COVARIANCE FUNCTIONS FOR LITTER SIZE IN PIGS USING A RANDOM REGRESSION MODEL

Transcription

1 UNIVERSITY OF LJUBLJANA BIOTECHNICAL FACULTY ZOOTECHNICAL DEPARTMENT Zoran LUKOVIĆ COVARIANCE FUNCTIONS FOR LITTER SIZE IN PIGS USING A RANDOM REGRESSION MODEL DOCTORAL DISSERTATION KOVARIANČNE FUNKCIJE ZA VELIKOST GNEZDA PRI PRAŠIČIH V MODELU Z NAKLJUČNO REGRESIJO DOKTORSKA DISERTACIJA Ljubljana, 2006

2 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 II The present dissertation thesis is conclusion of a doctoral study. The research work was performed at the Zootechnical Department of Biotechnical Faculty (Slovenia). Litter records from three farm were supplied by the Slovenian pig breeding organization. Senate of Biotechnical Faculty nominated Prof. dr. Milena Kovač as supervisor for this doctoral dissertation. Commission for evaluation and justification: Chairperson: Prof. dr. Jurij POHAR University of Ljubljana, Biotechnical Faculty, Zootech. Dept. Member: Prof. Milena KOVAČ, PhD University of Ljubljana, Biotechnical Faculty, Zootech. Dept. Member: Prof. dr. Marija UREMOVIĆ University of Zagreb, Faculty of Agriculture, Croatia Date of justification: July 10th 2006 The thesis is result of my own research work. Zoran Luković

3 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 III KEY WORDS DOCUMENTATION DN Dd DC UDC :519.22:57.087(043.3)=20 CX livestock production/genetic evaluation/random regression models/longitudinal data/litter size/pigs CC AGRIS L10/U10/5300 AU LUKOVIĆ, Zoran AA KOVAČ, Milena (supervisor) PP SI-1230 Domžale, Groblje 3 PB University of Ljubljana, Biotechnical Faculty, Zootechnical Department PY 2005 TI COVARIANCE FUNCTIONS FOR LITTER SIZE IN PIGS USING A RANDOM RE- GRESSION MODEL DT Doctoral Dissertation NO XIV, 111 p., 30 tab., 19 fig., 117 ref. LA en AL en/sl AB Litter records from three large farms were used. Each farm had two data sets. The first one included records from the first to the sixth parity, and the second data set included records from the first to the tenth parity. Sows had between 3.08 and 3.50 litters in the first data set, and in the second data set between 3.56 and 4.16 litters. Estimates of variances in repeatability model, covariance components for multiple-trait analysis and for random-regression coefficients were estimated by the REML method and the VCE5 software package. Fixed effects in model for the number of piglets born alive included sow genotype, parity, weaning to conception, mating season and service sire as class effects. In fixed part of the model previous lactation length as linear regression and age at farrowing as quadratic regression were included. Model for NBA included direct additive genetic, permanent environmental and common litter environmental effect, except in multiple-trait model that did not include permanent environmental effect. Orthogonal Legendre polynomials (LG) of different order were fit to random effects in random regression model. LG with four coefficients were found sufficient. Heritability estimates were around 10 % in repeatability model, and between 10 and 14 % in multipletrait analysis and random regression model. Estimates of permanent environmental effect were between 5 and 6 % in repeatability model, and between 0.04 and 0.10 in the random regression model. In repeatability model the ratio for the common litter environmental variance with respect to the total variance were between 1 and 2 %, in multiple-trait analysis and random regression model between 1 and 5 %. The eigenfunctions and corresponding eigenvalues showed that including higher parities in data sets two increased percentages of the total variability which were explained with individual production curve. In the second data sets around 85 to 90 % of the total genetic variability was explained by the constant term in regression, while 10 to 15 % was genetic variability in the shape of litter size curve.

