New measures for evaluation of environmental perturbations using Before-After-Control-Impact analyses

Before-After-Control-Impact (BACI) designs are powerful tools to derive inferences about environmental perturbations (e.g., hurricanes, restoration programs) when controlled experimental designs are unfeasible. Applications of BACI designs mostly rely on testing for a significant interaction between periods and treatments (so-called BACI contrast) to demonstrate the effects of the perturbation. However, significant interactions can emerge for several reasons, including when changes are larger in control sites, such that additional diagnostics must be performed to determine the full complexity of system changes. We propose two measures that detail the nature of change implied by BACI contrasts, along with its uncertainty. CI-divergence (Control-Impact divergence) quantifies to what extent control and impact sites have diverged between the after and the before period, whereas CI-contribution (Control-Impact contribution) quantifies to what extent the change between periods is stronger in impact sites relative to control sites. To illustrate how these two CI measures can be combined with BACI contrast to gain insights about effects of environmental perturbations, we used count data from the Swedish Breeding Bird Survey to investigate how hurricane Gudrun affected the long-term abundances of four bird species in forested areas of southern Sweden. Before-After-Control-Impact contrasts suggested the hurricane affected all four species. However, the values of the two CI measures strongly differed, even among species showing similar BACI contrasts. Those differences highlight qualitatively distinct population trajectories between periods and treatments requiring different ecological explanations. Overall, we show that BACI contrasts do not provide the full story in assessing the effects of environmental perturbations. The two CI measures can be used to assist ecological interpretations, or to specify detailed hypotheses about effects of restoration actions to allow stronger confirmatory inference about their outcomes. By providing a framework to develop more detailed explanations and hypotheses about ecological changes, the two CI measures can improve conclusions and strengthen evidence of effects of conservation actions and impact assessments under BACI designs.