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Egg production curves describe the laying patterns of hen populations over time. The objectives of this study were to fit the weekly egg production rate of selected and nonselected lines of a White Leghorn hen population, using nonlinear and segmented polynomial models, and to study how the selection process changed the egg-laying patterns between these 2 lines. Weekly egg production rates over 54 wk of egg production (from 17 to 70 wk of age) were measured from 1,693 and 282 laying hens from one selected and one nonselected (control) genetic line, respectively. Six nonlinear and one segmented polynomial models were gathered from the literature to investigate whether they could be used to fit curves for the weekly egg production rate. The goodness of fit of the models was measured using Akaike's information criterion, mean square error, coefficient of determination, graphical analysis of the fitted curves, and the deviations of the fitted curves. The Logistic, Yang, Segmented Polynomial, and Grossman models presented the best goodness of fit. In this population, there were significant differences between the parameter estimates of the curves fitted for the selected and nonselected lines, thus indicating that the effect of selection changed the shape of the egg production curves. The selection for egg production was efficient in modifying the birds' egg production curve in this population, thus resulting in genetic gain from the 5th to the 54th week of egg laying and improved the peak egg production and the persistence of egg laying.

We estimated genetic parameters for egg production in different periods by means of random regression models, aiming at selection based on partial egg production from a generation of layers. The production was evaluated for each individual by recording the number of eggs produced from 20 to 70 weeks of age, with partial records taken every three weeks for a total of 17 periods. The covariance functions were estimated with a random regression model by the restricted maximum likelihood method. A model composed of third-order polynomials for the additive effect, ninth-order polynomials for the permanent environment, and a residual variance structure with five distinct classes, was found to be most suitable for adjusting the egg production data for laying hens. The heritability estimates varied from 0.04 to 0.14. The genetic correlations were all positive, varying from 0.10 to 0.99. Selection applied in partial egg production periods will result in greater genetic profit for the adjacent periods. However, as the distance in time between periods increases, selection becomes less efficient. Selection based on the second period (23 to 25 weeks of age), where greater heritability was estimated, would note benefit the final egg-laying cycle periods.

The objectives of this paper were to identify the phenotypic egg-laying patterns in a White Leghorn line mainly selected for egg production, to estimate genetic parameters of traits related to egg production and to evaluate the genetic association between these by principal components analysis to identify trait(s) that could be used as selection criteria to improve egg production. Records of 54 wk of egg production from a White Leghorn population were used. The data set contained records of the length:width ratio of eggs at 32, 37, and 40 wk of age; egg weight at 32, 37, and 40 wk of age; BW at 54 and 62 wk of age; age at first egg; early partial egg production rate from 17 to 30 wk and from 17 to 40 wk of age; late partial egg production rate from 30 to 70 wk and from 40 to 70 wk of age; and total egg production rate (TEP). The estimates of genetic parameters between these traits were estimated by the restricted maximum likelihood method. Multivariate analyses were performed: a hierarchical cluster analysis, a nonhierarchical clustering analysis by the k-means method of weekly egg production rate to describe the egg-laying patterns of hens, and a principal components analysis using the breeding values of all traits. The highest heritability estimates were obtained for BW at 54 wk of age (0.68 ± 0.07) and age at first egg (0.53 ± 0.07). It is recommended that a preliminary clustering analysis be performed to obtain the population structure that takes into account the pattern of egg production, rather than the TEP, because hens may have the same final egg production with different patterns of egg laying. Early partial production periods were not good indicators for use in improving total egg production because these traits presented an overestimated genetic correlation with TEP because of the part-whole genetic correlation component. Egg production might be improved by selecting individuals based on TEP.