According to animal breeding theory, profit after, say, 10 generations of selection is maximized when the usually non-linear profit function is approximated by a linear breeding goal where the linearization is at the population mean in generation 10 and the linear breeding goal is subsequently predicted by a linear index for which the animals are selected. The prediction of the population mean at generation 10 requires linear relationships among the traits that constitute the non-linear profit, because otherwise this prediction becomes very complicated.
A non-linear index is proposed that simply estimates the non-linear goal H =f(u) by Ĥ =f(û), where u = vector of genetic values for the traits and u is its (BLUP) estimate. This non-linear index does not require predictions of (future) population means and does not require linearly related traits.
To test these indices a simple meat production example was constructed where the non-linearity between the traits was due to the competition between weight and probability of survival for the same resources from food intake. In the model selection for weight and, in particular, for weight over costs (mainly food) led to reduced profits due to large reductions of survival rates. Although, the example was oversimplified, this should provide a warning for the use of oversimplified breeding goals, e.g. fitness traits may reduce by more than expected from base population genetic parameters.
When probability of survival and weight were measured, a non-linear index of these non-linear traits gave the greatest genetic gains. Failure to update genetic parameters each generation severely reduced genetic gain and, if linear indices were used, it was also important to update the economic weights. When probability of survival was measured, profit could be calculated on each animal and included as a trait in the calculation of estimated breeding value. This yielded high genetic gain and did not require updating of genetic parameters or economic weights.