What constrains food webs? A maximum entropy framework for predicting their structure with minimal biases.

Food webs are complex ecological networks whose structure is both ecologically and statistically constrained, with many network properties being correlated with each other. Despite the recognition of these invariable relationships in food webs, the use of the principle of maximum entropy (MaxEnt) in network ecology is still rare. This is surprising considering that MaxEnt is a statistical tool precisely designed for understanding and predicting many types of constrained systems. This principle asserts that the least-biased probability distribution of a system's property, constrained by prior knowledge about that system, is the one with maximum information entropy. MaxEnt has been proven useful in many ecological modeling problems, but its application in food webs and other ecological networks is limited. Here we show how MaxEnt can be used to derive many food-web properties both analytically and heuristically. First, we show how the joint degree distribution (the joint probability distribution of the numbers of prey and predators for each species in the network) can be derived analytically using the number of species and the number of interactions in food webs. Second, we present a heuristic and flexible approach of finding a network's adjacency matrix (the network's representation in matrix format) based on simulated annealing and SVD entropy. We built two heuristic models using the connectance and the joint degree sequence as statistical constraints, respectively. We compared both models' predictions against corresponding null and neutral models commonly used in network ecology using open access data of terrestrial and aquatic food webs sampled globally (N = 257). We found that the heuristic model constrained by the joint degree sequence was a good predictor of many measures of food-web structure, especially the nestedness and motifs distribution. Specifically, our results suggest that the structure of terrestrial and aquatic food webs is mainly driven by their joint degree distribution.

Mismatch between IUCN range maps and species interactions data illustrated using the Serengeti food web.

Background: Range maps are a useful tool to describe the spatial distribution of species. However, they need to be used with caution, as they essentially represent a rough approximation of a species' suitable habitats. When stacked together, the resulting communities in each grid cell may not always be realistic, especially when species interactions are taken into account. Here we show the extent of the mismatch between range maps, provided by the International Union for Conservation of Nature (IUCN), and species interactions data. More precisely, we show that local networks built from those stacked range maps often yield unrealistic communities, where species of higher trophic levels are completely disconnected from primary producers. Methodology: We used the well-described Serengeti food web of mammals and plants as our case study, and identify areas of data mismatch within predators' range maps by taking into account food web structure. We then used occurrence data from the Global Biodiversity Information Facility (GBIF) to investigate where data is most lacking. Results: We found that most predator ranges comprised large areas without any overlapping distribution of their prey. However, many of these areas contained GBIF occurrences of the predator. Conclusions: Our results suggest that the mismatch between both data sources could be due either to the lack of information about ecological interactions or the geographical occurrence of prey. We finally discuss general guidelines to help identify defective data among distributions and interactions data, and we recommend this method as a valuable way to assess whether the occurrence data that are being used, even if incomplete, are ecologically accurate.

A roadmap towards predicting species interaction networks (across space and time).

Networks of species interactions underpin numerous ecosystem processes, but comprehensively sampling these interactions is difficult. Interactions intrinsically vary across space and time, and given the number of species that compose ecological communities, it can be tough to distinguish between a true negative (where two species never interact) from a false negative (where two species have not been observed interacting even though they actually do). Assessing the likelihood of interactions between species is an imperative for several fields of ecology. This means that to predict interactions between species-and to describe the structure, variation, and change of the ecological networks they form-we need to rely on modelling tools. Here, we provide a proof-of-concept, where we show how a simple neural network model makes accurate predictions about species interactions given limited data. We then assess the challenges and opportunities associated with improving interaction predictions, and provide a conceptual roadmap forward towards predictive models of ecological networks that is explicitly spatial and temporal. We conclude with a brief primer on the relevant methods and tools needed to start building these models, which we hope will guide this research programme forward. This article is part of the theme issue 'Infectious disease macroecology: parasite diversity and dynamics across the globe'.

Revisiting the Links-Species Scaling Relationship in Food Webs.

Predicting the number of interactions among species in a food web is an important task. These trophic interactions underlie many ecological and evolutionary processes, ranging from biomass fluxes, ecosystem stability, resilience to extinction, and resistance against novel species. We investigate and compare several ways to predict the number of interactions in food webs. We conclude that a simple beta-binomial model outperforms other models, with the added desirable property of respecting biological constraints. We show how this simple relationship gives rise to a predicted distribution of several quantities related to link number in food webs, including the scaling of network structure with space and the probability that a network will be stable.