Roczniki Naukowe Polskiego Towarzystwa Zootechnicznego, t. 5 (2009), nr 2

Heritability and breeding valueof sheep fertility estimated by meansof the linear and threshold model

Dariusz Piwczyński, Sławomir Mroczkowski

University of Technology and Life Sciences, Department of Genetics and AnimaI Breeding,Str. Mazowiecka 28, 85-084 Bydgoszcz

The research was conducted on 2790 Polish Merino ewes born in the years 1991-2002. Theanimals were maintained in 6 flocks from the Kujawy and Pomorze region. Fertility of ewesin 3 subsequent lambings was controlled. The explorative analysis of the said trait provedthat its statistically significant source of variability were flock, year of birth, successivelambing, as well as the flock*year of birth interaction. In order to estimate genetic parametersof fertility, Gibbs sampling method was applied, using univariate linear (LM) and threshold(TM) animai models. Estimated heritability of fertility depending on the model was 0.01 (LM)and 0.06 (TM), whereas repeatability 0.09 (LM) and 0.23 (TM). Based on the obtainedcomponents of variance, the breeding value of animals was estimated by means of the BLUPmethod and two alternative models - linear and threshold. The rankings obtained for thebreeding value with use of the linear and threshold models were strongly correlated(rs=0.992). Positive genetic trend s were found as regards Certility at the level of 0.0015/year.

KEY WORDS: sheep / fertility / heritability / threshold model / BLUP

Reproduction traits, such as fertility, num ber of lambs bom or reared, belon g tothreshold traits, i.e. traits which are not continuous in their phenotypic expression, butwith a continuous genetic variability [2]. Their characteristic pro perty is that exceedingthe so-called threshold relating to the possessed genes leads to a fundamental changeof the phenotype. A special case of a threshold trait is dam fertility measured in a par-ticular reproduction season, which may be either O or 1. The importance of the fertilityindex in defining profitability of sheep production is high, especially in meat-orienteduse. As Al-Shorepy and Notter [1] have noted, improving sheep in terms of fertility,one may expect a correlated selection effect on the number of lambs bom in alitter.Mroczkowski [9] has proved that the traits concerning the body weight of ew es arefavourably genetically correlated with future fertility. Piwczyński [14] has also foundfavourable positive genetic dependencies between fertility and prolificacy as well asreproduction performance.

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Estimation of genetic parameters and breeding value in terms of their binominaltraits is done with the use of various methods and models [7, 9, 11, 16, 18]. Some ofthe methods used for this purpose are the REML method or the Gibbs sampling method,as well as Iinear and threshold models. In the literature on (he subject, studies may befound where prior to estimation of a binominal trait heritability, probit transformationswere applied [12]. Moreover, it is possible to convert heritability obtained with the useof the linear model from discrete source data into a continuous scale [19]. In somepapers, estimates of parameters are presented which were obtained based on averagefrom several consecutive ewe performance values (e.g. 2 or 3), or else based on the lifeperformance [9, 14].

The aim of the paper was to estimate heritability and breeding value as regardsfertility of Polish Merino ewes, obtained in selected flocks in the Kujawsko-PomorskieProvince by means of the Gibbs sampling method, using univariate linear (LM) andthreshold (TM) animaI models.

Materiał and methods

The research was conducted on Polish Merino sheep maintained in 6 flocks produ-cing breeding rams, located in the Pomorze and Kujawy region. Data concerningfertility of 2790 ewes came from breeding documentation from the years 1995-2004,made available by the Regional Association of Sheep and Goat Breeders, Bydgoszcz.

The assessed ewes were from the years 1991-2002, and they were used between1995 and 2004. Ewe fertility was analysed in the three consecutive first reproductionseasons, gathering information on 8102 lambings. The pedigree information of exami-ned population of animals was completed as far as possible up to 3rd generation. Intotal, the pedigree base was constituted by 5123 animals. Ewes controlled in terms offertility had complete pedigree information on the parents, 92.44% had pedigree infor-mation on grandparents, and 57.19% on great grandparents. In order to calculate theinbreed coefficient in the analysed population, the authors used the INBREED proce-dure from the SAS package [15]. This, however, showed that there were no inbredanimals.