4 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 IV KLJUČNA DOKUMENTACIJSKA INFORMACIJA ŠD Dd DK UDK :519.22:57.087(043.3)=20 KG živinoreja/genetski parametri/modeli z naključno regresijo/zaporedne meritve/velikost gnezda/prašiči KK AGRIS L10/U10 AV LUKOVIĆ, Zoran, mag., dipl. ing. agr. SA KOVAČ, Milena (mentor) KZ SI-1230 Domžale, Groblje 3 ZA Univerza v Ljubljani, Biotehniška fakulteta, Oddelek za zootehniko LI 2005 IN KOVARIANČNE FUNKCIJE ZA VELIKOST GNEZDA PRI PRAŠIČIH V MODELU Z NAKLJUČNO REGRESIJO TD Doktorska disertacija OP XIV, 111 str., 30 pregl., 19 sl., 117 vir. IJ en JI en/sl AI Podatke o velikosti gnezda s treh farm smo analizirali tako, da smo jih razdelili glede na število prasitev. V prvi niz podatkov smo vključili meritve gnezda od prve do šeste prasitve. Drugi niz je obsegal podatke od prve do desete prasitve. Število gnezd na svinjo se je razlikovalo in sicer so v prvem nizu podatkov imele svinje med 2.88 in 3.50 gnezd. V drugem nizu podatkov je bila ta vrednost večja in je variirala od 3.56 do 4.16 gnezd. Za oceno varianc v ponovljivostnem modelu ter komponent kovarianc v večlastnostnem modelu in v modelu z naključno regresijo smo uporabili metodo REML v statističnem paketu VCE5. V model za število živorojenih pujskov smo vključili naslednje sistematske vplive z nivoji: genotip svinje, zaporedno prasitev, poodstavitveni premor, sezono pripusta in merjasca. V sistematski del modela smo vključili še dolžino predhodne laktacije kot linearno regresijo in starost ob prasitvi kot kvadratno regresijo. Naključni del modela za število živorojenih pujskov je vseboval direktni aditivni genetski vpliv, vpliv permanentnega okolja in vpliv skupnega okolja v gnezdu. Večlastnostni model je bil brez vpliva permanentnega okolja. Ortogonalne Legendrove polinome različnih stopenj smo uporabili za modeliranje naključnih vplivov v modelu z naključno regresijo in ugotovili, da je najprimernejši Legendrov polinom tretje stopnje. Ocenjena heritabiliteta za velikost gnezda je bila 10 % v ponovljivostnem modelu, med 10 in 14 % pa v večlastnostnem modelu in v modelu z naključno regresijo. Delež permanentnega okoljskega vpliva je znašal med 5 in 6 % v ponovljivostnem modelu in med 4 in 10 % v modelu z naključno regresijo. Delež skupnega okolja v gnezdu je zajel od 1 do 2 % variabilnosti v ponovljivostnem modelu ter med 1 in 5 % v večlastnostnem modelu in modelu z naključno regresijo. Lastne funkcije s pripadajočimi lastnimi vrednostmi so pokazale, da se z vključitvijo višjih zaporednih prasitev v podatke povečuje delež skupne variabilnosti pojasnjene z individualno proizvodno krivuljo. V podatkih, kjer smo vključevali tudi meritve od sedme do desete prasitve, je med 85 in 90 % skupne genetske variabilnosti pojasnil konstantni člen, med tem ko oblika proizvodne krivulje za velikost gnezda pojasni med 10 in 15 % genetske variabilnosti.

5 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 V TABLE OF CONTENTS p. Key words documentation (KWD) Ključna dokumentacijska informacija (KDI) Table of contents List of Tables List of Figures Abbreviations and symbols III IV V VIII XII XV 1 INTRODUCTION 1 2 LITERATURE REVIEW SELECTION FOR LITTER SIZE FACTORS AFFECTING LITTER SIZE IN PIGS Age at farrowing Lactation length and weaning to conception interval Season Genotype Direct additive genetic effect Maternal additive genetic effect Sire effect Common litter environmental effect Permanent environmental effect GENETIC CORRELATIONS STATISTICAL MODELS FOR GENETIC EVALUATION OF LITTER SIZE Repeatability model Multiple-trait model Random regression model 23 3 MATERIAL AND METHODS MATERIAL DATA FILE ORGANIZATION 30

6 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 VI 3.3 METHODS Model development Implemented models Models in matrix notation and covariance structure Eigenvalues and eigenfunctions Breeding values 39 4 RESULTS MODEL SELECTION Fixed effects Age at farrowing and parity Service sire Weaning to conception interval Mating season Previous lactation length Sow genotype Random effects COMPUTATIONAL REQUIREMENTS REPEATABILITY MODEL MULTIPLE-TRAIT ANALYSIS Variance components Correlations RANDOM REGRESSION MODEL Eigenvalues and eigenfunctions Covariance components Correlations Breeding values 76 5 DISCUSSION CHOICE OF THE MODEL AND ESTIMATION OF FIXED EFFECTS COMPUTATION REQUIREMENTS REPEATABILITY MODEL 85

7 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 VII 5.4 MULTIPLE-TRAIT ANALYSIS Covariance components Correlations RANDOM REGRESSION MODEL Eigenvalue analysis Covariance components Correlations Breeding values 88 6 CONCLUSIONS 89 7 SUMMARY (POVZETEK) SUMMARY POVZETEK 95 8 REFERENCES 103 ACKNOWLEDGEMENTS ZAHVALA

8 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 VIII LIST OF TABLES p. Table 1: Number of piglets born alive by different genotypes Tabela 1: Število živorojenih pujskov pri različnih genotipih 10 Table 2: Heritability estimates for number of piglets born alive from the literature Tabela 2: Ocene heritabilitete za število živorojenih pujskov iz literature 12 Table 3: Tabela 3: Table 4: Genetic correlation for the number of piglets born alive between successive parities Primerjava genetskih korelacij za število živorojenih pujskov med zaporednimi prasitvami 17 Fixed effects in the models for the number of piglets born alive Tabela 4: Pregled sistematskih vplivov v modelih za število živorojenih pujskov 20 Table 5: Tabela 5: Table 6: Elimination criteria for age at farrowing by parity Kriterij za izločitev podatkov zaradi starosti ob prasitvi po zaporednih prasitvah 25 Data structure for data sets DS1 and DS2 for farms A, B, and C Tabela 6: Struktura podatkov za niza podatkov DS1 in DS2 po farmah 26 Table 7: Tabela 7: Table 8: Tabela 8: Table 9: Number of animals, mean (x) and standard deviation (σ) for number of piglets born alive (NBA), age at farrowing (AF), previous lactation length (PLL) and mean and mode for weaning to conception interval (WCI) in data sets DS1 and DS2 within farms Število živali, povprečje in standardni odklon za število živorojenih pujskov, starost ob prasitvi, dolžino predhodne laktacije ter povprečje in modus za poodstavitveni premor v nizih podatkov DS1 in DS2 po farmah 27 Number of records, mean and standard deviation for the number of piglets born alive (NBA), previous lactation length (PLL) and mean and mode for weaning to conception interval (WCI) by sow genotype and farm for data set DS2 Število meritev, povprečje in standardni odklon za število živorojenih pujskov (NBA), dolžino predhodne laktacije (PLL) ter povprečje in modus za poodstavitveni premor (WCI) po genotipu svinje po farmah v nizu podatkov DS2 28 Pedigree structure within farms

