Food webs: Ordering species according to body size yields high degree of intervality

Food webs, the networks describing “who eats whom” in an ecosystem, are nearly interval, i.e. there is a way to order the species so that almost all the resources of each consumer are adjacent in the ordering. This feature has important consequences, as it means that the structure of food webs can be described using a single (or few) species' traits. Moreover, exploiting the quasi-intervality found in empirical webs can help build better models for food web structure. Here we investigate which species trait is a good proxy for ordering the species to produce quasi-interval orderings. We find that body size produces a significant degree of intervality in almost all food webs analyzed, although it does not match the maximum intervality for the networks. There is also a great variability between webs. Other orderings based on trophic levels produce a lower level of intervality. Finally, we extend the concept of intervality from predator-centered (in which resources are in intervals) to prey-centered (in which consumers are in intervals). In this case as well we find that body size yields a significant, but not maximal, level of intervality. These results show that body size is an important, although not perfect, trait that shapes species interactions in food webs. This has important implications for the formulation of simple models used to construct realistic representations of food webs.     

Phylogeny versus body size as determinants of food web structure

Food webs are the complex networks of trophic interactions that stoke the metabolic fires of life. To understand what structures these interactions in natural communities, ecologists have developed simple models to capture their main architectural features. However, apparently realistic food webs can be generated by models invoking either predator-prey body-size hierarchies or evolutionary constraints as structuring mechanisms. As a result, this approach has not conclusively revealed which factors are the most important. Here we cut to the heart of this debate by directly comparing the influence of phylogeny and body size on food web architecture. Using data from 13 food webs compiled by direct observation, we confirm the importance of both factors. Nevertheless, phylogeny dominates in most networks. Moreover, path analysis reveals that the size-independent direct effect of phylogeny on trophic structure typically outweighs the indirect effect that could be captured by considering body size alone. Furthermore, the phylogenetic signal is asymmetric: closely related species overlap in their set of consumers far more than in their set of resources. This is at odds with several food web models, which take only the view-point of consumers when assigning interactions. The echo of evolutionary history clearly resonates through current food webs, with implications for our theoretical models and conservation priorities.     

The role of body mass in diet contiguity and food-web structure

1. The idea that species occupy distinct niches is a fundamental concept in ecology. Classically, the niche was described as an n-dimensional hypervolume where each dimension represents a biotic or abiotic characteristic. More recently, it has been hypothesised that a single dimension may be sufficient to explain the system-level organization of trophic interactions observed between species in a community. 2. Here, we test the hypothesis that species body mass is that single dimension. Specifically, we determine how the intervality of food webs ordered by body size compares to that of randomly ordered food webs. We also extend this analysis beyond the community level to the effect of body mass in explaining the diets of individual species. 3. We conclude that body mass significantly explains the ordering of species and the contiguity of diets in empirical communities. 4. At the species-specific level, we find that the degree to which body mass is a significant explanatory variable depends strongly on the phylogenetic history, suggesting that other evolutionarily conserved traits partly account for species' roles in the food web. 5. Our investigation of the role of body mass in food webs thus helps us to better understand the important features of community food-web structure and the evolutionary forces that have led us to the communities we observe.     

Relevance of evolutionary history for food web structure

Explaining the structure of ecosystems is one of the great challenges of ecology. Simple models for food web structure aim at disentangling the complexity of ecological interaction networks and detect the main forces that are responsible for their shape. Trophic interactions are influenced by species traits, which in turn are largely determined by evolutionary history. Closely related species are more likely to share similar traits, such as body size, feeding mode and habitat preference than distant ones. Here, we present a theoretical framework for analysing whether evolutionary history--represented by taxonomic classification--provides valuable information on food web structure. In doing so, we measure which taxonomic ranks better explain species interactions. Our analysis is based on partitioning of the species into taxonomic units. For each partition, we compute the likelihood that a probabilistic model for food web structure reproduces the data using this information. We find that taxonomic partitions produce significantly higher likelihoods than expected at random. Marginal likelihoods (Bayes factors) are used to perform model selection among taxonomic ranks. We show that food webs are best explained by the coarser taxonomic ranks (kingdom to class). Our methods provide a way to explicitly include evolutionary history in models for food web structure.     

