Genetic evaluation of laying hens under fixed regression animal models

Monthly egg production in laying hens was studied under fixed regression models. The data of 37071 birds from three strains under long term selection were analysed. The covariates from four production curves were included in nested and non-nested form. From linearized functions the model of Ali and Schaeffer most adequately described the egg production. Akaike Information Criterion favoured models with nested covariates. The following genetic parameters were estimated: heritability 0.02-0.2, 0.03-0.06, 0.03-0.20 repeatability 0.11-0.23, 0.21-0.30, 0.34-0.43 for A22, A88 and K66 lines, respectively. In conclusion, regression models could be considered in genetic evaluation of laying hens.


Introduction
In XX th century genetic evaluation of laying hens on egg production was usually based on single measurement-cumulative production.Such an approach was recommended due to simplicity and relatively small computing demands.However, egg production is a trait that is expressed over a long trajectory of time and as such undergoes both genetic and environmental effects.Knowledge about the patterns of egg-laying might contribute to more accurate prediction of genetic effects.There are several studies on monthly egg production reporting genetic parameters (ZIĘBA, 1990;PREISINGER and SAVAS, 1997;SAVAS et al., 1998;ANANG et al., 2000;NURGIARTININGSIH et al., 2002NURGIARTININGSIH et al., , 2005)).In the last years the rapid development of regression methodology is observed.It provides a tool to analyse longitudinal records in animal breeding that reveal specific patterns of change over a trajectory.Regression models have already been implemented in dairy cattle breeding programs (SCHAEFFER et al., 2000, AMIN 2001), but their possible advantages, like higher accuracy of selection, the use of information on course of traits, and the possibility to change course of trait through selection have been also suggested for other farm animals like pigs (HUISMAN, 2002) and sheep (HORSTICK and DISTL, 2002).It is well known, that although it is not steady process over time, egg production in poultry shows a regularity, that is generally denoted as the egg production curve, especially when summarised on a weekly or monthly basis in a group of hens (YANG et. al., 1989).To describe trajectory of production curves over time many regression models have been suggested (JAMROZIK et al, 1997).An average egg production curve can be included as the fixed or random part of the model.In second case, the individual genetic curve is estimated for each bird.Using such approach the birds with most desired laying trace can be selected.The biologically meaningful curve parameters like persistency or decreasing slope can be directly selected for.The objective of this study was to estimate genetic parameters of monthly egg production under fixed regression model.Goodness of fit of some egg production curves was examined as well.

Material and methods
The laying performance data of three lines (denoted as A22, A88 and K66) from Poultry Research Branch at Zakrzewo were analyzed.Birds were kept in single cages with environmental factors e.g.light, temperature, humidity, and feeding automatically controlled according to standard schedules.Altogether 37071 hens (13770 of A22, 13950 of A88 and 9351 of K66) were recorded in six generations.From crossbreeding perspective two of the lines (A22 and A88) are maternal -Rhode Island White lines selected on egg production and shell colour.The third line (K66) is a paternal Rhode Island Red line selected on egg weight and shell colour.Brief statistical description of the analyzed populations was given on Figure 1.
As the lines were purebreds the data was analyzed within lines.The daily records were cumulated into monthly production from fixed day of minimum 5% egg production in given line.The analysis was performed based on two classes of fixed regression animal models.First group models can be noted as follow: where: y ijkl is a number of eggs per month within hatch period -generation (year) group for the k-th layer, HY i is a fixed effect of hatch period -year group, f(x) i -fixed effect of consecutive month (included as respective egg production curve -see below); a k is a random additive genetic effect; p k is a random permanent environmental effect, e ijkl is a residual effect connected with ijkl-th observation.
Second class of models included covariates nested within hatch period -year groups.Thus: where: HY[f(x) j ] i is the fixed effect of covariate nested within hatch period -year group, y ijkl , a k , p k and e ijkl -as above.
Goodness of fit of the models was checked by Akaike Information Criterion (AKAIKE, 1977).Variance components were estimated by the use of the Average Information Restricted Maximum Likelihood algorithm (JOHNSON and THOMPSON, 1995) where y is the production in time x, a, b, c, d, e are the parameters estimated in the models.
Curves were compared based on the adjusted coefficient of multiple determination (R a 2 ), which indicates which part of sum of squares can be eliminated by using multiple regression equation with adjustment for the number of parameters in the model (SHERROD, 1998) and Durbin-Watson statistics (D-W), which is used to test for the presence of the first-order autocorrelation in the residuals of a regression equation (JENSEN, 2005).The NLREG program (SHERROD, 1998) was used to asses goodness of fit of the curves.