9 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 IX Tabela 9: Struktura porekla po farmah 30 Table 10: Representation of prepared data structure Tabela 10: Izsek iz pripravljenih podatkov 30 Table 11: Modelling of the fixed effects Tabela 11: Modeliranje sistematskih vplivov 32 Table 12: Tabela 12: Table 13: Tabela 13: Table 14: Tabela 14: Table 15: Tabela 15: Table 16: Coefficients of determination (R 2 ) and degrees of freedom (d.f.) for different models per farm Koeficienti determinacije (R 2 ) in stopnje prostosti (d.f.) za različne modele po farmah 41 Number of levels for mating season and service sire effect, degrees of freedom (d.f.) for model, coefficient of determination (R 2 ) and standard deviation (σ) on three farms Število nivojev za sezono pripusta in merjasca očeta gnezda, stopnje prostosti za model (d.f.), koeficient determinacije (R 2 ) in standardni odklon (σ) po farmah 41 Change in the coefficient of determination ( R 2 ) from the R 2 obtained with full model for individual effect per farm Sprememba koeficienta determinacije ( R 2 ) od koeficienta determinacije polnega modela za posamezne vplive po farmah 42 Estimates of regression coefficients with standard errors (SEE) for age at farrowing nested within parity class per farm Ocene regresijskih koeficientov in njihove standardne napake (SEE) za starost ob prasitvi po zaporednih prasitvah in farmah 45 Effect of weaning to conception interval (WCI) on litter size expressed as a deviation from day 5 per farm Tabela 16: Vpliv poodstavitvenega premora (WCI) na velikost gnezda kot odstopanje od petega dneva po farmah 49 Table 17: Tabela 17: Table 18: Tabela 18: Estimates of linear regression coefficient with standard errors (SEE) for lactation length per farm Ocene linearnih regresijskih koeficientov in njihove standardne napake (SEE) za dolžino laktacije po farmah 53 Comparison among sow genotypes on three farms Ocene razlik* med genotipi svinj s standardnimi napakami (SEE) po farmah 54

10 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 X Table 19: Estimates of (co)variance matrices with standard errors of estimate in the model with maternal additive genetic effect on three farms Tabela 19: Table 20: Ocene matrik kovarianc sa standardnimi napakami ocen v modelu z maternalnim aditivnim genetskim vplivom 55 Computational requirements in repeatability model (REP), multiple-trait model (MTM) and random regression model (RRM) with different order of Legendre polynomials (LG1 LG3) for DS1 and DS2 for farm B Tabela 20: Poraba računalniških kapacitet v ponovljivostnem modelu (REP), večlastnostnem modelu (MTM) in modelu z naključno regresijo (RRM) z različnim stopnjam Legendrovih polinomov (LG1 LG3) za nize podatkov DS1 in DS2 pri farmi B 56 Table 21: Tabela 21: Table 22: Tabela 22: Table 23: Tabela 23: Table 24: Tabela 24: Table 25: Tabela 25: Estimates of variance components and ratios of phenotypic variance for the number of piglets born alive by farms with repeatability model for data set DS2 Ocene komponent varianc in deleži fenotipske variance za število živorojenih pujskov po farmah v ponovljivostnem modelu za niz podatkov DS2 57 Estimated variance components with standard errors of estimates in multiple-trait model Ocene komponent variance in standardne napake ocen v večlastnostnem modelu 60 Estimates of direct additive genetic (above diagonal) and phenotypic correlations (below diagonal) by multiple-trait model for data set DS1 Ocene direktnih aditivnih genetskih (nad diagonalo) in fenotipskih korelacij (pod diagonalo) v večlastnostnem modelu za niz podatkov DS1 61 Estimates of common litter environmental (above diagonal) and residual (below diagonal) correlations by multiple-trait model for data set DS1 Ocene korelacij za skupno okolje v gnezdu (nad diagonalo) in za ostanek (pod diagonalo) v večlastnostnem modelu za niz podatkov DS1 62 Eigenvalues of estimated covariance matrices of random-regression coefficients with proportion (in parenthesis) of the total variability for random effects in data sets DS1 with different order of Legendre polynomials (LG1 LG3) Lastne vrednosti za ocenjene matrike kovarianc za naključne regresijske koeficiente z deležem (v oklepajih) v celotni varianci za naključne vplive v nizih podatkov DS1 za različne stopnje Legendrovih polinomov (LG1 LG3) 64

