Detecting ecological responses to flow variation using Bayesian hierarchical models

1. Inferring effects of environmental flows is difficult with standard statistical approaches because flow-delivery programs are characterised by weak experimental design, and monitoring programs often have insufficient replication to detect ecologically significant effects. Bayesian hierarchical approaches may be more suited to the task, as they are more flexible and allow data from multiple non-replicate sampling units ( e. g. rivers) to be combined, increasing inferential strength. 2. We assessed the utility of Bayesian hierarchical models for detecting ecological effects of flow variation by conducting both hierarchical and non-hierarchical analyses on two environmental endpoints. We analysed effects of discharge on salinity in the Wimmera and Glenelg rivers (Victoria, Australia) using a linear regression with autocorrelation terms, and on Australian smelt in the Thomson River (Victoria, Australia) using a multilevel covariate model. These analyses test some of the hypotheses upon which environmental flow recommendations have been made for these rivers. 3. Discharge was correlated with reduced salinity at six of 10 sites, but with increased salinity at two others. The results were very similar for hierarchical and non-hierarchical models. For Australian smelt, the hierarchical model found some evidence that excess summer discharge reduces abundance in all river reaches, but the non-hierarchical model was able to detect this response in only one reach. 4. The results highlight the power and flexibility of Bayesian analysis. Neither of the models fitted would have been amenable to more widely used statistical approaches, and it is unlikely that we would have detected responses to flow variation in these data had we been using such techniques. Hierarchical models can greatly improve inferential strength in the data-poor situations that are common in ecological monitoring, and will be able to be used to assess the effectiveness of environmental flow programs and maximise the benefits of large-scale environmental flow monitoring programs.