A quantitative theory for genomic offset statistics

Genomic offset statistics assess the maladaptation of populations to rapid habitat alteration based on association of genotypes with environmental variation. Despite substantial evidence for empirical validity, genomic offset statistics have well-identified limitations, and lack a theory that would facilitate interpretations of predicted values. Here, we clarified the theoretical relationships between genomic offset statistics and adaptive traits, and proposed a new measure to predict fitness after rapid change in local environment. The predictions of our theory were verified in computer simulations and in empirical data on African pearl millet ( Cenchrus americanus ) obtained from a common garden experiment. Our results proposed a unified perspective on genomic offset statistics, and outlined their importance for conservation management in the face of environmental change. Significance/Author’s summary Maladaptation to altered habitat resulting from global warming is likely to cause shifts in adaptive traits of natural populations. Adaptive shifts are best evaluated from experiments in which organisms are placed into an environment that differs from the one in which the traits evolved. Those experiments are costly and time-consuming, and adaptive traits are not always easily measureable. Genomic offset statistics use environmental and genomic data to predict shifts in adaptive traits without direct observations of those traits. Similar to the theory of genetic load, we developed a mathematical model to predict fitness in local populations after rapid change in their environmental conditions when adaptive traits are unobserved. Our theory not only introduces a new measure of genomic offset, the genetic gap, but also unifies previously proposed measures into a common statistical framework. Validations from simulated and empirical data sets provided support for the theory, that paves the way for further improvements of population genomic measures of maladaptation. ### Competing Interest Statement The authors have declared no competing interest.