Inferring species interaction networks from species abundance data: A comparative evaluation of various statistical and machine learning methods

Abstract

The complexity of ecosystems is staggering, with hundreds or thousands of species interacting in a number of ways from competition and predation to facilitation and mutualism. Understanding the networks that form the systems is of growing importance, e.g. to understand how species will respond to climate change, or to predict potential knock-on effects of a biological control agent. In recent years, a variety of summary statistics for characterising the global and local properties of such networks have been derived, which provide a measure for gauging the accuracy of a mathematical model for network formation processes. However, the critical underlying assumption is that the true network is known. This is not a straightforward task to accomplish, and typi- * Corresponding author. Tel: +44 (0) cally requires minute observations and detailed field work. More importantly, knowledge about species interactions is restricted to specific kinds of interactions. For instance, while the interactions between pollinators and their host plants are amenable to direct observation, other types of species interactions, like those mentioned above, are not, and might not even be clearly defined from the outset. To discover information about complex ecological systems efficiently, new tools for inferring the structure of networks from field data are needed. In the present study, we investigate the viability of various statistical and machine learning methods recently applied in molecular systems biology: graphical Gaussian models, L1-regularised regression with least absolute shrinkage and selection operator (LASSO), sparse Bayesian regression and Bayesian networks. We have assessed the performance of these methods on data simulated from food webs of known structure, where we combined a niche model with a stochastic population model in a 2-dimensional lattice.We assessed the network reconstruction accuracy in terms of the area under the receiver operator characteristics (ROC) curve, which was typically in the range between 0.75 and 0.9, corresponding to the recovery of about 60% of the true species interactions at a false prediction rate of 5%. We also applied the models to presence/absence data for 39 European warblers, and found that the inferred species interactions showed a weak yet significant correlation with phylogenetic similarity scores, which tended to weakly increase when including bio-climate covariates and allowing for spatial autocorrelation. Our findings demonstrate that relevant patterns in ecological networks can be identified from large-scale spatial data sets with machine learning methods, and that these methods have the potential to contribute novel important tools for gaining deeper insight into the structure and stability of ecosystems.

Incorporating uncertainty in predictive species distribution modelling

“…Implementing such 'secondgeneration' SDMs will require further statistical research developing methods to identify biotic interactions and to develop specific hierarchical models relevant to this problem. The bases for such models are already available [59,60], and progress in these areas will likely be rapid: any attempt to move models from a simple pattern-based approach to a more fundamental understanding of ecological processes is to be welcomed.…”

Hierarchical Bayesian models in ecology: Reconstructing species interaction networks from non-homogeneous species abundance data

“…We included a comparison with L1-regularized linear regression (LASSO: Tibshirani (1996Tibshirani ( , 2011), using the optimization algorithm proposed by Grandvalet (1998). This method is widely applied in molecular systems biology (van Someren et al, 2006), has been recommended to be used more widely in ecology (Dahlgren, 2010), and was found to outperform all competing methods by Faisal et al (2010). The regularization parameter λ that controls the network sparsity was inferred with 10-fold cross-validation, which led to better results than optimizing the BIC score.…”

“…In our case, spatial autocorrelation could lead to the identification of spurious interactions as a mere consequence of two species cooccurring in similar geographical regions. To incorporate potential spatial autocorrelation into the model, we follow an approach proposed by Faisal et al (2010) and illustrated in Figure 1b. The idea is to connect each node in the network to an enforced parent node that represents the average population at neighboring cells, weighted inversely proportional to the distance of the neighbors:…”

“…For a more realistic evaluation, we followed Faisal et al (2010) and generated data from an ecological simulation that combines a niche model (Williams and Martinez, 2000) with a stochastic population model (Lande et al, 2003) in a 2-dimensional lattice.…”

“…discovering transcriptional regulatory networks from datasets on gene expression (Friedman et al, 2000) and neural information flow from brain activity (Smith et al, 2006). These methods present an avenue for revealing ecological interactions from, rather than observation of interaction, more easily obtainable data on species incidence (Milns et al, 2010;van Oijen et al, 2010;Amstrup et al, 2008;Faisal et al, 2010). Also, by inferring interactions based upon their influence on species distribution, there is no a priori restriction to specific relationship types, allowing competition and other relationships to be revealed alongside trophic interactions.…”