Cookies on this website

We use cookies to ensure that we give you the best experience on our website. If you click 'Accept all cookies' we'll assume that you are happy to receive all cookies and you won't see this message again. If you click 'Reject all non-essential cookies' only necessary cookies providing core functionality such as security, network management, and accessibility will be enabled. Click 'Find out more' for information on how to change your cookie settings.

Best linear unbiased prediction (BLUP) is a method for obtaining point estimates of a random effect in a mixed effect model. Over the past decade it has been used extensively in ecology and evolutionary biology to predict individual breeding values and reaction norms. These predictions have been used to infer natural selection, evolutionary change, spatial-genetic patterns, individual reaction norms, and frailties. In this article we show analytically and through simulation and example why BLUP often gives anticonservative and biased estimates of evolutionary and ecological parameters. Although some concerns with BLUP methodology have been voiced before, the scale and breadth of the problems have probably not been widely appreciated. Bias arises because BLUPs are often used to estimate effects that are not explicitly accounted for in the model used to make the predictions. In these cases, predicted breeding values will often say more about phenotypic patterns than the genetic patterns of interest. An additional problem is that BLUPs are point estimates of quantities that are usually known with little certainty. Failure to account for this uncertainty in subsequent tests can lead to both bias and extreme anticonservatism. We demonstrate that restricted maximum likelihood and Bayesian solutions exist for these problems and show how unbiased and powerful tests can be derived that adequately quantify uncertainty. Of particular utility is a new test for detecting evolutionary change that not only accounts for prediction error in breeding values but also accounts for drift. To illustrate the problem, we apply these tests to long-term data on the Soay sheep (Ovis aries) and the great tit (Parus major) and show that previously reported temporal trends in breeding values are not supported.

Original publication




Journal article


Am Nat

Publication Date





116 - 125


Animals, Bayes Theorem, Biological Evolution, Breeding, Computer Simulation, Ecology, Genetic Drift, Genetic Variation, Likelihood Functions, Linear Models, Selection, Genetic, Sheep, Domestic, Uncertainty