Matching-centrality decomposition and the forecasting of new links in networks

Indirect effects shape species fitness in coevolved mutualistic networks

Ecological interactions are one of the main forces that sustain Earth's biodiversity. A major challenge for studies of ecology and evolution is to determine how these interactions affect the fitness of species when we expand from studying isolated, pairwise interactions to include networks of interacting species^1-4. In networks, chains of effects caused by a range of species have an indirect effect on other species they do not interact with directly, potentially affecting the fitness outcomes of a variety of ecological interactions (such as mutualism)^5-7. Here we apply analytical techniques and numerical simulations to 186 empirical mutualistic networks and show how both direct and indirect effects alter the fitness of species coevolving in these networks. Although the fitness of species usually increased with the number of mutualistic partners, most of the fitness variation across species was driven by indirect effects. We found that these indirect effects prevent coevolving species from adapting to their mutualistic partners and to other sources of selection pressure in the environment, thereby decreasing their fitness. Such decreases are distributed in a predictable way within networks: peripheral species receive more indirect effects and experience higher reductions in fitness than central species. This topological effect was also evident when we analysed an empirical study of an invasion of pollination networks by honeybees. As honeybees became integrated as a central species within networks, they increased the contribution of indirect effects on several other species, reducing their fitness. Our study shows how and why indirect effects can govern the adaptive landscape of species-rich mutualistic assemblages.

Stability of multi-layer ecosystems

Community structure is reported to play a critical role in ecosystem stability, which indicates the ability of a system to return to equilibrium after perturbations. However, current studies rely on the assumption that the community consists of only a single-layer structure. In practice, multi-layer structures are common in ecosystems, e.g. the distributions of both microorganisms in strata and fish in the ocean usually stratify into multi-layer structures. Here we use multi-layer networks to model species interactions within each layer and between different layers, and study the stability of multi-layer ecosystems under different interaction types. We show that competitive interactions within each layer have a more substantial stabilizing effect in multi-layer ecosystems relative to their impact in single-layer ecosystems. Surprisingly, between different layers, we find that competition between species destabilizes the ecosystem. We further provide a theoretical analysis of the stability of multi-layer ecosystems and confirm the robustness of our findings for different connectances between layers, numbers of species in each layer, and numbers of layers. Our work provides a general framework for investigating the stability of multi-layer ecosystems and uncovers the double-sided role of competitive interactions in the stability of multi-layer ecosystems.

A size-constrained feeding-niche model distinguishes predation patterns between aquatic and terrestrial food webs

Understanding the formation of feeding links provides insights into processes underlying food webs. Generally, predators feed on prey within a certain body-size range, but a systematic quantification of such feeding niches is lacking. We developed a size-constrained feeding-niche (SCFN) model and parameterized it with information on both realized and non-realized feeding links in 72 aquatic and 65 terrestrial food webs. Our analyses revealed profound differences in feeding niches between aquatic and terrestrial predators and variation along a temperature gradient. Specifically, the predator-prey body-size ratio and the range in prey sizes increase with the size of aquatic predators, whereas they are nearly constant across gradients in terrestrial predator size. Overall, our SCFN model well reproduces the feeding relationships and predation architecture across 137 natural food webs (including 3878 species and 136,839 realized links). Our results illuminate the organisation of natural food webs and enables novel trait-based and environment-explicit modelling approaches.

Addressing the Eltonian shortfall with trait-based interaction models

We have very limited knowledge of how species interact in most communities and ecosystems despite trophic relationships being fundamental for linking biodiversity to ecosystem functioning. A promising approach to fill this gap is to predict interactions based on functional traits, but many questions remain about how well we can predict interactions for different taxa, ecosystems and amounts of input data. Here, we built a new traits-based model of trophic interactions for European vertebrates and found that even models calibrated with 0.1% of the interactions (100 out of 71 k) estimated the full European vertebrate food web reasonably well. However, predators were easier to predict than prey, especially for some clades (e.g. fowl and storks) and local food web connectance was consistently overestimated. Our results demonstrate the ability to rapidly generate food webs when empirical data are lacking-an important step towards a more complete and spatially explicit description of food webs.

A methodological framework to analyse determinants of host-microbiota networks, with an application to the relationships between Daphnia magna's gut microbiota and bacterioplankton

The past 30 years have seen both a surge of interest in assessing ecological interactions using tools borrowed from network theory and an explosion of data on the occurrence of microbial symbionts thanks to next-generation sequencing. Given that classic network methods cannot currently measure the respective effects of different environmental and biological drivers on network structure, we here present two methods to elucidate the determinants of bipartite interaction networks. The first method is based on classifications and compares communities within networks to the grouping of nodes by treatment or similar controlling groups. The second method assesses the link between multivariate explanatory variables and network structure using redundancy analyses after singular value decomposition. In both methods, the significance of effects can be gauged through two randomizations. Our methods were applied to experimental data on Daphnia magna and its interactions with gut microbiota and bacterioplankton. The whole network was affected by Daphnia's diet (algae and/or cyanobacteria) and sample type, but not by Daphnia genotype. At coarse grains, bacterioplankton and gut microbiota communities were different. At this scale, the structure of the gut microbiota-based network was not linked to any explanatory factors, while the bacterioplankton-based network was related to both Daphnia's diet and genotype. At finer grains, Daphnia's diet and genotype affected both microbial networks, but the effect of diet on gut microbiota network structure was mediated solely by differences in microbial richness. While no reciprocal effect between the microbial communities could be found, fine-grained analyses presented a more nuanced picture, with bacterioplankton likely affecting the composition of the gut microbiota. Our methods are widely applicable to bipartite networks, can elucidate both controlled and environmental effects in experimental setting using a large amount of sequencing data and can tease apart reciprocal effects of networks on one another. The twofold approach we propose has the advantage of being able to tease apart effects at different scales of network structure, thus allowing for detailed assessment of reciprocal effects of linked networks on one another. As such, our network methods can help ecologists understand huge datasets reporting microbial co-occurrences within different hosts.