Exploring the evolutionary signature of food webs' backbones using functional traits

Increasing evidence suggests that an appropriate model for food webs, the network of feeding links in a community of species, should take into account the inherent variability of ecological interactions. Harnessing this variability, we will show that it is useful to interpret empirically observed food webs as realisations of a family of stochastic processes, namely random dot‐product graph models. These models provide an ideal extension of food‐web models beyond the limitations of current deterministic or partially probabilistic models. As an additional bene?t, our RDPG framework enables us to identify the pairwise distance structure given by species' functional food‐web traits: this allows for the natural emergence of ecologically meaningful species groups. Lastly, our results suggest the notion that the evolutionary signature in food webs is already detectable in their stochastic backbones, while the contribution of their ?ne wiring is arguable. Synthesis Food webs are influenced by many stochastic processes and are constantly evolving. Here, we treat observed food webs as realisations of random dot‐product graph models (RDPG), extending food‐web modelling beyond the limitations of current deterministic or partially probabilistic models. Our RDPG framework enables us to identify the pairwise‐distance structure given by species' functional food‐web traits, which in turn allows for the natural emergence of ecologically meaningful species groups. It also provides a way to measure the phylogenetic signal present in food webs, which we find is strongest in webs' low‐dimensional backbones.     

When should we expect early bursts of trait evolution in comparative data? Predictions from an evolutionary food web model

Conceptual models of adaptive radiation predict that competitive interactions among species will result in an early burst of speciation and trait evolution followed by a slowdown in diversification rates. Empirical studies often show early accumulation of lineages in phylogenetic trees, but usually fail to detect early bursts of phenotypic evolution. We use an evolutionary simulation model to assemble food webs through adaptive radiation, and examine patterns in the resulting phylogenetic trees and species' traits (body size and trophic position). We find that when foraging trade-offs result in food webs where all species occupy integer trophic levels, lineage diversity and trait disparity are concentrated early in the tree, consistent with the early burst model. In contrast, in food webs in which many omnivorous species feed at multiple trophic levels, high levels of turnover of species' identities and traits tend to eliminate the early burst signal. These results suggest testable predictions about how the niche structure of ecological communities may be reflected by macroevolutionary patterns.     

The dynamics of multispecies, multi-life-stage models of aquatic food webs

We investigated the dynamics of models of aquatic food webs using stability analysis methods previously applied to other types of food web models. Our models expanded traditional Lotka-Volterra models of predator-prey interactions in several ways. We added life history structure to these models in order to investigate its effects. Life history omnivory is different life history stages of a species feeding in trophically different positions in a food web. Such a species might appear omnivorous, integrating across all stages, but the individual stage might not be. Other important additions to the basic models included stock-recruitment relationships between adults and young and food-dependent maturation rates for early life history stages. Complex models of multispecies interactions were built from basic ones by adding new features sequentially. Our analysis revealed five major features of our multispecies, multi-life-stage models. Omnivory reduces stability, as it does in food web models without life history structure. However, life history omnivory reduces stability much less than single life stage omnivory does. Stock recruitment relationships affect the likelihood of finding stable models. If the maturation rate of young varies with their food supply, the chance of finding stable models decreases. Finally, predation loops of the type A eats B, B eats A, or A eats B, B eats C, C eats A greatly reduce model stability. We present both biological and mathematical explanations for these findings. We also discuss their implications for management of marine resources.     

Evolutionary food web models: effects of an additional resource

Many empirical food webs contain multiple resources, which can lead to the emergence of sub-communities—partitions—in a food web that are weakly connected with each other. These partitions interact and affect the complete food web. However, the fact that food webs can contain multiple resources is often neglected when describing food web assembly theoretically, by considering only a single resource. We present an allometric, evolutionary food web model and include two resources of different sizes. Simulations show that an additional resource can lead to the emergence of partitions, i.e. groups of species that specialise on different resources. For certain arrangements of these partitions, the interactions between them alter the food web properties. First, these interactions increase the variety of emerging network structures, since hierarchical bodysize relationships are weakened. Therefore, they could play an important role in explaining the variety of food web structures that is observed in empirical data. Second, interacting partitions can destabilise the population dynamics by introducing indirect interactions with a certain strength between predator and prey species, leading to biomass oscillations and evolutionary intermittence.     

Connectance and parasite diet breadth in flea-mammal webs

The number of links in webs of species interactions, which lies at the heart of the biodiversity-stability debate, has given rise to controversy during the last 20 yr. Studies exploring these web properties have mainly focused on symmetric webs where each species can potentially feed on any other species; asymmetric webs such as host-parasite webs, where one set of species feed on another set of species, have been overlooked. However, food webs are incomplete without parasites and the study of parasite-host sub-web properties deserves attention. Here, using a large database involving 33 regional interaction webs between mammals and their flea parasites, we found a negative relationship between species richness and host-parasite connectance. We suggest that some phylogenetic constraints on flea diet may explain our observed patterns because we found that parasite diet breadth, measured as host taxonomic diversity, was invariant along our host richness gradient. We found that the slope of the logarithmic relationship between the number of realized links and species richness is lower than slope values reported for food webs. We suggest that connectance may not respond to increasing species richness as rapidly in host-parasite webs as in predator-prey food webs due to stronger coevolutionary requirements.     

