Analyses of mathematical models for Yangzhou geese egg-laying curves.

Mathematical models of the egg-laying curves for Yangzhou geese exposed to both natural and artificial photoperiods were established to optimise the parameters for maximising geese reproductive performance and for the development of precision feeding methods. With the natural photoperiod, egg-laying starts in autumn when daily photoperiod decreases, but accelerates after the winter solstice, and reaches the peak in spring when photoperiod increases. An accumulating model was constructed based on the hypothesis that the egg-laying capacity of geese was determined by two components of the photoperiod: photo-stimulation and photo-inhibition. In addition, a second segmented model was constructed based on the hypothesis that the photo-stimulation only occurred with lengthening photoperiods after the winter solstice, and the lesser laying rate in autumn could be attributed to the non-photo-dependent animal-husbandry technologies. This model consists of a logistic model before the winter solstice, and an accumulating model after this solstice. The use of the logistic and accumulating resulted in more precise predictions that occurred with use of Model 1 with a greater R and lesser RMSE, AIC and BIC. Likewise, the egg-laying curves when there was consideration of artificial photoperiods could also be constructed with consideration of stimulatory and inhibitory photoperiodic effects. The model consists of an initial logistic and subsequently a quadratic polynomial model. With use of this model, there is consideration of changes in egg-laying patterns when there is a fixed photoperiod, with the model parameters reflecting the effects by photoperiod control-programs and age of the geese. In conclusion, new mathematical models have been developed to best fit egg-laying curves when there are both natural and artificial photoperiods. These models can contribute to development of precision-feeding technologies for breeding geese in future.