[en] Highlights: • An alternative approach to the CR model for human food chain and wildlife. • The approach represents a scientifically based extrapolation methodology. • The first REML model for terrestrial wildlife presented in the refereed literature. - Abstract: Radionuclide activity concentrations in food crops and wildlife are most often predicted using empirical concentration ratios (CRs). The CR approach is simple to apply and some data exist with which to parameterise models. However, the parameter is highly variable leading to considerable uncertainty in predictions. Furthermore, for both crops and wildlife we have no, or few, data for many radionuclides and realistically, we are never going to have specific data for every radionuclide - wildlife/crop combination. In this paper, we present an alternative approach using residual maximum likelihood (REML) fitting of a linear mixed effects model; the model output is an estimate of the rank-order of relative values. This methodology gives a less uncertain approach than the CR approach, as it takes into account the effect of site; it also gives a scientifically based extrapolation approach. We demonstrate the approach using the examples of Cs for plants and Pb for terrestrial wildlife. This is the first published application of the REML approach to terrestrial wildlife (previous applications being limited to the consideration of plants). The model presented gives reasonable predictions for a blind test dataset.