The characteristics of species in an evolutionary food web model

We explore the consequences of modifying the way in which species are defined in an evolutionary food web model. In the original version of the model, the species were defined in terms of a fixed number of features, chosen from a large number of possibilities. These features represented phenotypic and behavioural characteristics of the species. Speciation consisted in occasionally replacing one of the features by another. Here we modify this scheme by firstly allowing for a richer structure and secondly by testing whether we are able to eliminate the need for an explicit choice of features altogether. In the first case we allow for changing the number of features which define a species, as well as their nature, and find that in the resulting webs the higher trophic levels typically contain species with the greatest number of features. In the second case, by a simplification of the mechanisms for inter and intra-species competition, we construct a model without any explicit features and find that we are still able to grow model food webs. We assess the quality of the food webs produced and discuss the consequences of our findings for the future modelling of food webs.     

Parasites in food webs: the ultimate missing links

Parasitism is the most common consumer strategy among organisms, yet only recently has there been a call for the inclusion of infectious disease agents in food webs. The value of this effort hinges on whether parasites affect food‐web properties. Increasing evidence suggests that parasites have the potential to uniquely alter food‐web topology in terms of chain length, connectance and robustness. In addition, parasites might affect food‐web stability, interaction strength and energy flow. Food‐web structure also affects infectious disease dynamics because parasites depend on the ecological networks in which they live. Empirically, incorporating parasites into food webs is straightforward. We may start with existing food webs and add parasites as nodes, or we may try to build food webs around systems for which we already have a good understanding of infectious processes. In the future, perhaps researchers will add parasites while they construct food webs. Less clear is how food‐web theory can accommodate parasites. This is a deep and central problem in theoretical biology and applied mathematics. For instance, is representing parasites with complex life cycles as a single node equivalent to representing other species with ontogenetic niche shifts as a single node? Can parasitism fit into fundamental frameworks such as the niche model? Can we integrate infectious disease models into the emerging field of dynamic food‐web modelling? Future progress will benefit from interdisciplinary collaborations between ecologists and infectious disease biologists.     

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.     

Evidence for the existence of a robust pattern of prey selection in food webs

Food webs aim to provide a thorough representation of the trophic interactions found in an ecosystem. The complexity of empirical food webs, however, is leading many ecologists to focus dynamic ecosystem studies on smaller microcosm or mesocosm studies based upon community modules, which comprise three to five species and the interactions likely to have ecological relevance. We provide here a structural counterpart to community modules. We investigate food-web 'motifs' which are n-species connected subgraphs found within the food web. Remarkably, we find that the over- and under-representation of three-species motifs in empirical food webs can be understood through comparison to a static food-web model, the niche model. Our result conclusively demonstrates that predation upon species with some 'characteristic' niche value is the prey selection mechanism consistent with the structural properties of empirical food webs.     

Identifying conversion efficiency as a key mechanism underlying food webs adaptive evolution: a step forward,or backward?

Body size or mass is one of the main factors underlying food webs structure. A large number of evolutionary models have shown that indeed, the adaptive evolution of body size (or mass) can give rise to hierarchically organised trophic levels with complex between and within trophic interactions. However, these models generally make strong arbitrary assumptions on how traits evolve, casting doubts on their robustness. In particular, biomass conversion efficiency is always considered independent of the predator and prey size, which contradicts with the literature. In this paper, we propose a general model encompassing most previous models which allows to show that relaxing arbitrary assumptions gives rise to unrealistic food webs. We then show that considering biomass conversion efficiency dependent on species size is certainly key for food webs adaptive evolution because realistic food webs can evolve, making obsolete the need of arbitrary constraints on traits' evolution. We finally conclude that, on the one hand, ecologists should pay attention to how biomass flows into food webs in models. On the other hand, we question more generally the robustness of evolutionary models for the study of food webs.     