11 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 XI Table 26: Eigenvalues of estimated covariance matrices of random regression coefficients with proportion (in parenthesis) of the total variability for random effects in data sets DS2 with different order of Legendre polynomials (LG1 LG3) Tabela 26: Table 27: Tabela 27: Table 28: Tabela 28: Table 29: Tabela 29: Table 30: Tabela 30: Lastne vrednosti za ocenjene matrike kovarianc za naključne regresijske koeficiente z deležem (v oklepajih) v celotni varianci za naključne vplive v nizu podatkih DS2 za različne stopnje Legendrovih polinomov (LG1 LG3) 65 Estimated variance components and proportions in the phenotypic variation for NBA in random regression model with cubic Legendre polynomial for three farms in data set DS1 Ocene komponent variance in deleži v fenotipski varianci za model z naključno regresijo z uporabljenim Legendrovim polinomom tretje stopnje po farmah za niz podatkov DS1 67 Estimated variance components and proportions of phenotypic variation for NBA in random regression model with cubic Legendre polynomial for the three farms in data set DS2 Ocene komponent variance in deleži od fenotipske variance v modelu z naključno regresijo z uporabljenim Legendrovim polinomom tretje stopnje po farmah za niz podatkov DS2 71 Estimates of direct additive genetic (above diagonal) and phenotypic correlations (below diagonal) by RRM for data set DS2 Ocene direktnih aditivnih genetskih (nad diagonalo) in fenotipskih korelacij (pod diagonalo) v modelu z naključno regresijo v nizu podatkih DS2 75 Estimates of residual common litter environment (above diagonal) and permanent environment correlations (below diagonal) by RRM for data set DS2 Ocene korelacij za skupno okolje v gnezdu (nad diagonalo) in za permanentno okolje (pod diagonalo) v modelu z naključno regresijo v nizih podatkov DS2 77

12 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 XII LIST OF FIGURES p. Figure 1: Relationship between genotypes Slika 1: Razmerje med genotipi 9 Figure 2: Structure of random effects Slika 2: Struktura naključnih vplivov 18 Figure 3: Relative frequency of sows per common litter by farm Slika 3: Relativna frekvenca svinj na gnezdo po farmah 27 Figure 4: Slika 4: Figure 5: Slika 5: Figure 6: Slika 6: Figure 7: Slika 7: Figure 8: Slika 8: Figure 9: Slika 9: Averages and phenotypic variances for the number of piglets born alive by parity Povprečja in fenotipske variance za število živorojenih pujskov po zaporednih prasitvah 29 Relationship between age at farrowing and the number of piglets born alive nested within parity for farm B Povezava med starostjo ob prasitvi in številom živorojenih pujskov znotraj zaporedne prasitve na farmi B 43 Relationship between the age at farrowing and the number of piglets born alive nested within three parity class per farm Povezava med starostjo ob prasitvi inštevilom živorojenih pujskov znotraj razredov zaporedne prasitve po farmah 44 Estimates of the service sire effect on the number of piglets born alive for farm B Ocene za vpliv merjasca - očeta gnezda za število živorojenih pujskov na farmi B 46 The average number of piglets born alive and distribution of weaning to conception interval per farm Povprečno število živorojenih pujskov in porazdelitev poodstavitvenega premora po farmah 48 Parametrical function for description of relationship between weaning to conception interval and the number of piglets born alive Parametrična funkcija za opis povezave med poodstavitvenim premorom in številom živorojenih pujskov 50

13 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 XIII Figure 10: Estimates of mating season effect on number of piglets born alive per farm Slika 10: Ocene vpliva sezone pripusta na število živorojenih pujskov po farmah 52 Figure 11: Slika 11: Figure 12: Slika 12: Figure 13: Slika 13: Figure 14: Slika 14: Figure 15: Slika 15: Figure 16: Slika 16: Figure 17: Slika 17: Relationship between the number of piglets born alive and previous lactation length per farm Povezava med dolžino predhodne laktacije in številom živorojenih pujskov po farmah 53 Estimated genetic eigenfunctions from random regression model with cubic power for number of piglets born alive on farm B Ocenjene genetske lastne funkcije za Legendrov polinom tretje stopnje v modelu z naključno regresijo za število živorojenih pujskov na farmi B 66 Comparison of ratios in the phenotypic variance with random regression model (lines) and multiple-trait model (triangles) for data set DS1 over parities per farm Primerjave deležev od fenotipske variance v modelu z naključno regresijo (črte) in v večlastnostnem modelu (trikotniki) za niz podatkov DS1 po zaporednih prasitvah po farmah 69 Phenotypic variances and proportions of the phenotypic variance over parities with Legendre polynomials of the cubic power for the number of piglets born alive Fenotipske variance in deleži od fenotipskih varianc po zaporednih prasitvah z uporabljenim Legendrovim polinomom tretje stopnje za število živorojenih pujskov 72 Comparison of estimates for ratios in the phenotypic variance between data sets DS1 and DS2 per farm Primerjava ocen deležev fenotipske variance med nizi podatkov DS1 in DS2 po farmah 74 Genetic correlation for the number of piglets born alive between parities using RRM for farm B Genetske korelacije za število živorojenih pujskov med zaporednimi prasitvami v modelu z naključno regresijo za farmo B 76 Estimated breeding values for number of piglets born alive over parities for seven sires Napovedi plemenskih vrednosti za število živorojenih pujskov po zaporednih prasitvah pri sedmih merjascih 78

