A Bayesian synthesis of predictions from different models for setting water quality criteria

Skeptical views of the scientific value of modelling argue that there is no true model of an ecological system, but rather several adequate descriptions of different conceptual basis and structure. In this regard, rather than picking the single “best-fit” model to predict future system responses, we can use Bayesian model averaging to synthesize the forecasts from different models. Does the combination of several models of different complexity improve our capacity to synthesize different perceptions of the ecosystem functioning and therefore the value of the modelling enterprise in the context of ecosystem management? Our study addresses this question using a complex (14 state-variable) eutrophication model along with a simpler modelling construct that considers the interplay among phosphate, detritus, and generic phytoplankton and zooplankton state variables. Using Markov Chain Monte Carlo simulations, we calculate the relative mean standard error to assess the posterior support of the two models after considering the available data from the system. Predictions from the two models are then combined using the respective standard error estimates as weights in a weighted model average. The model averaging approach is used to examine the robustness of predictive statements made from our earlier work regarding the response of Hamilton Harbour (Ontario, Canada) to the different nutrient loading reduction strategies. In particular, we consolidate the finding that the existing total phosphorus goal (<17μgL−1) is most likely unattainable, and therefore we identify the most achievable ambient target under the most stringent (but realistic) nutrient loading reduction scenario. Finally, the discrepancy between the chlorophyll a predictions of the two models pinpoint the need to delve into the dynamics of phosphorus in the sediment–water column interface, as the internal nutrient loading can conceivably be a regulatory factor of the duration of the transient phase and the recovery resilience of the system.