Modelling ecological communities when composition is manipulated experimentally

1. In an experimental setting, the composition of ecological communities can be manipulated directly. Starting from a pool of n species, it is possible to co-culture species in different combinations, ranging from monocultures, to pairs, and all the way up to the full species pool. Leveraging datasets with this experimental design, we advance methods to infer species interactions using density measurements taken at a single time point across a variety of distinct community compositions.2. First, we introduce a fast and robust algorithm to estimate parameters for simple statistical models describing these data, which can be combined with likelihood maximization approaches. Second, we derive from consumer- resource dynamics a family of statistical models with few parameters, which can be applied to study systems where only a small fraction of the potential community compositions have been observed. Third, we show how a Weighted Least Squares framework can be used to account for the fact that species abundances often display a strong relationship between means and variances.3. To illustrate our approach, we analyse datasets spanning plant, bacteria and phytoplankton communities, as well as simulations, consistently recovering a good fit to the data and demonstrating the ability of our methods to predict equilibrium densities in out - of-sample communities.4. By combining more robust model structures and fitting procedures along with a more flexible error model, we greatly extend the applicability of recently proposed methods to model community composition from experimental data, opening the door for the analysis of larger pools of species using sparser and noisier datasets than was previously possible.