14 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 XIV Figure 18: Phenotypic averages for the number of piglets born alive over parities for seven sires Slika 18: Figure 19: Slika 19: Fenotipska povprečja za število živorojenih pujskov po zaporednih prasitvah pri sedmih merjascih 79 Deviations from the phenotypic average for the number of piglets born alive over parities for seven sires Odstopanja od fenotipskega povprečja za število živorojenih pujskov po zaporednih prasitvah pri sedmih merjascih 80

15 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, 2006 XV ABBREVIATIONS AND SYMBOLS AF BLUP d.f. DS GLM LGn MTM MMM NBA PLL REML RRM R 2 WCI L Age at farrowing Best linear unbiased prediction Degrees of freedom Data set General linear model Legendre polynomial of order n Multiple-trait model Mixed model methodology Number of piglets born alive Previous lactation length Restricted maximum likelihood Random regression model Coefficient of determination Weaning to conception interval Kronecker product Direct sum

16 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, INTRODUCTION Selection in pigs is conducted for many years to increase growth, carcass merit and sow productivity. After an efficient improvement of growth and carcass traits, commercial breeding programmes placed a great emphasis on improving reproductive traits for maternal breeds and lines. Many analyses confirmed that genetic advance in overall reproductive efficiency can be attained most effectively by selection for litter size. Litter size is relatively easy to measure, thus including this trait in a selection programmes is often warranted. Improvement of litter size in pigs through selection was considered a difficult task in the past. Reproductive traits were not included prominently in commercial breeding programmes in the past due to slow improvement by traditional selection techniques in contrast to growth and carcass traits. Low heritability, negative correlation between direct additive genetic and maternal effect, limited size of the nucleus population, expression only in females, and relatively late age of measurements, were the main reasons for slow improvement. From these reasons, selection for litter size was considered a long time as noneffective. On the other hand, existence of large direct additive genetic variance for litter size and availability of records on many relatives, provides possibility for successful selection on litter size. Dividing pig breeding programmes into specialized sire and dam lines resulted in a higher emphasis on selection for litter size in the dam lines. Worldwide, pig breeders actually proved that selection for litter size can be successful. An important step was the development in computer technology and use of the mixed model methodology (MMM). The use of the MMM has become a standard in most farm animal species to estimate dispersion parameters by residual maximum likelihood (REML) method and to predict breeding values of animals by best linear unbiased prediction (BLUP). It provides simultaneously estimates of genetic and environmental parameters, taking into account the relationship among animals. Although, selection for traits with low heritability often relies on use of molecular genetic, selection based on MMM and numerous measurements is still very powerful and cost effective. Litter size is a complex trait prenatally combined from the following components: ovulation rate, embryo survival, and uterine capacity. Postnatal litter size can be described as number of piglets born total, number of piglets born alive, and number of weaned piglets. Number of piglets at weaning is even of greater commercial importance than litter size at birth, but selection for it is impossible under conditions of crossfostering. High genetic correlation between number of piglets born and number of piglets born alive makes selection on only one of them sufficient. Selection for number of piglets born also increases number of stillborn piglets. Therefore, number of piglets born alive is the selection trait of choice in improvement of litter size in most breeding programmes. Number of piglets born alive is affected by numerous environmental and genetic factors and interactions between them. On large farms some effects were recorded. Data recording used firstly for management monitoring and for pedigree control. These data were also used for selection purposes. Data on sow fertility provide satisfactory description of effects for litter size and prediction of breeding values using MMM. Fixed part of the model for genetic evaluation of litter size includes often

17 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, effects as parity, different description of mating or farrowing season, service sire and breed of service sire, age at farrowing, and different reproductive intervals which affect litter size as well as overall efficiency of sow production. Most frequently used reproductive intervals are lactation length, weaning to conception interval, and farrowing interval. Beside direct additive genetic effect used for breeding value estimation, random part of the models for litter size also includes other genetic and environmental effects provided by data. Scientists in the area of animal genetics are trying to develop statistical models for litter size, that also include other genetic effects (additive maternal, paternal and non-additive genetic effect as dominance). In the past, these effects were not included in models, mainly because of small computer power and lack of general software packages. The most common used environmental effects are permanent and common litter effect. Genetic evaluation in litter size is in many countries based on repeatability model. Low genetic correlations between litter size in different parities is reason for use of multiple-trait analysis, although it is rarely used. In the recent period, study of random regression models in different areas of animal production increased. Random regression models are especially suitable for longitudinal traits that change over time. Litter size is measured more than once in a sow lifetime and can be consider as longitudinal trait too. There are ideas for using random regression model in modeling of discrete traits, where litter size belongs. The aims of thesis were: - to develop appropriate fixed part of the model for genetic evaluation for litter size, - to determine covariance functions for number of piglets born alive, - to estimate genetic and environmental parameters using a repeatability model, multiple-trait analysis and random regression and compare them, - to check possibility for using random regression in genetic evaluation of litter size.

