Abstract
Abstract Isoscapes are maps depicting the continuous spatial (and sometimes temporal) variation in isotope composition. They have various applications ranging from the study of isotope circulation in the main earth systems to the determination of the provenance of migratory animals. Isoscapes can be produced from the fit of statistical models to observations originating from a set of discrete locations. Mixed models are powerful tools for drawing inferences from correlated data. While they are widely used to study non-spatial variation, they are often overlooked in spatial analyses. In particular, they have not been used to study the spatial variation of isotope composition. Here, we introduce this statistical framework and illustrate the methodology by building isoscapes of the isotope composition of hydrogen (measured in δ2H) for precipitation water in Europe. For this example, the approach based on mixed models presents a higher predictive power than a widespread alternative approach. We discuss other advantages offered by mixed models including: the ability to model the residual variance in isotope composition, the quantification of prediction uncertainty, and the simplicity of model comparison and selection using an adequate information criterion: the conditional AIC (cAIC). We provide all source code required for the replication of the results of this paper as a small R package to foster a transparent comparison between alternative frameworks used to model isoscapes.
Abbreviations used in this paper
AIC: Akaike Information Criterion
BLUP: Best Linear Unbiased Predictor
BWR: a method for building isoscape introduced by Bowen and Wilkinson (2002) and Bowen and Revenaugh (2003)
cAIC: conditional Akaike Information Criterion
DHGLM: Double Hierarchical Generalised Linear Model
GLM: Generalised Linear Model
GLMM: Generalised Linear Mixed-effects Model
GNIP: Global Network for Isotopes in Precipitation
LM: Linear Model
LMM: Linear Mixed-effects Model
MAE: Mean Absolute Error
ML: Maximum Likelihood
REML: Restricted Maximum Likelihood
RMSE: Root Mean Squared Error
Abbreviations used in this paper
