5 Inferring species interactions from observational data is one of the most controversial tasks in 6 community ecology. One difficulty is that a single pairwise interaction can ripple through an 7 ecological network and produce surprising indirect consequences. For example, two 8 competing species would ordinarily correlate negatively in space, but this effect can be 9 reversed in the presence of a third species that is capable of outcompeting both of them 10 when it is present. Here, I apply

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... dels from statistical physics, called Markov networks or 11 Markov random fields, that can predict the direct and indirect consequences of any possible 12 species interaction matrix. Interactions in these models can be estimated from observational 13 data via maximum likelihood. Using simulated landscapes with known pairwise interaction 14 strengths, I evaluated Markov networks and several existing approaches. The Markov 15 networks consistently outperformed other methods, correctly isolating direct interactions 16 between species pairs even when indirect interactions or abiotic environmental effects largely 17 overpowered them. A linear approximation, based on partial covariances, also performed well 18 as long as the number of sampled locations exceeded the number of species in the data. 19 Indirect effects reliably caused a common null modeling approach to produce incorrect 20 inferences, however. 21