A model for individual egg production in chickens

Our primary objective was to improve on an existing model for the individual weekly egg production curve by modeling the curve as a sum of logistic functions: one for the increasing phase of production and a sum for the decreasing phases. To illustrate the model, we used four data sets from two pairs of individuals. For these data, the model consisted of an increasing phase and a single decreasing phase of production: y(t) = m k1((1 - e(-t))/(1 + e(-t))) - m(k1 - k2)((1 - e(-t))/(1 + e(-(t-c2)))) where y(t) is egg production at week t, m is maximum production during a specific time interval, k1 is proportion of maximum production for the increasing phase, k2 is proportion of maximum production for the decreasing phase, and c2 is point of inflection from the upper level of the increasing phase to the lower level of the decreasing phase; thus, c2 is a measure of persistency of egg production. For one pair of individuals, production was about 88% of maximum (k1) for the increasing phase and about 76% of maximum (k2) for the decreasing phase. For the other pair, production was about 91% of maximum (k1) for the increasing phase and about 75% of maximum (k2) for the decreasing phase. Persistency (c2) was about 25 wk for one pair and about 28 wk for the other. Predicted total 52-wk production was within one or two eggs of actual production. The secondary objective was to improve estimation of model parameters by summarizing egg production data by 1-wk, 2-wk, or 4-wk intervals and by using cumulative egg production instead of weekly production. For weekly production, estimates of parameters changed only slightly, as intervals increased from 1 wk to 2 wk or to 4 wk. Predicted total 52-wk production, however, decreased up to five eggs as interval increased from 1 wk to 4 wk. For cumulative egg production by time t, Yt, the model was Yt = 7 k1[2 Ln((1 + e(t))/2) - t] - 7(k1 - k2)[(1 + e(-2)2) Ln((e(c2) + e(t))/(1 + e2c)) - te(-c2)]. For cumulative production, estimates of parameters changed only slightly, if at all, as intervals increased from 1 wk to 4 wk. Predicted 52-wk production, however, approached the actual number as interval increased from 1 wk to 4 wk. Prediction of annual (52-wk) egg production based on part-record production for only the first 22 wk might lead to over-prediction because persistency of production lasted longer than the part record. Genetic gain from selection to improve annual production, therefore, might be increased if selection accounted for persistency of production and for the multiphasic shape of the individual egg production curve, and if data were summarized by 4-wk intervals and cumulated.