Results
Average egg production curves were shown on Figure 2. K66 line showed the most desired shape of the egg production curve with the peak production of 91.2% achieved already in the second month of lay and the highest persistency (both defined as number of weeks in which the highest production is maintained or as the decreasing slope after the peak).The highest peak production 92% was recorded in A22 line in the third month of lay however due to faster decrease after the peak this line showed lower overall production.The egg production curve of A88 line was similar to the other Road Island White line with slightly lower production level.Goodness of fit criteria for the chosen mathematical models were included in Table 1.Except for the Wilmink's function the adjusted coefficient of multiple determination was about 0.9.Slightly worse performance of Wilmik's curve results from the fact that it has only three parameters to describe the data.For K66 line the curves, except for Yang's model, did not follow the rapid increasing phase at the beginning of production.
Because the Yang's function can not be linearized it was not used as a part of regression models.Heritability estimates were listed in Table 2. Generally, the heritability of egg production in the studied populations was low.It ranged from 0.02 to 0.1, 0.02 to 0.06, 0.03 to 0.2 for A22, A88 and K66 lines, respectively.From the groups of models Akaike Information Criterion favours the models with covariates nested within hatch-year classes (see Table 3).The lowest error variance was also found in this class of models.In all classes of models function of Ali and Schaeffer outperformed other models and resulted in the highest heritability estimates.It can be noticed that for models ignoring hatch-year effects the highest heritability was estimated however they were characterised by lower adequacy.It can be explained by the fact that part of variance resulting from differences between generations was in these models attributed to genetic progress.The repeatability was relatively high comparing to heritability and reached the value of 0.43 in K66 line.Repeatability was stable between classes of models but it was consistently lower for models using regression of Wilmink.It confirms worse fit of Wilmink's model to describe egg production.For models including hatch-year effect similar heritability was obtained for the analyzed populations, whereas ignoring of this effect resulted in higher estimates for K66 line.For all models repeatability was the highest in K66 line and the lowest in A22 line.
Discussion Fixed regression models with nested covariates have been suggested for evaluation of test day yields in dairy cattle by PTAK and SCHAEFFER (1993) as they take into account the differences in shape of production curve between groups of animals.They have been successfully implemented in routine genetic evaluation of milk production in Canada and Germany (SWALVE, 2000).In Canada they became a step towards implementation of random regression models for national evaluation.Fixed regression models were proved to be efficient in exploiting the information from part-production data (MRODE et al., 2002).The study continues the research obtained under repeatability and cumulative models on the same data set (WOLC, 2006).Low heritability (h 2 <0.2) was estimated.Low heritability of egg production under fixed regression models was also reported by ANANG et al. (2001).The estimates for initial egg production or longer periods vary across populations (SZWACZKOWSKI, 2003).For instance, WEI and VAN DER WERF (1993) reported heritability exceeding 0.5 for one of the studied lines.Some authors (WEI and VAN DER WERF, 1993;PRESSINGER and SAVAS, 1997) concluded that estimates of h 2 decreased with consecutive periods of egg production.The study confirmed the results of ANANG et al. (2001) who found that monthly models with nested covariates produced slightly higher estimates of heritability than those obtained from the models with non-nested covariates and the model without covariates.So far there are only a few publications reporting genetic parameters of egg production based on the concept of test day record analysis in dairy cattle.However, the achievements in statistical methodology could possibly improve the accuracy and efficiency of selection in laying hens and might become next step in evolution of poultry evaluation (BEAUMONT and CHAPUIS, 2004).In general, all mathematical models (used for description of egg production over time) lead to satisfactory approximation of real egg production for three studied lines.However, it should be stressed that Ali-Schaeffer function is most adequate.It corresponds with some studies on lactation curves (KISTEMAKER, 1997;PTAK, 2004).On the other hand, from numerical perspective (number of estimated parameters), the function is more computationally demanding compared to other ones.It was concluded the heritability and repeatability estimates were relatively low, except for results obtained by model without hatch-year effect for K66.The models with nested covariates were most adequate.Whereas the Ali-Schaeffer function better described the egg production compared to other curves studied.In general, the regression model methodology can be recommended for genetic evaluation in laying hens.

Table 1
Adequacy of chosen mathematical models to describe egg production in the studied populations (Güte der verglichenen mathematischen Modelle hinsichtlich der dargestellten Eierleistungen)

Table 2
Genetic parameters of monthly egg production in the studied populations (Genetische Parameter der monatlichen Eiproduktion bei den drei Selektionslinien)