Trajectories of genetic correlations in populations under selection: from theory to a case-study

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Abstract
Background: Breeding programs select for multiple commercial traits, aiming to achieve genetic progress for all. Often, selection is based on a selection index, i . e . a linear combination of traits with weights defined by, among other information, the genetic correlation between traits. These correlations are typically estimated as a static parameter, and assumed equal to all individuals and generations. While research on the consequences of selection to genetic variances (Bulmer effect) is widely available, only a few studies focused on the consequences of selection to genetic correlations. Our study extended the already existing inferences about how selection affects genetic variances, to how multi-trait selection affects genetic correlations. In order to further our understanding of genetic correlations, we also proposed an alternative method to calculate genetic correlations between traits at the individual level, called by us as individualized sire genetic correlation (iSGC), obtained through the estimated breeding values (EBV) from evaluated daughters. Lastly, a case-study was performed on thirty years of data from the French Holstein dairy cattle population, for five traits studied pairwise: milk and protein yield, milking speed, somatic cell score, and cow conception rate. Results: Theory revealed that multi-trait selection leads to an attenuation (decrease) of positive genetic correlations, with potential to revert them to negative values, if initially low. Uncorrelated traits will become negatively correlated, and negative genetic correlations will be either intensified or attenuated (decrease or increase, respectively), depending on selection intensity, weights applied to the selection index, and the initial genetic correlation. Conclusion: Both theory and empirical results on real data confirm that selection does change the genetic correlation between traits in a population under selection. Moreover, empirical trajectories of the iSGC were in better agreement with the theory, than trajectories of populational genetic correlations. The iSGC searches for individual-specific patterns of correlations, and since it is measured on sires through the EBV of their daughters, it also considers the recombination of the genetic background. Along with the fact that trajectories of iSGC were in better agreement with theory, we believe it to be a potentially less biased measure of genetic correlations between traits.

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