Abstract Inferring species interactions from co‐occurrence data is one of the most controversial tasks in community ecology. One difficulty is that a single pairwise interaction can ripple through an ecological network and produce surprising indirect consequences. For example, the negative correlation between two competing species can be reversed in the presence of a third species that outcompetes both of them. Here, I apply models from statistical physics, called Markov networks or Markov random fields, that can predict the direct and indirect consequences of any possible species interaction matrix. Interactions in these models can be estimated from observed co‐occurrence rates via maximum likelihood, controlling for indirect effects. Using simulated landscapes with known interactions, I evaluated Markov networks and six existing approaches. Markov networks consistently outperformed the other methods, correctly isolating direct interactions between species pairs even when indirect interactions or abiotic factors largely overpowered them. Two computationally efficient approximations, which controlled for indirect effects with partial correlations or generalized linear models, also performed well. Null models showed no evidence of being able to control for indirect effects, and reliably yielded incorrect inferences when such effects were present.