Comparison of nonlinear mixed-effects models with different levels of spatial aggregation.

The null models nm0a and nm0b were fitted with common fixed effects for all regions, model nm2 with separate fixed effects for the tropical and the European region and nm4 with separate fixed effects for northern, central, southern Europe and the tropical region. For fixed effects the complete set of parameters of the Lactin-2 model (ρ, Tmax, Δ and λ; cf. Eq.1) was used in all cases. In model nm0a, all four parameters were also used as random effects, while for models nm0b, nm2, and nm4 only Tmax, Δ and λ were used.