How much are stranding records affected by variation in reporting rates? A case study of small delphinids in the Bay of Biscay
Marine vertebrate strandings offer an opportunistic sampling scheme that can provide abundant data over long periods. Because the stranding process involves biological, physical and sociological parameters, confounding complicates the interpretation of results. The statistical analysis of these data relies on generalized linear or additive models in order to infer long-term trends, but does not easily account for drift or variation in reporting rates. Here, we capitalized on county-level (administrative) variation following the passing of a law for compulsory reporting of stranded marine mammals in France to investigate how variation in reporting rates may affect the observed trend in stranded small delphinids in the Bay of Biscay. Using a time-series spanning more than 30 years across eight administrative counties, we built variance partitioning models for the analysis of count data. We discussed the choice of an appropriate likelihood to conclude the Negative Binomial useful and interpretable in the context of small delphinid strandings. We expanded the model with a recent methodology to detect structural breaks in the time series, focusing on overdispersion. We performed statistical robustness checks with respect to variations in reporting rates and discuss their causal interpretation in the context of observational data. Stranding frequencies increased on average 7-fold over 30 years. We conclude that reporting rates to the French stranding network have been stable since the early 1990s, and the average 3-fold increase in stranded small delphinids observed in the Bay of Biscay since 1990 is due to other factors, including bycatch. Codes and data are available to replicate the analysis to other national stranding networks.