18 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, LITERATURE REVIEW 2.1 SELECTION FOR LITTER SIZE Early experiments on selection for litter size were successful only marginally. Many of these experiments produced no significant genetic or phenotypic trends. Several selection methods were used. According to literature the method of independent culling level was mainly used. A certain level of litter size was established, and all individuals below that level were culled. Selection experiments based on an independent culling level in Sweden (Johansson, 1981) did not improve litter size in the period of twenty years. Short duration of experiments, small population sizes as well as existence of maternal effects, which may be negatively correlated to direct genetic effect, were reported as the reasons for non significant trend from direct litter size selection (Vangen, 1981). Little or no response have been also explained by a low heritability for litter size and a failure to achieve sufficient selection intensity (Ollivier, 1982), as well as by low genetic correlations between parities (Bolet et al., 1989). Results like these discouraged pig producers from including litter size in selection objectives. Thus, there was insufficient selection pressure on litter size in breeding herds until the late 1980s. Selection index method implemented by Hazel (1943) presents the overall net merit of the individual considering several traits of economic importance. It provided a superior selection criterion compared to other forms of selection including single trait selection and multiple-trait selection via independent culling level used before. Litter size has been included to selection index since the 60 s. In the middle of the 1970 s in USA, litter size started to improve using Sow Productivity Index which included the number of piglets born alive and 21 day litter weight. In gilts, Neal and Irvin (1992) achieved a difference of 1.43 liveborn piglets between the select and control line after ten generations of selection on Sow Productivity Index. Family selection was introduced in the dam lines to select for litter size (Avalos and Smith, 1987; Haley et al., 1988) by the end of the 80 s. Family selection was a selection method where superior families rather than superior individuals were chosen for breeding. High rate of genetic improvement was expected theoretically selecting on family index (Avalos and Smith, 1987). In a deterministic study, they showed that given a heritability of 0.10 and the use of all family information in selection, an improvement of litter size of 0.50 piglets per year could be expected. Indirect selection on litter size was studied for the ovulation rate, embryonic survival, and uterine capacity. Selection for ovulation rate resulted in a correlated increase in litter size, and the obtained difference was maintained during a period of relaxed selection (Cunningham et al., 1979). Nine generations of selection for higher ovulation rate were followed by two generations of random selection and then eight generations of selection for increased litter size at birth, decreased age at puberty, or continued random selection in the high ovulation rate line (Lamberson et al., 1991). Estimate of response to selection for litter size was 1.06 piglets per litter (P<0.01) with regression on generation number, and 0.48 piglets per litter with animal model. Cumulative response in litter size to selection for the ovulation rate and then litter size was 1.8 and 1.4 piglets per litter estimated by the two methods. Johnson and Cassady (1998) attempted to improve litter size with ten generations of index

19 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, selection for increased ovulation rate and embryonal survival followed by one generation of random selection and three generations of litter size selection. Response at end of the experiment was 1.2 piglets born alive (P<0.05). Gama and Johnson (1993) reported selection response of one piglet after eight generations of selection for litter size, following selection on ovulation rate. The conclusion was that selection for ovulation rate would improve litter size, but selection was very inefficient as only 20 to 30 % of the increase in ovulation rate was expressed in litter size (Gama and Johnson, 1993). Furthermore, these selection experiments require expensive investments of time and equipment, and are not practical for most selection programmes (Johnson, 1992). Hyperprolific selection scheme was an effective way of improving litter size. Legault and Gruand (1976) proposed to use large-scale computerized recording systems in order to identify exceptionally prolific sows, so called hyperprolific sows. By repeated backcrosses to hyperprolific sows, the genetic merit of their boar progenies was progressively raised to the level of the dams. The selection scheme has been successfully applied to the French Large White population (Bidanel et al., 1994). In a hyperprolific Large White experimental herd, the average litter size of hyperprolific sows exceeded the normal Large White contemporaries by 2.6 piglet per litter born and 1.5 piglet per litter born alive. Although the experiment resulted in an initial increase on the female side of one piglet, continuous screening of hyperprolific females was less effective because multiplication phase took many generations to obtain a sizable population of descendants to start a new round of intense selection (Avalos and Smith, 1987). Therefore, hyperprolific selection scheme can be useful for setting up a nucleus herd from a previously unselected population, but not for achieving high continuous response. Overall annual genetic gain was much smaller, because of backcrossing. Noguera et al. (1998) showed that selection for litter size could be successful, if a hyperprolific breeding scheme and mixed model methodology were combined. The average estimated difference between selected and control line was 0.57 piglets born alive (P<0.05) in favour of line selected for prolificacy. Bolet et al. (2001) reported about selection experiment on litter size for seventeen generation. Selection was performed for eleven generations in a closed line, and after that period, the selected line was opened to gilt daughters of hyperprolific boars and sows. After eleven generations of selection in a closed line, response in litter size was not significant. The total genetic gain of about 1.4 piglets per litter at birth was a consequence of migration (0.8 piglets per litter) and a within-line selection (0.6 piglets per litter). Mixed model methodology in litter size has been used since the late 80 s due to improved knowledge of quantitative genetics and computer development. Application of mixed model methodology using residual maximum likelihood method and best linear unbiased predictor was an important step, resulted in clear genetic progress for litter size in dam lines. In their theoretical study Belonsky and Kennedy (1988) have pointed out that higher genetic trends could be obtained by using mixed model methodology with animal model than traditional selection index procedures, especially for traits with low heritability as litter size. In a closed pig herd, response to selection on best linear unbiased predictor was greater than selection on phenotype selection by 55 % (without additional culling) to 81 % (with additional culling). Similar results were also obtained by Sorensen (1988). Selection response