Stability of complex food webs: resilience, resistance and the average interaction strength

In the face of stochastic climatic perturbations, the overall stability of an ecosystem will be determined by the balance between its resilience and its resistance, but their relative importance is still unknown. Using aquatic food web models we study ecosystem stability as a function of food web complexity. We measured three dynamical stability properties: resilience, resistance, and variability. Specifically, we evaluate how a decrease in the strength of predator-prey interactions with food web complexity, reflecting a decrease in predation efficiency with the number of prey per predator, affects the overall stability of the ecosystem. We find that in mass conservative ecosystems, a lower interaction strength slows down the mass cycling rate in the system and this increases its resistance to perturbations of the growth rate of primary producers. Furthermore, we show that the overall stability of the food webs is mostly given by their resistance, and not by their resilience. Resilience and resistance display opposite trends, although they are shown not to be simply opposite concepts but rather independent properties. The ecological implication is that weaker predator-prey interactions in closed ecosystems can stabilize food web dynamics by increasing its resistance to climatic perturbations.     

Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces

Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.     

Food-web complexity emerging from ecological dynamics on adaptive networks

Food webs are complex networks describing trophic interactions in ecological communities. Since Robert May's seminal work on random structured food webs, the complexity-stability debate is a central issue in ecology: does network complexity increase or decrease food-web persistence? A multi-species predator-prey model incorporating adaptive predation shows that the action of ecological dynamics on the topology of a food web (whose initial configuration is generated either by the cascade model or by the niche model) render, when a significant fraction of adaptive predators is present, similar hyperbolic complexity-persistence relationships as those observed in empirical food webs. It is also shown that the apparent positive relation between complexity and persistence in food webs generated under the cascade model, which has been pointed out in previous papers, disappears when the final connection is used instead of the initial one to explain species persistence.     

Effects of evolutionary changes in prey use on the relationship between food web complexity and stability

The relationship between food web complexity and stability has been the subject of a long-standing debate in ecology. Although rapid changes in the food web structure through adaptive foraging behavior can confer stability to complex food webs, as reported by Kondoh (Science 299:1388–1391, 2003), the exact mechanisms behind this adaptation have not been specified in previous studies; thus, the applicability of such predictions to real ecosystems remains unclear. One mechanism of adaptive foraging is evolutionary change in genetically determined prey use. We constructed individual-based models of evolution of prey use by predators assuming explicit population genetics processes, and examined how this evolution affects the stability (i.e., the proportion of species that persist) of the food web and whether the complexity of the food web increased the stability of the prey–predator system. The analysis showed that the stability of food webs decreased with increasing complexity regardless of evolution of prey use by predators. The effects of evolution on stability differed depending on the assumptions made regarding genetic control of prey use. The probabilities of species extinctions were associated with the establishment or loss of trophic interactions via evolution of the predator, indicating a clear link between structural changes in the food web and community stability.     

Modelling Size Structured Food Webs Using a Modified Niche Model with Two Predator Traits

The structure of food webs is frequently described using phenomenological stochastic models. A prominent example, the niche model, was found to produce artificial food webs resembling real food webs according to a range of summary statistics. However, the size structure of food webs generated by the niche model and real food webs has not yet been rigorously compared. To fill this void, I use a body mass based version of the niche model and compare prey-predator body mass allometry and predator-prey body mass ratios predicted by the model to empirical data. The results show that the model predicts weaker size structure than observed in many real food webs. I introduce a modified version of the niche model which allows to control the strength of size-dependence of predator-prey links. In this model, optimal prey body mass depends allometrically on predator body mass and on a second trait, such as foraging mode. These empirically motivated extensions of the model allow to represent size structure of real food webs realistically and can be used to generate artificial food webs varying in several aspects of size structure in a controlled way. Hence, by explicitly including the role of species traits, this model provides new opportunities for simulating the consequences of size structure for food web dynamics and stability.     

Assessing concurrent patterns of environmental niche and morphological evolution among species of horned lizards (Phrynosoma)

The prediction that variation in species morphology is related to environmental features has long been of interest to ecologists and evolutionary biologists. Many studies have demonstrated strong associations between morphological traits and local habitat characteristics, but few have considered the extent to which morphological traits may be associated with environmental features across broad geographic areas. Here, we use morphological, environmental and phylogenetic data compiled from Phrynosoma species to examine morphological and climatic variation across the geographic ranges of these species in an evolutionary context. We find significant phylogenetic signal in species’ environmental niches, but not in morphological traits. Furthermore, we demonstrate a significant correlation between species’ environmental niches and morphological traits when phylogenetic history is accounted for in the analysis. Our results suggest the importance of climatic variables in influencing morphological variation among species, and have implications for understanding how species distributions are constrained by environmental variation.     

