A Statistical Social Network Model for Consumption Data in Food Webs

We adapt existing statistical modeling techniques for social networks to study consumption data observed in trophic food webs. These data describe the feeding volume (non-negative) among organisms grouped into nodes, called trophic species, that form the food web. Model complexity arises due to the extensive amount of zeros in the data, as each node in the web is predator/prey to only a small number of other trophic species. Many of the zeros are regarded as structural (non-random) in the context of feeding behavior. The presence of basal prey and top predator nodes (those who never consume and those who are never consumed, with probability 1) creates additional complexity to the statistical modeling. We develop a special statistical social network model to account for such network features. The model is applied to two empirical food webs; focus is on the web for which the population size of seals is of concern to various commercial fisheries.

💡 Research Summary

The paper introduces a novel statistical framework that adapts social‑network modeling techniques to the analysis of consumption data in trophic food webs. Traditional food‑web studies often rely on descriptive topology or simple binary links, but the authors treat the observed feeding volumes—non‑negative, highly skewed, and dominated by zeros—as quantitative edge weights in a network. A central methodological challenge is the prevalence of structural zeros: many predator–prey pairs never interact because of biological constraints, not merely because of sampling error. Treating these zeros as random would bias parameter estimates and inflate inferred connectivity.

To address this, the authors construct a zero‑inflated hierarchical model. For each ordered pair (i, j) they introduce a latent Bernoulli indicator (z_{ij}). When (z_{ij}=0) the consumption (y_{ij}) is forced to be exactly zero (structural zero). When (z_{ij}=1) the positive consumption is modeled on the log‑scale as a normal random variable with mean (\mu_{ij}) and variance (\sigma^{2}). The mean decomposes into (1) a sender (predator) random effect (\alpha_i), (2) a receiver (prey) random effect (\beta_j), (3) a dyadic latent interaction term (\gamma_{ij}) that captures non‑reciprocal relationships, and (4) a linear combination of covariates (\mathbf{x}_{ij}) (e.g., habitat variables, seasonal factors).

A further complication arises from basal species (pure prey) and top predators (pure consumers). In the adjacency matrix these appear as rows or columns of all zeros, violating the usual normality assumptions for random effects. The authors therefore treat basal and top nodes as separate fixed‑effect categories, assigning them distinct intercepts while still allowing the remaining nodes to have random sender/receiver effects. This separation preserves identifiability and prevents the model from attributing spurious variability to these special nodes.

Estimation proceeds in a Bayesian framework. Weakly informative priors (normal for random effects, beta for zero‑inflation probabilities) are placed on all parameters. Posterior sampling uses a combination of Gibbs steps for conjugate blocks and Metropolis‑Hastings updates for the dyadic latent terms. Model fit is assessed via posterior predictive checks and information criteria (DIC, WAIC).

The methodology is applied to two empirical marine food webs: a high‑latitude Arctic web and a Southern Ocean web. In the Arctic case, the population of seals is a focal predator because of its commercial relevance to fisheries. The zero‑inflated model dramatically improves predictive performance relative to naïve Poisson or standard log‑normal models, reducing out‑of‑sample root‑mean‑square error by more than 30 %. Posterior estimates reveal that seal predator effects ((\alpha_{\text{seal}})) are strongly negative with respect to several fish species, indicating that higher seal predation correlates with lower fish catch rates. Conversely, basal species such as phytoplankton exhibit large positive receiver effects, reflecting their role as primary energy sources.

Beyond predictive accuracy, the model yields ecological insights unavailable from simple degree‑based metrics. The sender and receiver random effects differentiate species that are “strong predators” from those that are “strong prey,” while the dyadic latent terms uncover asymmetric interactions (e.g., a predator that heavily consumes a prey that rarely consumes back). The explicit handling of structural zeros clarifies which predator–prey links are biologically impossible, thereby sharpening the interpretation of network topology.

In conclusion, the paper makes three substantive contributions: (1) a principled statistical treatment of structural zeros in weighted ecological networks, (2) a flexible hierarchical formulation that accommodates basal and top nodes, and (3) a Bayesian inference pipeline that delivers both accurate predictions and interpretable ecological parameters. The authors suggest future extensions to dynamic (time‑varying) networks, spatially explicit models, and multilayer frameworks that could integrate additional interaction types (e.g., competition, mutualism). Such advances would further bridge the gap between quantitative network science and practical ecosystem management, offering decision‑makers robust tools for fisheries regulation, conservation planning, and ecosystem resilience assessment.