Estimation of direct and correlated responses to selection using univariate animal models.

Analytic results obtained using simple models show that estimates of selection response of univariate experiments using animal models are completely dependent on the heritability used as prior when fixed effects are nested within generations, and both on the prior and on the true heritability parameter when fixed effects overlap across generations. Univariate animal model estimators of correlated changes of a trait not selected directly are usually biased. The absolute value of the estimate of the correlated response is smaller than the true value when the traits are only genetically correlated and larger than the expected value of zero when they are only environmentally correlated. The validity of the results derived from the analysis of simple models is confirmed using computer simulations, which illustrate the magnitude of the bias. It is emphasized that use of univariate animal models to estimate response in breeding programs whose breeding objectives include several correlated traits may lead to erroneous conclusions.