##
COS 84-5
Exploring food-web structure with latent traits models

**Background/Question/Methods**

Food webs are complex objects and models have been devised to capture the basic processes underlying their structure. While these approaches are interesting, one drawback is that models based on different assumptions can lead to very similar structures. To solve this problem, we introduce statistical approaches to study food-web structure. The models we present are based on the estimation of latent traits, which represents variables that are thought to be important, but not measured. However, they can be estimated directly from the food-web matrix with MCMC or Simulated annealing methods.

**Results/Conclusions **

First, we use a simple logistic regression, with body size in terms of an optimal ratio between prey and predator as explanatory variable, to study the interactions in a food web. Such a model is able to predict on average 20% of the observed interactions in a dataset of 12 food webs. We show that introducing latent traits can improve substantially the performance of the model. Latent traits represent non-measured characteristics of species, which are estimated directly from the data. We then introduce a very general model for network structure, the matching-centrality model, based on latent variables only. This model decomposes the adjacency (or food-web) matrix into a set of quantitative variables for each species. The interest of the approach is that these variables can then be related to external information about the species, allowing the exploration of characteristics that may underlie network structure. Additionally, we show how the model can be used firstly to predict interactions that are not observed (missing links), and secondly to forecast the links that a novel species would create when joining an existing food web.