three different herds.The influence of FSHB was not very conclusive in the studied populations; it was different depending on the herd in which the sows were kept or on the set of analyzed litters.The polymorphisms of ESR1, FSHB and RBP4 genes (PCR-SSCP, PCR and PCR-RFLP) in a Large White herd and in a Landrace herd were detected by WANG et al. (2006).They found polymorphisms for the three genes in Large White besides the ESR1 and RBP4 genes in Landrace.The results showed that the highest genotype effects were exerted by ESR1 among these three genes.
According to VINCENT et al. (1998) PRLR gene seems to have a similar effect like ESR gene, but rather in the lines of Landrace origin, while the effect of ESR receptor is expressed mainly in Large White and Meishan breeds.DRÖGEMÜLLER et al. (2000) reported that in the Duroc breed a difference between genotypes AA and BB was 1 piglet born alive per litter; VAN RENS and VAN DER LENDE (2002) stated that (Large White × Meishan) gilts of genotype AA of PRLR genotype delivered more piglets born and born alive that gilts of genotype BB.
The objective of statistical evaluation was to find out whether the genetic endowment of the gilt was born with is a high-quality discriminator for prediction of its future classification to the HPL.

Material and methods
Data from performance testing of reproductive traits of Czech Large White sows coming from three elite breeding herds were used in this study.We evaluated 98 sows with known genotypes of three candidate genes for reproduction: oestrogen receptor It is so called »training set« (in accordance with statistical terminology).Out of the studied sows, 51 sows were classified to the HPL while 47 sows were classified to the basic herd (x).Genotypes were determined by molecular genetics methods PCR-RFLP in Laboratory of Applied Genetics of Mendel University of Agriculture and Forestry in Brno (LamGen).DNA was isolated from blood samples with the addition of anticoagulant EDTA.
The statistical analysis of data was based on methods of discriminant analysis when we used the discriminant analysis for two groups (HPL, basic herd).The genotypes (ESR, FSHB and PRLR) are specific because they are discrete random variables.Therefore the methods of discrimination for categorical data were used (AITCHISON & AITKEN 1976, HALL 1981, ČERMÁKOVÁ & FORBELSKÁ 2004).The personal study was employed for these purposes because commercial statistical software packages do not comprise any discrete models.
For discrimination were applied both parametric discrimination (see models with the multinomial estimator) and nonparametric discrimination based on kernel estimators of probability functions figuring in decision rules (see models with binary or nominal kernel estimator).The quality of discrimination was evaluated by estimations of probabilities of misclassification, applying two methods: plug-in method and resubstitution method (ČERMÁKOVÁ & FORBELSKÁ 2004).These methods of statistical analyses were used because of the relatively small size of the training set.If we obtained significantly different results by different methods, generalisation for the population would not be correct.It is to note that we took advantage of nonparametric methods enabling to estimate posterior probability even when the particular combinations of alleles (e.g.DD, AB, BB) did not occur in the training set.Parametric methods do not provide such a possibility.The statistical analysis considered all theoretical variants, i.e. it was carried out for each separate gene, for combinations of two genes and for the vector of three genes.Taking into account the small size of the training set it can considerately be deduced from the results whether in relation to prolificacy the genes act either autonomously or it is possible to expect their interaction.

