How do MAR(1) models cope with hidden nonlinearities in ecological dynamics?

1. Multivariate autoregressive (MAR) models are an increasingly popular technique to infer interaction strengths between species in a community and to predict the community response to environmental change. The most commonly employed MAR(1) models, with one time lag, can be viewed either as multispecies competition models with Gompertz density dependence or, more generally, as a linear approximation of more complex, nonlinear dynamics around stable equilibria. This latter interpretation allows for broader applicability, but may come at a cost in terms of interpretation of estimates and reliability of both short- and long-term predictions. 2. We investigate what these costs might be by fitting MAR(1) models to simulated 2-species competition, consumer-resource and host-parasitoid systems, as well as a larger food web influenced by the environment. We review how MAR(1) coefficients can be interpreted and evaluate how reliable are estimates of interaction strength, rank, or sign; accuracy of short-term forecasts; as well as the ability of MAR(1) models to predict the long-term responses of communities submitted to environmental change such as PRESS perturbations. 3. The net effects of species j on species i are usually (90%-95%) well recovered in terms of sign or rank, with the notable exception of overcompensatory dynamics. In actual values, net effects of species j on species i are not well recovered when the underlying dynamics are nonlinear. MAR(1) models are better at making short-term qualitative forecasts (next point going up or down) than at predicting long-term responses to environmental perturbations, which can be severely over- as well as underestimated. 4. We conclude that when applying MAR(1) models to ecological data, inferences on net effects among species should be limited to signs, or the Gompertz assumption should be tested and discussed. This particular assumption on density-dependence (log-linearity) is also required for unbiased long-term predictions. Overall, we think that MAR(1) models are highly useful tools to resolve and characterize community dynamics, but we recommend to use them in conjunction with alternative, nonlinear models resembling the ecological context in order to improve their interpretation in specific applications.