As part of the conducted statistical procedure, the basie descriptive measures of ewefertility were calculated (Table l). The explorative analysis of ewe fertility was carriedout using multiple logistic regression. As part of the analysis, using the method of theforward selection type of regression model [13, 15], the following significant variabiesconnected with ewe fertility were selected: f1ock, dam's year of birth, dam's age, andf1ock*year of birth interaction. The assessment of significance of parameters, i.e. theselected variab\es, was carried out by means of the Wald statistics [15]. The statisticalanalysis was conducted by means of the SAS package, using the LOGISTIC procedure[15].

The estimators of the variance components were estimated by means of the Gibbssampling method, using univariate animaI models: linear and threshold (in the case of

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Table 1 - Tabela 1Descriptive characteristic offertility (%)Charakterystyka opisowa płodności (%)

n x SD

Tolal 8102 94.04 23.68Razem

Flock - StadoA 919 97.17 16.59B 868 94.24 23.31C 726 96.83 17.53D 594 96.97 17.16E 2922 93.36 24.90F 2073 91.70 27.59

Year of birth - Rok urodzenia1991 299 93.31 25.021992 401 93.52 24.651993 941 92.56 26.251994 924 94.16 23.471995 1066 94.56 22.691996 754 93.90 23.951997 852 94.01 23.741998 869 93.79 24.151999 983 95.32 21.132000 319 90.60 29.232001 537 95.72 20.272002 157 96.82 17.62

Successive lam bing - Kolejny wykotI 2925 93.09 25.362 2685 93.59 24.493 2492 9563 20.46

this model, the so-called "unobservable tendency" was modelled). The analysis modellooked as follows:

where:

y - 8102 x l observation vector;I3fr, 13" - fixed effects vectors: flock-year of birth (68 x 1), successive lambing of a ewe

(3 x l);a - 5123 x l vector of random genetic additive effects;pe - 5123 x 1 vector of random permanent influences of the animaI' s specific environ-

ment;Xfr, X" - incidence matrices for fixed effects: flock-year of birth (8102 x 68) and

successive lambing of the dam (8102 x 3);Za - 8102 x 5123 incidence matrix for random direct additive genetic effects;Zpe - 8102 x 5123 incidence matrix for random permanent influences of the animal's

specific environment;e - 8102 x 1 random error vector.

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The following assumptions regarding variance of the random effects of the modelwere made:

var( a) = Ao2a)2oartpe) = IqO pe,

2uarie) = InO e,where:

A - 5123 x 5123 dimensional matrix of additive relationship among animals;In, Iq - identity matrices;82

a - genetic additive direct variance;8,e - variance of random permanent inf1uences of the animaI' S specific environment;8 e - error variance (in the case of the threshold model, variance equals 1);82

p - phenotypic variance (82p = 82

a + 82pe + 82

e).

Heritability and repeatability were obtained with the use of the following formulas,respecti vel y:

h2 = d2a/d2p

r'= (rPa + 82pe)l82 p.

Estimating variance components by means of the threshold model, the same randomand fixed effects as in the linear model were taken into consideration. The heritability,estimated with the use of a linear model from "source" data (h2 d) was converted intocontinuous scale (h2x) according to formulas proposed by Żuk [19].

In order to estimate variance components, the Gibbs sampling method [8, 17] wasapplied. GIBBS 1F90 software [8] was used to estimate the genetic parameters offertility in accordance with the linear model, whereas THRGIBBS IF90 [17] in accor-dance with the threshold model.

