Nonlinear genetic relationships between traits and their implications on the estimation of genetic parameters.

To estimate nonlinear genetic relationships between traits, formulas based on the paternal halfsib analysis theory were derived. To illustrate the usefulness of the formulas, a series of data sets with halfsib structure for some preselected parameters and sample size situations were generated by means of Monte Carlo techniques. When a nonlinear relationship in the form of a polynomial relationship of degree two is present, the linear and quadratic regression coefficients can be estimated from a paternal halfsib analysis without bias. Some of the traditional linear genetic parameters need correction; however, their value is limited if the relationship between two traits is nonlinear. Although regression coefficients may be estimated appropriately in many situations, the application of the described method is restricted to situations in which the causal flow between the traits involved is clear and the heritability of the determining trait is larger than approximately .10. Further work should be directed to investigation of possibilities for including such parameters in selection decisions in a formalized way.