Reconstructing gene regulation networks from gene expression data is an important task in molecular biology for which various network inference methods have been developed. In ecology, species interaction networks serve a similar purpose, in that they show how different species relate to each other. We have investigated the possibility of applying the methods that were developed for gene regulation networks to reconstruct species interaction networks from species abundance data. We used a Lotka-Volterra style simulation model to produce synthetic data based on species interaction networks, and then tried to reconstruct the original network from this data using Bayesian networks, LASSO (Least Absolute Shrinkage and Selection Operator) and SBR (Sparse Bayesian Regression). We also developed extensions to these methods for dealing with the problem of spatial autocorrelation. Our experiments showed that we can retrieve many species interactions, while keeping the false positive rate low. We compared the different methods, and found that LASSO and Bayesian networks perform best.