Estimating variance components by means of the Gibbs sampling method, 100000sampies were generated, the first 30 000 of which were declared as initial sampies("bum in period"). The POSTGIBBS IF90 software [17] was the tool used to determinethe num ber of sampIes being initially rejected. Due to occurring autocorrelations bet-ween the results obtained from adjacent sampies, genetic parameters were determinedfrom values obtained from every tenth sample. Variance components as well as herita-bility and repeatability indices were therefore determined based on the results of 7 000sampies.

Standard errors of variance components and the genetic parameters determinedbased upon them were ca\culated as standard deviations of the value of those compo-nents and indices obtained in the said 7 000 sampIes.

The breeding value (BV) assessment of animals in terms of fertility was made bymeans of the BLUP-Animal Model, using the linear and threshold model. In the caseof the former, the BLUPF90 computer software [8] was used, and in the latter,CBLUP90THR [8]. One of the aspects of the conducted research was the determinationof dependencies among the ranking of animals as regards breeding value (BV), obtainedwith the use of the linear and threshold model. In order to do that, the Spearman's rankcorrelation coefficient [15] was ca\culated. The changes in the mean breeding value of

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l

1

I

animals born in subsequent years were depicted in the graphs, using for this purposeestimations from the application of the threshold model. Genetic trends of fertility weredetermined as the linear regression coefficient of mean breeding values for the animal'syear of birth.

ResuIts and discussion

The fertility of the contralled ewes was found on a high level, generally exceedingcorresponding indices pravided by the Polish Sheep Breeders Association [4] for thePolish Merino population in the years 2001-2007 (91.3-95.5%). The variabies selectedin the course of the analysis (f1ock, ewe's year of birth, successive lambing, f1ock*yearof birth interaction) were also indicated by other authors [7, 10, 13] as a potential sourceof variability in ewe fertility.

Table 2 shows heritability and repeatability estimated based on individual perfor-mance of ewes frorn subsequent reproduction seasons. The heritability of fertility ob ta-ined by means of the threshold model was approx. 0.06 and was six times highercompared to that obtained by means of the linear model (Table 2). The repeatabilityobtained by means of the threshold model was over two times higher than that usingthe linear model. It must be concluded that the obtained heritability values indicate thatthe influence of genetic assumptions on ewe fertility is low. This, however, is not farfrom what other authors have found [6, 7, 11, 12, 14, 16] in research where theheritability index f1uctuated between 0.02 and 0.17, although usually not exceeding 0.1.

Table 2 - Tabela 2Estimates of variance components, heritability and repeatability of fertilityEstymatory komponentów wariancji, odziedziczalności i powtarzalności płodności

Linear model Threshold modelModel liniowy Model progowy

52a ±SO 0.00055 ±0.OOO36 0.07972 ± 0.04037

5\, ±SO 0.00434 ±0.00I04 0.21893 ± 0.07990

52, ±SO 0.05060 ±0.00113

52p ±SO 0.05549 ±0.OOO90 1.29865 ± 0.07737

h2 ±SO 0.01 ±O.OOG 0.06 ±0.031

h2x 0.04

r' ±SO 0.09 ±0.Ol8 0.23 ±0.044

r, 0.992***

rs - correlation between rankings of breeding values of animals estimated using the linear and threshold models- zależność między uszeregowaniem wartości hodowlanych zwierząt oszacowanych za pomocą modeliliniowego i progowego

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Authors who eompared heritability estimated by means of different models [7, 11,16] registered a elear advantage of the indiees obtained with the use of threshold model srather than linear. Matos et al. [7] have found that heritability of fertility estimated bymeans of the animaI' s threshold model (0.10-0.17) was from three to four times higherthan when the linear model was used (0.03-0.04). On the other hand, the repeatabilityof a trait estimated with the use of sire's linear and threshold model s was similar. Olesenet al. [11] eompared estimated heritability values for the number of lambs bom in alitterobtained with the use of linear and threshold models. A three times higher heritabilityof the trait was found with the use of the threshold model. De Souse et al. [16] founda four times higher heritability of fertility estimated with the use of the threshold model(0.12) eompared to the linear model (0.03). As far as the number of weaned lambs iseoneerned the differenee was even five times higher. Considerably higher indexes ofheritability and repeatability obtained with the use of threshold model s as opposed tothe linear model s probably stem from the faet that threshold models explain the majorityof total variability [7,11].

