Effects of marine reserves in the context of spatial and temporal variation: an analysis using Bayesian zero-inflated mixed models

Abstract

Evaluating the effects of marine reserves on exploited species can be challenging because they occur within a context of natural spatial and temporal variation at many scales. For rigorous inferences to be made, such evaluations require monitoring programmes that are repli- cated at appropriate scales. We analysed monitoring data of snapper Pagrus auratus (Sparidae) in northeastern New Zealand, comprised of counts from baited-underwater-video surveys from inside and outside 3 marine reserves. Surveys were replicated at many levels, including areas inside and outside of marine reserves at 3 locations in 2 seasons, over a period of up to 14 yr, in an unbalanced design. The Bayesian modelling approach allowed the use of some familiar aspects of ANOVA, including mixed models of fixed and random effects, hierarchically nested structures, and variance decomposition, while allowing for overdispersion and excess zeros in the counts. Model selection and estimates of variance components revealed that protection by marine reserves was by far the strongest measured source of variation for relative densities of legal-sized snapper. The size of the effect varied across years among the 3 reserves, with relative densities between 7 and 20 times greater in reserves than in nearby areas. Other than the reserve effect, the temporal factors of season and year were generally more important than the spatial factors at explaining variation in counts. In particular, overall relative densities were ~2 to 3 times greater in autumn than in spring for legal-sized snapper, although the seasonal effect was also variable among locations and years. We consider that the Bayesian generalised linear mixed modelling approach, as used here, provides an extremely useful and flexible tool for estimating the effects of management actions and comparing them directly with other sources of spatial and temporal variation in natural systems.