Food web modularity and biodiversity promote species persistence in polluted environments

Pollution represents a major threat to biodiversity. A wide class of pollutants tends to accumulate within organisms and propagate within communities via trophic interactions. Thus the final effects of accumulable pollutants may be determined by the structure of food webs and not only by the susceptibility of their constituent species. Species within real food webs are typically arranged into modules, which have been proposed to be determinants of network stability. In this study we evaluate the effect of network modularity and species richness on long‐term species persistence in communities perturbed by pollutant stress. We built model food webs with different levels of modularity and used a bioenergetic model to project the dynamics of species. Further, we modeled the dynamics of bioaccumulated and environmental pollutants. We found that modularity promoted the stability of food webs subjected to pollutant stress. We also found that richer food webs were more robust at all modularity levels. Nevertheless, modularity did not promote stability of communities facing a perturbation that shared most features with the pollutant perturbation, but does not spread through trophic interactions. The positive effect of both modularity and species richness on species persistence was cancelled and even reversed when the structure of food web departed from a realistic body size distribution or a hierarchical feeding structure. Our results support the idea that modularity implies important dynamic consequences for communities facing pollution, highlighting a main role of network structure on ecosystem 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.     

Examining the potential effects of species aggregation on the network structure of food webs

One of the key measures that have been used to describe the topological properties of complex networks is the “degree distribution”, which is a measure that describes the frequency distribution of number of links per node. Food webs are complex ecological networks that describe the trophic relationships among species in a community, and the topological properties of empirical food webs, including degree distributions, have been examined previously. Previously, the “niche model” has been shown to accurately predict degree distributions of empirical food webs, however, the niche model-generated food webs were referenced against empirical food webs that had their species grouped together based on their taxonomic and/or trophic relationships (aggregated food webs). Here, we explore the effects of species aggregation on the ability of the niche model to predict the total- (sum of prey and predator links per node), in- (number of predator links per node), and out- (number of prey links per node) degree distributions of empirical food webs by examining two food webs that can be aggregated at different levels of resolution. The results showed that (1) the cumulative total- and out-degree distributions were consistent with the niche model predictions when the species were aggregated, (2) when the species were disaggregated (i.e., higher resolution), there were mixed conclusions with regards to the niche model's ability to predict total- and out-degree distributions, (3) the model's ability to predict the in-degree distributions of the two food webs was generally inadequate. Although it has been argued that universal functional form based on the niche model could describe the degree distribution patterns of empirical food webs, we believe there are some limitations to the model's ability to accurately predict the structural properties of food webs.     

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.     

Complexity and structural properties of food webs in the Barents Sea

A food web topology describes the diversity of species and their trophic interactions, i.e. who eats whom, and structural analysis of food web topologies can provide insight into ecosystem structure and function. It appears simple, at first sight, to list all species and their trophic interactions. However, the very large number of species at low trophic levels and the impossibility to monitor all trophic interactions in the ocean makes it impossible to construct complete food web topologies. In practice, food web topologies are simplified by aggregating species into groups termed trophospecies. It is not clear though, how much simplified versions of food webs retain the structural properties of more detailed networks. Using the most comprehensive Barents Sea food web to date, we investigate the performance of methods to construct simplified food webs using three approaches: taxonomic, structural and regular clustering. We then evaluate how topological properties vary with the level of network simplification. Results show that alteration of food web structural properties due to aggregation are highly sensitive to the methodology used for grouping species and trophic links. In the specific case of the Barents Sea, we show that it is possible to preserve key structural properties of the original complex food web in simplified versions when using taxonomic or structural clustering combined with intermediate 25% linkage for trophic aggregation.     

Estimating morphologically determined connectance and structure for food webs of freshwater invertebrates

1. Connectance is a parameter of central importance in determining food-web structure, but the processes determining its value remain unclear. In evaluating possible explanations it is useful to know what patterns, and values, of connectance occur in food webs assembled at random from a set of species in a regional species pool; i.e. where the number of links is determined by the morphological features of the species present, not by the immediate effects of energetics or stability on the particular web. 2. This study examines, by means of laboratory experiments, the occurrence of potential feeding interactions among a set of freshwater invertebrate species randomly selected from different freshwater sites in a geographical region. The results from pairwise feeding trials are used to construct two ‘theoretical’ food webs, in which the patterns and values of connectance are examined. 3. Analyses of these webs indicate that their structure is consistent with the observed values in previously documented ‘real’ webs. Directed connectance values of 0.12–0.16 (or less) suggest that the assembled webs are no more connected than many freshwater webs from natural systems. The number of links per species increases curvilinearly with the number of species, during web assembly, consistent with recent hypotheses. 4. These results also indicate that quantifying, and understanding the determinants of, trophic generalism or specialism does have implications for understanding how connectance is constrained in real webs. Freshwater invertebrates seem to be relatively generalist, and freshwater food webs perhaps correspondingly highly connected. Such arguments have implications for interpreting other aspects of food-web structure in these systems, and for parameterizing models that are based on connectance.     