Finding missing links in interaction networks

Documenting which species interact within ecological communities is challenging and labor intensive. As a result, many interactions remain unrecorded, potentially distorting our understanding of network structure and dynamics. We test the utility of four structural models and a new coverage-deficit model for predicting missing links in both simulated and empirical bipartite networks. We find they can perform well, although the predictive power of structural models varies with the underlying network structure. The accuracy of predictions can be improved by ensembling multiple models. Augmenting observed networks with most-likely missing links improves estimates of qualitative network metrics. Tools to identify likely missing links can be simple to implement, allowing the prioritization of research effort and more robust assessment of network properties.

Towards a predictive model of species interaction beta diversity

Species interactions are fundamental to community dynamics and ecosystem processes. Despite significant progress in describing species interactions, we lack the ability to predict changes in interactions across space and time. We outline a Bayesian approach to separate the probability of species co-occurrence, interaction and detectability in influencing interaction betadiversity. We use a multi-year hummingbird-plant time series, divided into training and testing data, to show that including models of detectability and occurrence improves forecasts of mutualistic interactions. We then extend our model to explore interaction betadiversity across two distinct seasons. Despite differences in the observed interactions among seasons, there was no significant change in hummingbird occurrence or interaction frequency between hummingbirds and plants. These results highlight the challenge of inferring the causes of interaction betadiversity when interaction detectability is low. Finally, we highlight potential applications of our model for integrating observations of local interactions with biogeographic and evolutionary histories of co-occurring species. These advances will provide new insight into the mechanisms that drive variation in patterns of biodiversity.

Matching consumer feeding behaviours and resource traits: a fourth-corner problem in food-web theory

For decades, food web theory has proposed phenomenological models for the underlying structure of ecological networks. Generally, these models rely on latent niche variables that match the feeding behaviour of consumers with their resource traits. In this paper, we used a comprehensive database to evaluate different hypotheses on the best dependency structure of trait-matching patterns between consumers and resource traits. We found that consumer feeding behaviours had complex interactions with resource traits; however, few dimensions (i.e. latent variables) could reproduce the trait-matching patterns. We discuss our findings in the light of three food web models designed to reproduce the multidimensionality of food web data; additionally, we discuss how using species traits clarify food webs beyond species pairwise interactions and enable studies to infer ecological generality at larger scales, despite potential taxonomic differences, variations in ecological conditions and differences in species abundance between communities.

Predicting cryptic links in host-parasite networks

Networks are a way to represent interactions among one (e.g., social networks) or more (e.g., plant-pollinator networks) classes of nodes. The ability to predict likely, but unobserved, interactions has generated a great deal of interest, and is sometimes referred to as the link prediction problem. However, most studies of link prediction have focused on social networks, and have assumed a completely censused network. In biological networks, it is unlikely that all interactions are censused, and ignoring incomplete detection of interactions may lead to biased or incorrect conclusions. Previous attempts to predict network interactions have relied on known properties of network structure, making the approach sensitive to observation errors. This is an obvious shortcoming, as networks are dynamic, and sometimes not well sampled, leading to incomplete detection of links. Here, we develop an algorithm to predict missing links based on conditional probability estimation and associated, node-level features. We validate this algorithm on simulated data, and then apply it to a desert small mammal host-parasite network. Our approach achieves high accuracy on simulated and observed data, providing a simple method to accurately predict missing links in networks without relying on prior knowledge about network structure.

Predictability of helminth parasite host range using information on geography, host traits and parasite community structure

Host-parasite associations are complex interactions dependent on aspects of hosts (e.g. traits, phylogeny or coevolutionary history), parasites (e.g. traits and parasite interactions) and geography (e.g. latitude). Predicting the permissive host set or the subset of the host community that a parasite can infect is a central goal of parasite ecology. Here we develop models that accurately predict the permissive host set of 562 helminth parasites in five different parasite taxonomic groups. We developed predictive models using host traits, host taxonomy, geographic covariates, and parasite community composition, finding that models trained on parasite community variables were more accurate than any other covariate group, even though parasite community covariates only captured a quarter of the variance in parasite community composition. This suggests that it is possible to predict the permissive host set for a given parasite, and that parasite community structure is an important predictor, potentially because parasite communities are interacting non-random assemblages.

Matching-centrality decomposition and the forecasting of new links in networks

Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and centrality components provides a comprehensive and unifying quantification of their architecture. The matching term quantifies the assortative structure in which node makes links with which other node, whereas the centrality term quantifies the number of links that nodes make. We show, for a diverse set of networks, that this decomposition can provide a tight fit to observed networks. Then we provide three applications. First, we show that the model allows very accurate prediction of missing links in partially known networks. Second, when node characteristics are known, we show how the matching-centrality decomposition can be related to this external information. Consequently, it offers us a simple and versatile tool to explore how node characteristics explain network architecture. Finally, we demonstrate the efficiency and flexibility of the model to forecast the links that a novel node would create if it were to join an existing network.