The objective of this study was to estimate genetic parameters and phenotypic parameters of egg production curve, using the segmented polynomial model( " x p " - the peak age of the birds in attitude, "P" - at peak production level, "s" - rate of decline in weekly egg production after peak, and "t" - time between the onset of lay and peak egg production). We used data from the weekly egg production from 25 to 64 weeks of age from 2,398 arrays of a lineage of broilers chickens. Estimation of covariance components, heritability and correlations for these parameters curve posture were obtained by restricted maximum likelihood. Genetic trends were estimated with the average breeding values the of parameters of the curve as a function of birth year of the arrays. The mean heritabilities were low to medium magnitude, 0.25 (x p), 0.18 (P), 0.17 (s) e 0.10 (t). Genetic correlations among the parameter "t" and the other parameters of the curve were positive ranging from 0.21 to 1.00, being lower between "t" and "s", and higher between the parameters x p and t. Between the parameters x p and P the correlation was also positive, of an average magnitude (0.39). Correlations were negative between parameters "s" and "x p", and "s" and "P", presenting itself lower between "s" and "x p" (-0.17) and higher between "s" and "P" (-0.91). The genetic trends found for the parameters of the model indicated a reduction in time between the production's onset and peak, and age at production's peak. The level of production showed a decline in breeding value over the period evaluated. It can be observed a potential genetic gain for the egg's production parameters' curve; however, it must be paid special attention to the positive genetic correlations between the parameter x p and P. What can lead to an increase in the level of production and may lead to an increase in age at peak production. The same applies to the parameters x p indicating that birds with earlier peaks may present lower persistence.
curve posture; segmented polynomial; regression non linear
