Progressive-Change BACIPS: a flexible approach for environmental impact assessment

The Before-After Control-Impact Paired Series (BACIPS) design distinguishes natural spatial and temporal variability from variation induced by an environmental impact (or intervention) of interest. BACIPS is a powerful tool to derive inferences about interventions when classic experimental approaches (e.g. which rely on spatial replicates and random assignment of treatments) are not feasible or desirable. Previously applied BACIPS designs generally assume that effects are sudden, constant and long-lived: that is, that systems exhibit step-changes' in response to interventions. However, complex ecological interactions or gradual interventions may create delayed and/or progressive responses, potentially impeding the reliability of classic (step-change) analyses. We propose a novel approach, the Progressive-Change BACIPS, which generalizes and expands the scope of BACIPS analyses. We evaluate the relative performance of this approach using both simulated and real data that exhibit step-change, linear, asymptotic and sigmoid responses following an intervention. We quantify the statistical power and accuracy of the Progressive-Change BACIPS under varying initial population densities, intensity of spatial sampling, effect sizes and number of sampling dates After the intervention. We show that Progressive-Change BACIPS identified the correct model among the set of candidate models under most conditions and led to accurate estimates of the parameters that were used to generate the simulated data. When data were sparse, and the dynamics complex, simpler (more parsimonious) models were favoured over the more complex models that actually generated the simulated data. Application of the Progressive-Change BACIPS to existing data sets from the literature led to strong support for specific models (over alternatives) and led to more specific inferences than possible under the classic BACIPS approach. The Progressive-Change BACIPS proposed here is more flexible than the original BACIPS formulation because the data are used to inform the form of the final model, rather than having the form of the model imposed on the data. This leads to better estimates of the effects of environmental impacts and the time-scales over which they operate. As a result, the Progressive-Change BACIPS should be applicable to a wide range of studies and should help improve investigation of time-dependent effects. R code to perform Progressive-Change BACIPS analysis is provided.