Results and discussion
The summary of classification results of parametric (multinomial) model and two nonparametric (binary and nominal kernel) models and error rates are presented in Figures 1 through 7. The left horizontal stacked bar graph shows estimated posterior probabilities of individual genotypes.The right horizontal bar graph shows the achieved contribution of individual genotypes (scores qi) to the total error rate (ER) based on posterior probabilities (plug-in estimates).For estimating error rates, the resubstitution method (apparent error rate APER) is also available.
Figures 1-7 show that the results obtained by parametric and nonparametric methods do not differ significantly from each other.
Therefore we can draw a conclusion that gene ESR (Figure 1) if its effect is not decreased through interaction with other genes influences reproductive traits in this sense: the gilt that will be born with genotype CC of ESR gene will be classified in high probability to HPL (pHPL,CC=0.75).The probability of misclassification of CC genotype to HPL is not very high.The two remaining genotypes are indifferent for the prediction of future classification of gilts to HPL (posterior probability is slightly below the level 0.5, so it is not possible to draw a conclusion concerning the future with sufficient reliability).LEGAULT et al. (1996) did not report any significant differences in the genotype frequency of ESR gene between HPL and control group of Large White breed, the genotypes did not show a significant effect on litter size in any line.MATOUŠEK et al. (2003) analysed the relationship of ESR genotypes with the traits of litter size in sows in two elite breeding herds.In one herd, sows of genotype DD had a significantly higher number of piglets while in the other herd the examined reproductive traits were higher in sows of genotype CC.
The statistical analysis did not indicate a significant effect of FSHB gene on their future classification to HPL (Figure 2).The value of posterior probabilities is about 0.5; so FSHB gene does not appear to be a high-quality discriminator between the two classes in the Czech Large White breed.But it does not imply that it does not contribute to discrimination in interaction with other genes.HUANG et al. (2000) found out by 0.55-2.21piglets born alive more per litter in gilts of genotype BB compared to gilts of genotype AA.
PRLR gene belongs to high-quality discriminators.Figure 3 illustrates that the gilt with genotype BB will be classified in high probability to HPL (pHPL,BB=0.8).This conclusion is supported by the fact that the probability of misclassification of the gilt with genotype BB of PRLR gene is low (it lies deep below the mean value of scores).The gilt with genotype AA would seem not to have a very high chance to be classified to HPL.But we cannot draw such a conclusion due to high probability of misclassification.According to DVOŘÁK (1999) the average effect of allele B of PRLR gene in parity 1 is 0.25 piglet more.DRÖGEMÜLLER et al. (2001) observed a small additive effect of allele B of PRLR gene on litter size in the Duroc line (linear model).VAN RENS et al. (2003) believed that PRLR gene was a candidate gene for ovulation rate rather than for litter size (linear model).
If we predict future classification of sows from the aspect of genetic endowment on the basis of parallel analysis of two or even three genes (Figures 4-7), we have to be considerate because only very few animals can have the particular genotype combination.
It seems that FSHB gene that was not a good discriminator (Figure 2) will express itself in combination with ESR (Figure 4) or PRLR (Figure 6) gene.Genotype BB of FSHB gene in synergy with the genotype of ESR gene or PRLR gene increases more or less the probability that the adult gilt will be classified to HPL.E.g. in the combination of genotype BB of FSHB gene and genotype CC of ESR gene posterior probability will increase from the value pHPL,CC=0.75(Figure 1) to the value pHPL,CC&BB=0.85(Figure 4).In the combination of genotype BB of FSHB gene and genotype BB of PRLR gene (Figure 6) posterior probability increased from pHPL,BB=0.8(Figure 3) to pHPL,BB&BB=0.9(Figure 6).Genotype AB of FSHB gene and genotype DD of ESR gene significantly increase the probability of classification to HPL from pHPL,DD<0.5 (Figure 1) to pHPL,DD&AB>0.5 (Figure 4) while genotype AB of FSHB gene and genotype BB of PRLR gene decrease such probability (Figure 6).It is possible to conclude from the analysis of pairs of these genes that the adult gilt born with genotype CC of ESR gene and genotype BB of FSHB gene will have the highest probability of being classified to HPL whereas the prediction score is low (Figure 4); the same will apply to genotype BB of PRLR gene and FSHB gene, also with the low score of prediction error (Figure 6).On the contrary, very low probability of classification to HPL was determined in gilts with scarce combinations of genotypes, i.e. genotype CD (and/or CC) of ESR gene and genotype AA (and/or AB) of FSHB gene (Figure 4) and genotype AA of PRLR gene and FSHB gene (Figure 6).CHEN et al. (2001) drew a conclusion that the effect of ESR and FSHB genes on litter size made it possible to improve reproductive traits through markerassisted selection.
The analysis of the pair of ESR and PRLR genes provided interesting results (Figure 5).The effect of PRLR gene was dominant in this pair.Genotype BB of PRLR gene (it is the most beneficial of all genotypes from the aspect of future classification of a gilt to HPL) markedly enhances posterior probability of ESR gene alleles.E.g. in genotype CD of ESR gene (p=0.4),i.e. on the basis of the analysis through ESR gene only, it is not possible to predict the classification of a gilt to HPL, but in the combination of genotype CD of ESR gene and genotype BB of PRLR gene it can be stated in high probability that this gilt will be classified to HPL.Genotype AB of PRLR gene behaves indifferently in relation to ESR gene while genotype AA of PRLR gene decreases the effect of ESR gene with respect to the future classification of gilts to HPL.E.g. if we analysed ESR gene only, the probability of the gilt with genotype CC to be classified to HPL would be high.However, if we also consider PRLR gene and if the gilt is of genotype AA, its probability of being classified reliably to HPL at an adult age will decrease to p=0.5.VAN RENS (2001) analysed the combinations of ESR and PRLR genotypes.She reported that each gene influenced different components of litter size.SOUTHWOOD et al. (1999) did not detect any interactions between genes for prolactin and oestrogen receptor.
If the gilt classification to HPL is predicted by the analysis of all three genes, the results of partial analyses are mostly confirmed: e.g. a marked contribution of genotype CC of ESR gene with the positive association of genotype BB of FSHB gene and augmentation effect of genotype BB of gene PRLR.The results of the experiment indicate a possible prediction of sows on the basis of their genetic »endowment«, i.e. of a particular genotype for the classification of sows to HPL, but it is not possible to prove that the identified »beneficial« genotype will always be expressed by an increase in reproductive traits in different populations.The results of DRÖGEMÜLLER 'S et al. (2001) study demonstrated that the expressions of alleles between lines or populations differed.It may be caused by diverse linkages between alleles of markers and by random mutations of different lines.The results may also be explained by a high number of minor genes influencing the litter size.The authors are convinced that a selection strategy should be defined for each line separately and possible pleiotropic effects should always be considered.
The originality of the paper consists in the application of discriminant analysis to predict the classification of gilts to a HPL when three selected genetic markers are determined.The studies that have been published until now demonstrate in different pig populations that the association of the genotype and alleles of genetic markers in relation to reproductive traits is not quite unambiguous.But these authors carried out »ex post« analyses, i. e. analyses of a reality only when such reality existed.The isolated evaluation of a single gene will always have a limited informative capacity and will provide applicable results only if the effect of this gene is very high and relatively independent of the genome residue and environmental conditions.
All estimated values of the total error rate are in the range: 0.36-0.39.Each of the methods classifies sow with genotype DD of ESR gene into not HPL (posterior probabilities pHPL,DD < pX,DD) and sow with genotype CC into HPL (pHPL,CC >pX,CC).