20 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, for a single trait with heritability of 10 % was up to 25 % smaller in selection index than in animal model. Smaller response using selection index in relation to response obtained with animal model Sorensen (1988) assigned to the sources of bias introduced in the construction of the selection index owing to genetic trend and the smaller accuracy of the selection index relative to animal model. Lofgren et al. (1994) obtained an increase of approximately 0.1 liveborn piglets per litter per year in the period from 1987 to Genetic response after nine generations of selection estimated breeding value for the number of piglets born alive using the animal model differed by 0.08 piglets/year between the control and selected line (Holl and Robison, 2002). The result was 0.12 piglets per year in phenotypic trend. 2.2 FACTORS AFFECTING LITTER SIZE IN PIGS Many environmental and genetic factors, as well as complex interactions between them, influence litter size in pigs. They could be arranged into two major groups (Clark and Leman, 1986a). The first group includes factors which are often recorded by commercial pig producers and contains effects like parity, sow breed or genotype, age at farrowing, lactation length, weaning to conception interval etc. The data were used for management and selection purposes. The second group includes factors such as husbandry practices, nutrition, and diseases. Although they are very important, data on these factors are not always available and often cannot be evaluated Age at farrowing Age at farrowing can be described in two different ways: chronologically and physiologically. Chronological age is expressed by age in days, months, or years, while physiological age is used to indicate maturation process. In gilts, it is expressed by the number of oestruses before the first mating, while in sows by parities. In gilts, litter size increases with age at the first mating. The relationship is explained as a consequence of higher ovulation rate in later oestruses (Brooks and Smith, 1980). More recently, results by Tummaruk et al. (2001) showed that a 10 day increase in age at first mating in gilts resulted in an increase (P<0.001) of about 0.1 piglet born alive. In the same study, they also reported the effect of age at first mating on litter size in higher parities. A 10 day increase in age at first mating resulted in a decrease (P<0.05) in litter size in sows in parities 4 and 5. Usually, the second or third oestrus is prefered for the first mating of gilts what coincides with age at first mating between 210 and 240 days. Clark et al. (1988) reported that age at conception did not influence litter size after 245 days of age. In other words, litter size in gilts was increasing up to one year. Later, litter size had a tendency to be on the same level or was slowly decreasing. Southwood and Kennedy (1991) showed a significant increase in litter size for 0.18 piglets per month. Although age at farrowing had a significant influence on first parity litter size, Culbertson and Mabry (1995) stated that benefit in increased litter size greatly decreased in the second parity and was non-existent in any later parities.

21 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, In sows, litter size changes with parity. After the first parity, it increases gradually to a maximum in the third to fifth parity and slowly decreases through higher parities (Koketsu and Dial, 1997; Tummaruk et al., 2000a). Lower ovulation rate and smaller uterine capacity in gilts (Gama and Johnson, 1993) as well as the fact that gilts and younger sows are more sensitive to environmental factors (Clark et al., 1988) than older sows are the possible reasons for smaller litter size in the first few parities. Changes in ovulation rate and uterine capacity with increasing parity (Gama and Johnson, 1993) and sow ageing may have contributed to the parity influence on litter size. Decrease in litter size was especially noticed after the seventh parity (Koketsu and Dial, 1997). Investigation of late parity decline in litter size would be of great importance in order to determine culling policy and give a possibility for selection on the persistency of litter size. The combination of age at farrowing and parity is the way to present interaction between these two effects. Age at farrowing and parity cointeract, especially in the first litters. Differences in the age when gilts reach puberty, as well as pregnancy failure in gilts and sows result in considerable variation in the age of sows within parity. Because of the wide range of possible ages within parity and the fact that litter size depends on age, there is a suggestion to combine those two effects. Interaction of age at farrowing and parity was presented in the study of Tribout et al. (1998) and Marois et al. (2000) Lactation length and weaning to conception interval Lactation length is one of the effects determined by management. In large scale farms lactation lasts mainly between three and four weeks. This is a sufficient period for uterine involution to be completed. Lactation length of less than 21 days is related to incomplete involution of the uterine endometrium and higher embryo mortality (Varley and Cole, 1976). Lactation length influence litter size at the subsequent parity. Shorter lactation is associated with a smaller litter size at the subsequent farrowing (Xue et al., 1993; Dewey et al., 1994). Tantasuparuk et al. (2000) reported no significant effect of lactation length on subsequent litter size in tropical conditions. As possible reasons they referred to a low variation in lactation length and lower reproductive efficiency under tropical climate conditions. Babot et al. (1994) reported increase of litter by 0.03 to 0.04 piglets born alive for each day of previous lactation length. Those results are in agreement with results by Xue et al. (1993). Smaller regression coefficient was obtained in study from Logar et al. (1999). Higher estimates were found in studies where records with short lactation length were excluded from analysis. Kovač et al. (1983) got an increase of piglets per litter per day when records with lactation length under 18 days were discarded. Marois et al. (2000) noticed that a linear regression on previous lactation length could predict litter size well, except in case of lactation length shorter than 7 days. Acceptance of recent directives of the European Communities (EC No 316/ , 2001) that order a minimum length of lactation of 28 days on large farms could decrease adverse effect of very short lactation on litter size. On the other side, sows with lactation length longer than 28 days in inappropriate physiological state (exhaustion) due to suboptimal nutrition and increased requirements for milk production could be the reason for smaller litter size in subsequent parity.

