Network inference aims at unraveling the dependency structure relating jointly observed variables. Graphical models provide a general framework to distinguish between marginal and conditional dependency. Unobserved variables (missing actors) may induce apparent conditional dependencies. In the context of count data, we introduce a mixture of Poisson log-normal distributions with tree-shaped graphical models, to recover the dependency structure, including missing actors. We design a variational EM algorithm and assess its performance on synthetic data. We demonstrate the ability of our approach to recover environmental drivers on two ecological datasets. The corresponding R package is available from github.com/Rmomal/nestor.