Marine reserve spillover: Modelling from multiple data sources

• Abundance of fish decreases with distance from MPA.
• Distance-decay of abundance can have different functional form.
• Model-based geostatistics are efficient to model distance-decay of abundance and helpful to infer on spillover functional form.
• Abundance of diplodus decreases exponentially and negatively.
• MPA of Carry le Rouet (France) is efficient to protect Diplodus spp.

The functional form of spillover, measured as a gradient of abundance of fish, may provide insight about processes that control the spatial distribution of fish inside and outside the MPA. In this study, we aimed to infer on spillover mechanism of Diplodus spp. (family Sparidae) from a Mediterranean MPA (Carry-le-Rouet, France) from visual censuses and artisanal fisheries data. From the existing literature, three potential functional forms of spillover such as a linear gradient, an exponential gradient and a logistic gradient are defined. Each functional form is included in a spatial generalized linear mixed model allowing accounting for spatial autocorrelation of data. We select between the different forms of gradients by using a Bayesian model selection procedure. In a first step, the functional form of the spillover for visual census and artisanal fishing data is assessed separately. For both sets of data, our model selection favoured the negative exponential model, evidencing a decrease of the spatial abundance of fish vanishing around 1000 m from the MPA border. We combined both datasets in a joint model by including an observability parameter. This parameter captures how the different sources of data quantify the underlying spatial distribution of the harvested species. This enabled us to demonstrate that the different sampling methods do not affect the estimation of the underlying spatial distribution of Diplodus spp. inside and outside the MPA. We show that data from different sources can be pooled through spatial generalized linear mixed model. Our findings allow to better understand the underlying mechanisms that control spillover of fish from MPA.