Using trophic hierarchy to understand food web structure

Link arrangement in food webs is determined by the species' feeding habits. This work investigates whether food web topology is organized in a gradient of trophic positions from producers to consumers. To this end, we analyzed 26 food webs for which the consumption rate of each species was specified. We computed the trophic positions and the link densities of all species in the food webs. Link density measures how much each species contributes to the distribution of energy in the system. It is expressed as the number of links species establish with other nodes, weighted by their magnitude. We computed these two metrics using various formulations developed in the ecological network analysis framework. Results show a positive correlation between trophic position and link density across all the systems, regardless the specific formulas used to measure the two quantities. We performed the same analysis on the corresponding binary matrices (i.e. removing information about rates). In addition, we investigated the relation between trophic position and link density in: a) simulated binary webs with same connectance as the original ones; b) weighted webs with constant topology but randomized link strengths and c) weighted webs with constant connectance where both topology and link strengths are randomized. The correlation between the two indices attenuates, vanishes or becomes negative in the case of binary food webs and simulated data (weighted and unweighted).
According to our analysis, link density in food webs decreases with trophic position so that it is greatly reduced toward the top of the trophic hierarchy. This outcome, that seems to challenge previous conclusions based on null models, strongly depends on link quantification. Including interaction strengths may improve substantially our understanding of food web organization, and possibly contradict results based on the analysis of binary webs.     

Biodiversity lessens the risk of cascading extinction in model food webs

Due to the complex interactions between species in food webs, the extinction of one species could lead to a cascade of further extinctions and hence cause dramatic changes in species composition and ecosystem processes. We found that the risk of additional species extinction, following the loss of one species in model food webs, decreases with the number of species per functional group. For a given number of species per functional group, the risk of further extinctions is highest when an autotroph is removed and lowest when a top predator is removed. In addition, stability decreases when the distribution of interaction strengths in the webs is changed from equal to skew (few strong and many weak links). We also found that omnivory appears to stabilize model food webs. Our results indicate that high biodiversity may serve as an insurance against radical ecosystem changes.     

Shrinking by numbers: landscape context affects the species composition but not the quantitative structure of local food webs

1. With habitat fragmentation spreading around the world, there is a pressing need to understand its impacts on local food webs. To date, few studies have examined the effects of landscape context on multiple local communities in a quantitative, spatially realistic setting. 2. To examine how the isolation of a food web affects its structure, we construct local food webs of specialist herbivores and their natural enemies on 82 individual oaks (Quercus robur) growing in different landscape contexts. 3. Across this set of webs, we find that communities in isolated habitat patches not only contained fewer species than did well-connected ones, but also differed in species composition. 4. Surprisingly, the effects observed in terms of species composition were not reflected in the quantitative interaction structure of local food webs: landscape context had no detectable effect on either the interaction evenness, linkage density, connectance, generality or vulnerability of local webs. 5. We conclude that the quantitative structure of food webs may be stable in the face of habitat fragmentation, despite clear-cut impacts on individual species. This finding offers hope-inspiring news for conservation, but should clearly be verified by empirical studies across both naturally and more recently fragmented systems.     

Identifying compartments in ecological networks based on energy channels

It has been confirmed in many food webs that the interactions between species are divided into “compartments,” that is, subgroups of highly interacting taxa with few weak interactions between the subgroups. Many of the current methods for detecting compartments in food webs are borrowed from network theory, which do little to improve our understanding of the mechanisms underpinning them. Therefore, a method based on ecological context is needed. Here, we develop a new method for detecting compartments in food webs based on the reliance of each node on energy derived from basal resources (i.e., producers or decomposers). Additional Monte Carlo simulations were conducted to test the significance of the compartmentalization. Further, we applied a food web dynamics model to test whether the effects of permutation would be retained within a single compartment. The proposed method identified significant compartments in 23 of the 28 empirical food webs that were investigated. We further demonstrated that the effects of node removal were significantly higher within compartments than between compartments. Our methods and results emphasize the importance of energy channels in forming food web structures, which sheds light on the mechanisms of self‐organization within food webs.     

