Genetic parameters for various random regression models to describe total sperm cells per ejaculate over the reproductive lifetime of boars

The objective of this study was to model the variances and covariances of total sperm cells per ejaculate (TSC) over the reproductive lifetime of AI boars. Data from boars (n = 834) selected for AI were provided by Smithfield Premium Genetics. The total numbers of records and animals were 19,629 and 1,736, respectively. Parameters were estimated for TSC by age of boar classification with a random regression model using the Simplex method and DxMRR procedures. The model included breed, collector, and year-season as fixed effects. Random effects were additive genetic, permanent environmental effect of boar, and residual. Observations were removed when the number of data at a given age of boar classification was < 10 records. Preliminary evaluations showed the best fit with fifth-order polynomials, indicating that the best model would have fifth-order fixed regression and fifth-order random regressions for animal and permanent environmental effects. Random regression models were fitted to evaluate all combinations of first-through seventh-order polynomial covariance functions. Goodness of fit for the models was tested using Akaike's Information Criterion and the Schwarz Criterion. The maximum log likelihood value was observed for sixth-, fifth-, and seventh-order polynomials for fixed, additive genetic, and permanent environmental effects, respectively. However, the best fit as determined by Akaike's Information Criterion and the Schwarz Criterion was by fitting sixth-, fourth-, and seventh-order polynomials; and fourth-, second-, and seventh-order polynomials for fixed, additive genetic, and permanent environmental effects, respectively. Heritability estimates for TSC ranged from 0.27 to 0.48 across age of boar classifications. In addition, heritability for TSC tended to increase with age of boar classification.