It is worth noting that conversion of the heritability estimated with the use of theGibbs sampling method and the linear model into eontinuous seale (h2x) led to a resultlargely similar to the one obtained using the threshold model (Tab le 2). This suggeststhat in the breeding eonditions obtaining information on the degree of genetie eonditio-ning of sheep fertility with a similar level of aeeuraey is possible using the transforma-tion proposed by Żuk [19].

Taking into eonsideration standard deviations for heritability indices one may eon-elude that the estimates obtained with the use of the threshold model were relati velyless loaded (50 vs. 64%). Standard deviations for repeatability indexes did not differconsiderably between the models.

The breeding value of the analysed animaI population was estimated by means ofthe BLUP-Animal Model and two differing models - linear and threshold. Very highsignifieant dependeneies were found (P<O.OOl) between rankings of animals' breedingvalues obtained using the twa model s (Table 2). It is a predominant view in the scien-tific literature on the subject that the rankings of breeding values estimated with the useof linear and threshold models is very similar, if not identical [3, 5, 16]. Hence a eon-clusion that the results obtained in the authors' own researeh eorrespond with thosepresented in the literature on the subject [3, 5, 16], and that for the purpose of rankinganimals in terms of their breeding value of fertility both the linear as well as thresholdmodel s may be used.

The drawing 1 represents the genetic trend in respeet of fertility. Due to higherheritability obtained with the use of the threshold model, accompanied by a smallererror, as compared to the linear model, the further part of the paper analyses estimatesof breeding value obtained with the use this model. The breeding value of fertilitydisplayed a growing tendeney. A partieularly evident increase of the breeding value ofthe analysed population was notieeable sinee 1996. The calculated signifieant regressioncoeffieient (P=0.021) allows a conelusion that the genetic value of ewe fertility inere-ased annually by 0.0015 (SE=0.0006). The favourable tendency in terms of improve-

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ment of fertility may be a result of the correlated selection effect, resulting fromconducted direct selection, on ewe prolificacy [1].

0.0250

0.0200

0.0150

BV 0.0100

0.0050

0.0000

-0.0050t7::~~~::'(,9:7 19981999200020012oo2!J... . .

Lata - Years

Fig. Genetic trends for the fertility of ewesRys. Trendy genetyczne w zakresie płodności maciorek

Summing up the results of the research, one may conc\ude that the obtained fertility(94.04%) for the Polish Merino ewes from flocks in the Kujawsko-Pomorskie Provincewas usually on a higher level in comparison to the national average [4]. Significantfactors responsible for variability of ewe fertility were flock, successive larnbing, yearof birth, and flock*year of birth interaction. Heritability of ewe fertility estimated withthe use of the threshold model (0.06) was over six times higher than that obtained withthe use of the linear model (0.0 l), and was at the same time characterised by a smallererror. Therefore, it may be conc\uded that the heritability of fertility must estimated bymeans of the threshold model. It was found that the ranking of breeding values ofanimals obtained using the BLUP method and the linear and threshold models werepractically identical (rs=0.992). Positive genetic trends in terms of fertility were demon-strated, at the annual level of 0.15%.

REFERENCESl. AL-SHOREPY S.A., NOTTER D-R., 1997 - Response to selection for fertility in a fall-lam-

bing sheep flock, Iournal oj Animai Science 75, 2033-2040.