The robustness of the Webworld model to changes in its structure

We investigate the robustness of a co-evolutionary model of multi-species communities to changes in its structure. The model has both a conventional population dynamics and a network dynamics through which new species are introduced and unsuccessful species removed. The effect of choosing different forms of population dynamics has already been investigated for this model. Here we study the effects of changing the nature of species interactions and thresholds such as the number of individuals of a species required to be present before that species is said to be extinct. We find that the model is remarkably robust to these changes, with only a very few of the modifications leading to food webs which differ appreciably from those found in the original model. This indicates that many aspects of the structure of the model are not, in general, a factor in determining the nature of the food webs constructed.     

Soil fertility shapes belowground food webs across a regional climate gradient

Changes in soil fertility during pedogenesis affect the quantity and quality of resources entering the belowground subsystem. Climate governs pedogenesis, yet how climate modulates responses of soil food webs to soil ageing remains unexplored because of the paucity of appropriate model systems. We characterised soil food webs along each of four retrogressive soil chronosequences situated across a strong regional climate gradient to show that belowground communities are predominantly shaped by changes in fertility rather than climate. Basal consumers showed hump‐shaped responses to soil ageing, which were propagated to higher‐order consumers. There was a shift in dominance from bacterial to fungal energy channels with increasing soil age, while the root energy channel was most important in intermediate‐aged soils. Our study highlights the overarching importance of soil fertility in regulating soil food webs, and indicates that belowground food webs will respond more strongly to shifts in soil resources than climate change.     

Integrating ecosystem engineering and food webs

Ecosystem engineering, the physical modification of the environment by organisms, is a common and often influential process whose significance to food web structure and dynamics is largely unknown. In the light of recent calls to expand food web studies to include non‐trophic interactions, we explore how we might best integrate ecosystem engineering and food webs. We provide rationales justifying their integration and present a provisional framework identifying how ecosystem engineering can affect the nodes and links of food webs and overall organization; how trophic interactions with the engineer can affect the engineering; and how feedbacks between engineering and trophic interactions can affect food web structure and dynamics. We use a simple integrative food chain model to illustrate how feedbacks between the engineer and the food web can alter 1) engineering effects on food web dynamics, and 2) food web responses to extrinsic environmental perturbations. We identify four general challenges to integration that we argue can readily be met, and call for studies that can achieve this integration and help pave the way to a more general understanding of interaction webs in nature. Synthesis All species are affected by their physical environment. Because ecosystem engineering species modify the physical environment and belong to food webs, such species are potentially one of the most important bridges between the trophic and non‐trophic. We examine how to integrate the so far, largely independent research areas of ecosystem engineering and food webs. We present a conceptual framework for understanding how engineering can affect food webs and vice versa, and how feedbacks between the two alter ecosystem dynamics. With appropriate empirical studies and models, integration is achievable, paving the way to a more general understanding of interaction webs in nature.     

A modified niche model for generating food webs with stage‐structured consumers: The stabilizing effects of life‐history stages on complex food webs

1. Almost all organisms grow in size during their lifetime and switch diets, trophic positions, and interacting partners as they grow. Such ontogenetic development introduces life‐history stages and flows of biomass between the stages through growth and reproduction. However, current research on complex food webs rarely considers life‐history stages. The few previously proposed methods do not take full advantage of the existing food web structural models that can produce realistic food web topologies.
2. We extended the niche model developed by Williams and Martinez (Nature, 2000, 404, 180–183) to generate food webs that included trophic species with a life‐history stage structure. Our method aggregated trophic species based on niche overlap to form a life‐history structured population; therefore, it largely preserved the topological structure of food webs generated by the niche model. We applied the theory of allometric predator–prey body mass ratio and parameterized an allometric bioenergetic model augmented with biomass flow between stages via growth and reproduction to study the effects of a stage structure on the stability of food webs.
3. When life‐history stages were linked via growth and reproduction, more food webs persisted, and persisting food webs tended to retain more trophic species. Topological differences between persisting linked and unlinked food webs were small to modest. The slopes of biomass spectra were lower, and weak interaction links were more prevalent in the linked food webs than the unlinked ones, suggesting that a life‐history stage structure promotes characteristics that can enhance stability of complex food webs.
4. Our results suggest a positive relationship between the complexity and stability of complex food webs. A life‐history stage structure in food webs may play important roles in dynamics of and diversity in food webs.