Quantifying parameter uncertainty in a coral reef model using Metropolis-Coupled Markov Chain Monte Carlo

Abstract

Coral reefs are threatened ecosystems, so it is important to have predictive models of their dynamics. Most current models of coral reefs fall into two categories. The first is simple heuristic models which provide an abstract understanding of the possible behaviour of reefs in general, but do not describe real reefs. The second is complex simulations whose parameters are obtained from a range of sources such as literature estimates. We cannot estimate the parameters of these models from a single data set, and we have little idea of the uncertainty in their predictions. We have developed a compromise between these two extremes, which is complex enough to describe real reef data, but simple enough that we can estimate parameters for a specific reef from a time series. In previous work, we fitted this model to a long-term data set from Heron Island, Australia, using maximum likelihood methods. To evaluate predictions from this model, we need estimates of the uncertainty in our parameters. Here, we obtain such estimates using Bayesian Metropolis-Coupled Markov Chain Monte Carlo. We do this for versions of the model in which corals are aggregated into a single state variable (the three-state model), and in which corals are separated into four state variables (the six-state model), in order to determine the appropriate level of aggregation. We also estimate the posterior distribution of predicted trajectories in each case. In both cases, the fitted trajectories were close to the observed data, but we had doubts about the biological plausibility of some parameter estimates. We suggest that informative prior distributions incorporating expert knowledge may resolve this problem. In the six-state model, the posterior distribution of state frequencies after 40 years contained two divergent community types, one dominated by free space and soft corals, and one dominated by acroporid, pocilloporid, and massive corals. The three-state model predicts only a single community type. We conclude that the three-state model hides too much biological heterogeneity, but we need more data if we are to obtain reliable predictions from the six-state model. It is likely that there will be similarly large, but currently unevaluated, uncertainty in the predictions of other coral reef models, many of which are much more complex and harder to fit to real data.