22 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, Weaning to conception interval has an obvious influence on the subsequent litter size. Fahmy et al. (1979) reported an increase in litter size as the weaning to conception interval increased. They stated that there is a progressive increase in litter size with the delay of oestrus after 7 days. Babot et al. (1994) and Logar et al. (1999) assumed that the effect of previous weaning to conception interval on litter size is linear and the found linear regression coefficient ranged between and On the other hand, Dewey et al. (1994) found that relationship between previous weaning to conception interval and litter size can be presented with U - shaped curve with litter size at a minimum for sows conceiving at 7 to 10 days after weaning. More recent study by Marois et al. (2000) also showed that the effect is curvilinear with lowest litter size for previous weaning to conception interval between 7th to 10th day and can not be accommodated by linear, quadratic regression or any other common regressions. The specific U - shaped curve obtained using segmented polynomials Marois et al. (2000) explained by the following hypothesis. Sows with the shortest weaning to conception interval are those that show oestrus most quickly after weaning because they are in a good nutritional and physiological state (ten Napel et al., 1995). Because of a good state, they have larger litter size than sows conceiving later. The lowest litter size for previous weaning to conception interval between 7 to 10 days could be because these litters arise from late oestrus in sows in a poorer physiological state. Furthermore, the decrease of litter size could be a consequence of inappropriate management (Kemp and Soede, 1996). Mating in a suboptimal mating time resulted in a smaller litter size (Nissen et al., 1997). At still longer weaning to conception interval, larger litter sizes could be explained by conception at the second oestrus, which was generally recognized to give larger litter size than conception at the first oestrus. Tummaruk et al. (2000b) showed the difference in litter size between sows with a fourth day weaning to service interval and those mated on a tenth day after weaning. They also reported that litter size increased as weaning to service interval increased from 10 to 20 days. Weaning to conception interval decreases with the previous lactation length increase. Clark and Leman (1984) found that early weaning of piglets had no effect on subsequent litter size when the weaning to conception interval was greater than 14 days. However, when weaning to conception interval in those sows was less than 14 days, litter size reduced by 0.1 piglets per each day between the weaning age of 21 and 28 days. These findings showed the effects of lactation length on litter size are likely to be influenced by weaning to conception interval and, in order to avoid bias, previous lactation length and weaning to conception interval should be considered together (Clark and Leman, 1986b) Season Season effect on litter size is mainly presented as the effect of mating or rarely as farrowing season. The effect of season on litter size usually explains two sources of variation. Firstly, there are longterm changes as a consequence of better environment, management, and selection. Secondly, litter size oscillates due to short-term changes usually related to climate, as well as changes in technology

23 Doctoral Dissertation. Ljubljana, Univ. of Ljubljana, Biotechnical Faculty, Zootechnical Department, practices and other unknown sources of variation. The effect of season connected with climate can be divided into the effects of photoperiod and temperature as reviewed by Clark and Leman (1986a). The effects of photoperiod on litter size have not been adequately studied and often confounded with other effects. Better known is temperature effect. The effect of mating season on litter size is controversial. In many parts of the world, seasonal variation in pig herds is characterized in some cases by a decrease in litter size during some part of the year. Increased ambient temperature at mating time on commercial farms in warm temperate climatic zone in Australia showed to cause embryonic mortality (Love, 1979). The study by Paterson et al. (1978) when mean daily maximum temperature exceeded thermoneutral temperature suggested that heat stress imposed during early pregnancy caused loss of all embryos and the sow return to oestrus. Therefore, litter size of sows conceived during summer was not significantly different from sows conceiving at other seasons. In a temperate climate in Sweden, Tummaruk et al. (2000a) also reported no seasonal variation of litter size during three year period. On the other hand, Koketsu and Dial (1997) detected small litters in sows mated in hot summer months in southern Minnesota (USA). Effect of season or more specifically, ambient temperature on litter size may be partly confounded by other effects, for example by effect of prolonged weaning to conception interval. Britt et al. (1983) stated that sows which weaned in summer took longer to return to oestrus than sows which weaned at other seasons. In addition, sows during summer had shorter interval from onset of oestrus to ovulation and higher possibility to fail optimal mating time (Kemp and Soede, 1996). Therefore, inappropriate mating time could be the reason for smaller subsequent litter size of these sows (Nissen et al., 1997). On the other hand, Love (1979) showed that first parity sows which mated 12 days after weaning produced one piglet per litter more than sows with shorter weaning to conception interval. The negative effect of heat stress on litter size in commercial herds may be confounded with the positive effect of a delayed return to oestrus. Malovrh et al. (1996) found significant influence of month year interaction on litter size at birth under Slovenian condition. Changes in litter size with season were not periodical, which suggested that causes for those changes could be additional environmental factors, such as nutrition, management etc Genotype Genotype usually presents the effect of breed and/or crosses. In general, genotype affects litter size because all functions of the body are under genetic control to a greater or lesser extent. It seems obvious that all mechanisms which determine reproductive efficiency are directly influenced by genetics (Clark and Leman, 1986b). Some breeds have better reproductive performance than others (Rothschild and Bidanel, 1998; Tummaruk et al., 2000a), although differences within breed also exist (Table 1). Some local as well as terminal breeds have usually smaller litter size. The largest litter size was found in some Chinese breeds. Well known Chinese breed Meishan has on average 3 to 4 piglets at farrowing more than commercial modern breeds (Bidanel, 1990). Crossbred sows have larger litter