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According to two properties of the life cycle and to fluctuation with parities, four mathematical models, the Poisson cycle model, the cubic polynomial model, the modified quadratic polynomial modelⅠ and the modified quadratic polynomial model-Ⅱ,were used to fit the records of litter size in Jiangquhai sows. From the viewpoint of statistics and biological significance, the modified quadratic polynomial model-Ⅰ was found to be the optimum model. A single trait animal model and DFREML procedures were further used to estimate the heritability values of optimum model parameters. The results show that the heritability values for the coefficients A and B and the heritability value for the acme of the model pure quadriccurve are larger than the heritability value for the litter size. This suggests that selection for model parameters may be more effective than direct selection for litter size.