Defining and measuring trophic role similarity in food webs using regular equivalence

We present a graph theoretic model of analysing food web structure called regular equivalence. Regular equivalence is a method for partitioning the species in a food web into "isotrophic classes" that play the same structural roles, even if they are not directly consuming the same prey or if they do not share the same predators. We contrast regular equivalence models, in which two species are members of the same trophic group if they have trophic links to the same set of other trophic groups, with structural equivalence models, in which species are equivalent if they are connected to the exact same other species. Here, the regular equivalence approach is applied to two published food webs: (1) a topological web (Malaysian pitcher plant insect food web) and (2) a carbon-flow web (St. Marks, Florida seagrass ecosystem food web). Regular equivalence produced a more satisfactory set of classes than did the structural approach, grouping basal taxa with other basal taxa and not with top predators. Regular equivalence models provide a way to mathematically formalize trophic position, trophic group and trophic niche. These models are part of a family of models that includes structural models used extensively by ecologists now. Regular equivalence models uncover similarities in trophic roles at a higher level of organization than do the structural models. The approach outlined is useful for measuring the trophic roles of species in food web models, measuring similarity in trophic relations of two or more species, comparing food webs over time and across geographic regions, and aggregating taxa into trophic groups that reduce the complexity of ecosystem feeding relations without obscuring network relationships. In addition, we hope the approach will prove useful in predicting the outcome of predator-prey interactions in experimental studies.     

The phylogenetic structure of plant–pollinator networks increases with habitat size and isolation

Similarity among species in traits related to ecological interactions is frequently associated with common ancestry. Thus, closely related species usually interact with ecologically similar partners, which can be reinforced by diverse co‐evolutionary processes. The effect of habitat fragmentation on the phylogenetic signal in interspecific interactions and correspondence between plant and animal phylogenies is, however, unknown. Here, we address to what extent phylogenetic signal and co‐phylogenetic congruence of plant–animal interactions depend on habitat size and isolation by analysing the phylogenetic structure of 12 pollination webs from isolated Pampean hills. Phylogenetic signal in interspecific interactions differed among webs, being stronger for flower‐visiting insects than plants. Phylogenetic signal and overall co‐phylogenetic congruence increased independently with hill size and isolation. We propose that habitat fragmentation would erode the phylogenetic structure of interaction webs. A decrease in phylogenetic signal and co‐phylogenetic correspondence in plant–pollinator interactions could be associated with less reliable mutualism and erratic co‐evolutionary change.     

Diversity of plant evolutionary lineages promotes arthropod diversity

Large‐scale habitat destruction and climate change result in the non‐random loss of evolutionary lineages, reducing the amount of evolutionary history represented in ecological communities. Yet, we have limited understanding of the consequences of evolutionary history on the structure of food webs and the services provided by biological communities. Drawing on 11 years of data from a long‐term plant diversity experiment, we show that evolutionary history of plant communities – measured as phylogenetic diversity – strongly predicts diversity and abundance of herbivorous and predatory arthropods. Effects of plant species richness on arthropods become stronger when phylogenetic diversity is high. Plant phylogenetic diversity explains predator and parasitoid richness as strongly as it does herbivore richness. Our findings indicate that accounting for evolutionary relationships is critical to understanding the severity of species loss for food webs and ecosystems, and for developing conservation and restoration policies.     

Dynamics of compartmented and reticulate food webs in relation to energetic flows

Using simple food webs, we address how the interactions of food web structure and energetic flows influence dynamics. We examine the effect of food web topologies with equivalent energetics (i.e., trophic interactions are equivalent at each trophic level), following which we vary energetic flows to include weak and strong interactions or nonequivalent energetics. In contrast to some work (Pimm 1979), we find that compartmented webs are more stable than reticulate webs. However, we find that nonequivalent energetics can stabilize previously unstable reticulate structures. It is not only weak flows that can be stabilizing but also the arrangement of the flows that emphasizes stabilizing mechanisms. We find that the main stabilizing mechanism is asynchrony, where structures and energetic arrangements that decrease synchrony such as internal segregation or competition will stabilize dynamics. Since compartments allow prey dynamics to behave somewhat independently, compartmentation readily promotes stability. In addition, these results can be scaled from simple food webs to more complex webs with many interacting subsystems so that linking weak subsystems to strong ones can stabilize dynamics. We show that food web dynamics are determined not only by topology but also the arrangement of weak and strong energetic flows.