2. GIANOLA D., 1982 - Theory and analysis of threshold characters, Iournal oj Animai Science54, 1079-1096.

3. GATES PJ., URIOSTE J.I., 1995 - Heritability and sire genetic trend for litter size in Swedishsheep estimated with linear and threshold models. Acta Agriculturae Scandinavica, SectionA, Animul Science 45 (4), 228-235.

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4. Hodowla Owiec i Kóz w Polsce (w latach 2001-2007) - Polski Związek Owczarski, Warszawa,2002-2008.

5. JORGENSEN J.N., 1994 - Estimation of genetic parameters for litter size in sheep usingnon-linear method. Acta Agriculturae Scandinavica, Section A, Animai Science 44 (I), 8-11.

6. MATIKA O., VAN WYK J.B., ERASMUS G.J., BAKER R.L., 2003 - Genetic parameterestimates in Sabi sheep. Livestock Production Science 79 (I), 17-28.

7. MATOS C.A.P., THOMAS D.L., GIANOLA D., TEMPELMAN R.J., YOUNG L.D., 1997-Genetic analysis of discrete reproductive traits in sheep using linear and nonlinear models. I.Estimation of genetic parameters. [ournal oj Animai Science 75. 76-87.

8. MISZTAL 1., 2008 - BLUPF90 farnily of programs. http://nce.ads.uga.eduJ-ignacy/prog-rams.html

9. MROCZKOWSKI S., 1986 - Korelacje genetyczne i fenotypowe między płodnością i plen-nością a niektórymi innymi cechami młodych maciorek merynosowych. Zeszyty ProblemowePostępćw Nauk Rolniczych 303, 159-168.

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13. PIWCZYŃSKI D., MROCZKOWSKI S., 2005 - Zastosowanie regresji logistycznej w analiziewybranych cech rozrodu owiec. Roczniki Naukowe PTZ, Suplement I (2), 49-57.

14. PIWCZYŃSKI D., KOWALISZYN B., MROCZKOWSKI S., WŁODARCZAK M., 2004 -Parametry genetyczne cech reprodukcyjnych owiec rasy merynos polski oszacowane z wyko-rzystaniem różnych modeli liniowych. Zeszyty Naukowe Przeglądu Hodowlanego 72, z. 3,15-21.

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16. SOUSA W.H., PEREIRA C.S., BERGMANN JAG., DA SILVA F.L.R., 2000 - Estimatesof components of variance and genetic parameters for reproductive traits by means of linearand threshold models. Revista Brasileira de Zootecnia - Brazilian Iournal oj Animai Science29 (2),2237-2247.

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Dariusz Piwczyński, Sławomir Mroczkowski

Odziedziczalność i wartość hodowlana płodności owiecoszacowana za pomocą modelu liniowego i progowego

Streszczenie

Badaniami objęto 2790 matek rasy merynos polski urodzonych w latach 1991-2002, któreutrzymywano w 6 stadach z rejonu Pomorza i Kujaw. Płodność maciorek w 3 kolejnych wykotachanalizowano statystycznie za pomocą wielokrotnej regresji logistycznej. Wykazano statystycznywpływ stada, roku urodzenia, kolejnego wykotu i interakcji stado*rok urodzenia na płodnośćmaciorek. W celu oszacowania parametrów genetycznych zastosowano metodę próbkowania Gib-bsa, posługując się jednocechowymi modelami zwierzęcia - liniowym (LM) i progowym (TM).Szacowana odziedziczalność płodności, w zależności od modelu, wynosiła 0,01 (LM) i 0,06 (TM),zaś powtarzalności: 0,09 (LM) i 0,23 (TM). Uzyskane parametry genetyczne zostały następniewykorzystane do oszacowania wartości hodowlanych (BLUP) zwierząt w zakresie kontrolowanejcechy. Otrzymane rankingi wartości hodowlanych zwierząt w zakresie płodności za pomocą mo-deli liniowych i progowych były ze sobą silnie skorelowane (r5=0,992). Stwierdzono dodatnietrendy genetyczne płodności (0,15% na rok).

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