Figure 1
Figure 1 Probability of the future classification of sows to HPL determined by the analysis of genotypes of ESR gene Wahrscheinlichkeit künftiger Sauenzuordnung in die superfruchtbare Linie (HPL) auf Grund der Genotypenanalyse des ESR Gens

Figure 2
Figure 2 Probability of the future classification of sows to HPL determined by the analysis of genotypes of FSHB gene Wahrscheinlichkeit künftiger Sauenzuordnung in die HPL auf Grund der Genotypenanalyse des FSHB Gens

Figure 3
Figure 3 Probability of the future classification of sows to HPL determined by the analysis of genotypes of PRLR gene Wahrscheinlichkeit künftiger Sauenzuordnung in die HPL auf Grund der Genotypenanalyse des PRLR Gens

Figure 4
Figure 4 Probability of the future classification of sows to HPL determined by the analysis of genotypes of ESR and FSHB genes Wahrscheinlichkeit künftiger Sauenzuordnung in die HPL auf Grund der Genotypenanalyse der ESR-FSHB Gene

Figure 5
Figure 5 Probability of the future classification of sows to HPL determined by the analysis of genotypes of ESR and PRLR genes Wahrscheinlichkeit künftiger Sauenzuordnung in die HPL auf Grund der Genotypenanalyse der ESR-PRLR Gene

Figure 6
Figure 6 Probability of the future classification of sows to HPL determined by the analysis of genotypes of FSHB and PRLR genes Wahrscheinlichkeit künftiger Sauenzuordnung in die HPL auf Grund der Genotypenanalyse der FSHB-PRLR Gene

Figure 7
Figure 7 Probability of the future classification of sows to HPL determined by the analysis of genotypes of ESR, FSHB and PRLR genes Wahrscheinlichkeit künftiger Sauenzuordnung in die HPL auf Grund der Genotypenanalyse der ESR-FSHB-PRLR Gene