Using Bayesian hierarchical models to measure and predict the effectiveness of environmental flows for ecological responses

Abstract

Quantitative predictions of ecological responses to flow alterations are fundamental to the planning and delivery of environmental water. However, the majority of such predictions are often based on expert opinion, and lack a solid basis in empirical evidence. To derive evidence-based, defensible environmental flow recommendations, new approaches are required that make best use of the available data to predict ecological responses to flow alterations. In this study we use Bayesian hierarchical modelling to explore the impact of changed flow regime on terrestrial vegetation encroachment into river channels. In regulated rivers, encroachment of terrestrial vegetation into the channel is an issue of concern for managers because duration, frequency, and season of inundation are major determinants of plant community development. Environmental flows are often recommended as a way of reducing encroachment, but the assumed response has not been rigorously tested. Neither are there any general quantitative models that describe the predicted benefit (in terms of reduced terrestrial vegetation encroachment) of different flow regimes. In this paper we report a Bayesian approach that identifies the relationship between flow and vegetation encroachment revealed in seven integrated data sets from south eastern Australia. A principal advantage of Bayesian modelling is its flexibility. Thus, one is able to model physical and biological processes as part of a hierarchical statistical analysis. Here, we describe the relationship between terrestrial cover and inundation using a curvilinear function that combines both inundation duration and the number of inundation events. The model also incorporates hydrological data for the 5 years prior to vegetation sampling, weighting the most recent years most heavily. Finally, it accounts for effects of bank slope, season of inundation, and random effects associated with sampling (year of sampling, sampling transect, and uncertainty associated with the survey technique used). The model also improves the precision of estimates by using expert-derived prior probability distributions for model parameters, and by having a hierarchical structure among sites and rivers. Bayesian hierarchical models assume dependency amongst the sampling units, and therefore the model parameter values are assumed to be drawn from a larger common distribution. Relationships from each site 'borrow strength' from other sites, leading to robust influence despite the common problems associated with sample replication in environmental monitoring studies such as this. By combining data across seven different river systems, we are able to quantify relationships between different inundation durations and frequencies and the extent of terrestrial vegetation encroachment. This, in turn, allows us to make predictions of encroachment under different flow regimes. The hierarchical nature of the model allows us to report at the site and river level and also at the state level. These are the scales of interest to local stakeholders and the state funding agencies. Our results highlight the power and flexibility of Bayesian models to make quantitative, evidence-based predictions of ecological responses to changes in flow regimes. Such models will be vital for the future of environmental water management in data-poor situations that are common to environmental monitoring, and produce outcomes that are reportable at different stakeholder and governance levels.