Extending the causal inference toolkit for ecologists: A visualization method of indirect effects

Much ecological research focuses on phenomena where a given variable can affect another either directly or indirectly through the effect of one or more intervening variables. While various methods to quantify the magnitude of these effects are available, they can be difficult to interpret in a meaningful way, especially for indirect effects. Studies thus often quantity direct effects and infer indirect ones more or less formally. We propose a method for visualizing indirect effects by means of plotting model predictions of an outcome in the presence of both exposure and mediator variables. We demonstrate the method through simulations and apply them to a real-world example involving Tree Swallows (Tachycineta bicolor) and their obligatory hematophagous ectoparasites, Protocalliphora bird blowflies (Diptera: Calliphoridae). Our procedure, which can be seamlessly integrated into an analysts workflow using commonplace software, should prove instrumental to disentangle and interpret relationships among variables involved in ecological mechanisms.