A generalized approach to modeling and estimating indirect effects in ecology

The need to model and test hypotheses about complex ecological systems has led to a steady increase in use of path analytical techniques, which allow the modeling of multiple multivariate dependencies reflecting hypothesized causation and mechanisms. The aim is to achieve the estimation of direct, indirect, and total effects of one variable on another and to assess the adequacy of whole models. Path analytical techniques based on maximum likelihood currently used in ecology are rarely adequate for ecological data, which are often sparse, multi-level, and may contain nonlinear relationships as well as nonnormal response data such as counts or proportion data. Here I introduce a more flexible approach in the form of the joint application of hierarchical Bayes, Markov chain Monte Carlo algorithms, Shipley's d-sep test, and the potential outcomes framework to fit path models as well as to decompose and estimate effects. An example based on the direct and indirect interactions between ants, two insect herbivores, and a plant species demonstrates the implementation of these techniques, using freely available software.