Towards a causal understanding of bidirectional effects in ecology and evolution

Feedback loops govern many processes in the natural world and are ubiquitous in ecology and evolutionary biology. Despite their prevalence in theory, however, feedbacks and other forms of reciprocal causation are rarely quantified by empiricists working with observational datasets. This divide has been brought to the fore by the causal revolution in the natural sciences. When researchers aim to quantify causal effects, the bi-directional nature of feedbacks seems incompatible with standard tools, such as regression, which begin by distinguishing between 'response' and 'predictor' variables. This seems to leave empiricists in ecology and evolution with few tools, if any, to quantify bidirectional effects. First, we highlight that, when ignored, feedback can lead to bias in common statistical analyses. We then present several methods that can help researchers quantify causal effects when feedbacks are present, including models with discrete cross-lagged effects as well as continuous time models, both of which are suitable for longitudinal data. We also consider instrumental variables, which can help to disentangle bidirectional effects from cross-sectional data. Focusing on examples from ecology and evolutionary biology, our aim is to provide a general primer on the challenges and opportunities for the quantitative analysis of bidirectional causation.