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.     

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.     

Fertilizer addition lessens the flux of microbial carbon to higher trophic levels in soil food webs of grassland

Roots and root-derived C compounds are increasingly recognised as important resources for soil animal food webs. We used ¹³C-labelled glucose as a model C compound representing root exudates to follow the incorporation of root-derived C into the soil animal food web of a temperate grassland over a period of 52 weeks. We investigated variations in glucose C incorporation with fertilizer addition and sward composition, i.e. variations in plant functional groups. The approach allowed the differentiation of trophic chains based on primary decomposers feeding on litter and phytophagous species feeding on roots (i.e. not incorporating glucose C) from those based on secondary decomposers feeding on microorganisms (thereby assimilating glucose C). Each of the studied soil animal species incorporated glucose C, indicating that the majority of grassland soil animal species rely on microorganisms as food resources with microorganisms being fuelled by root exudates. However, incorporation of glucose C into soil animal species varied markedly with species identity, suggesting that detritivorous microarthropods complement each other in channelling microbial C through soil food webs. Fertilizer addition markedly reduced the concentration of glucose C in most soil animal species as well as the absolute transfer of glucose C into oribatid mites as major secondary decomposers. The results suggest that fertilizer addition shifts the basis of the decomposer food web towards the use of unlabelled resources, presumably roots, i.e. towards a herbivore system, thereby lessening the link between microorganisms and microbial grazers and hampering the propagation of microbial C to higher trophic levels.     

Current food web models cannot explain the overall topological structure of observed food webs

Topological food webs illustrating “who eats whom” in different systems exhibit similar, non‐random, structures suggesting that general rules govern food web structure. Current food web models correctly predict many measures of food web topology from knowledge of species richness and connectance (fraction of possible predator–prey links that actually occur), together with assumptions about the ecological rules governing “who eats whom”. However, current measures are relatively insensitive to small changes in topology. Improvement of, and discrimination among, current models requires development of new measures of food web structure. Here I examine whether current food web models (cascade, niche, and nested hierarchy models, plus a random null model) can predict a new measure of food web structure, structural stability. Structural stability complements other measures of food web topology because it is sensitive to changes in topology that other measures often miss. The cascade and null models respectively over‐ and underpredict structural stability for a set of 17 high‐quality food webs. While the niche and nested hierarchy models provide unbiased predictions on average, their 95% confidence intervals frequently fail to include the observed data. Observed structural stabilities for all models are overdispersed compared to model predictions, and predicted and observed structural stabilities are uncorrelated, indicating that important sources of variation in structural stability are not captured by the models. Crucially, poor model performance arises because observed variation in structural stability is unrelated to variation in species richness and connectance. In contrast, almost all other measures of food web topology vary with species richness and connectance in natural webs. No model that takes species richness and connectance as the only input parameters can reproduce observed variation in structural stability. Further progress in predicting and explaining food web topology will require fundamentally new models based on different input parameters.     

Newly proposed node segregation index is not suitable for analyzing unimode food webs

Strona and Veech (2015) developed a new node segregation (or node overlap) index for analysing ecological network structure based on the Veech (2013)’s species co-occurrence probabilistic model, which was originally applied to species-site matrices. However, a species-site matrix for analysing species co-occurrence patterns and an adjacency matrix for characterising unimode network structures are different. Directly applying Veech’s species co-occurrence probabilistic model to adjacency matrices in unimode food webs is problematic. The central critical problem is related to the number of free species (or nodes/vertices) in the unimode network that can be the neighbors (have links to connect) of a focused species or a focused pair of species. This number is typically less than the total number of species in real food webs. That is, species are not independent from each other in unimode networks. For a simple undirected unimode network without self-loops, based on the criterion whether there is a link between two species for a focused pair, a correct probabilistic model is developed to accurately compute the probability of observing some shared neighbors for a pair of species in the network. Numerical simulation show that the node overlap calculated using the correct and original probabilistic models present remarkable differences, especially when a unimode network is nested and contains generalists. In summary, The correct probabilistic model should be used if ones want Strona and Veech (2015)’s node segregation index to work for unimode food webs.     

Simple MaxEnt models explain food web degree distributions

Degree distributions are widely used to characterize networks, including food webs, and play a vital role in models of food web structure. To date, there have been no mechanistic or statistical explanations for the form of food web degree distributions. Here, I introduce models for food web degree distributions based on the principle of maximum entropy (MaxEnt) and show that the distributions of the number of consumers and resources in 23 (45%) and 35 (69%) of 51 food webs are not significantly different at a 95% confidence level from the MaxEnt distribution. These findings offer a new null model for the most probable degree distributions in food webs and other networks. They suggest that there is relatively little pressure favoring generalist or specialist consumption strategies but that biological drivers or methodological bias may force the consumer distribution away from the MaxEnt form.     

Energetics of microbial food webs

The energetic demand of microorganisms in natural waters and the flux of energy between microorganisms and metazoans has been evaluated by empirical measurements in nature, in microcosms and mesocosms, and by simulation models. Microorganisms in temperate and tropical waters often use half or more of the energy fixed by photosynthesis. Most simulations and some experimental results suggest significant energy transfer to metazoans, but empirical evidence is mixed. Considerations of the range of growth yields of microorganisms and the number of trophic transfers among them indicate major energy losses within microbial food webs. Our ability to verify and quantify these processes is limited by the variability of assimilation efficiency and uncertainty about the structure of microbial food webs. However, even a two-step microbial chain is a major energy sink. As an energetic link to metazoans, the detritus food web is inefficient, and its significance may have been overstated. There is not enough bacterial biomass associated with detritus to support metazoan detritivores. Much detritus is digestible by metazoans directly. Thus, metazoans and bacteria may to a considerable degree compete for a common resource. Microorganisms, together with metazoans, are important to the stability of planktonic communities through their roles as rapid mineralizers of organic matter, releasing inorganic nutrients. The competition for organic matter and the resultant rapid mineralization help maintain stable populations of phytoplankton in the absence of advective nutrient supply. At temperatures near O °C, bacterial metabolism is suppressed more than is the rate of photosynthesis. As a result, the products of the spring phytoplankton bloom in high-temperate latitudes are not utilized rapidly by bacteria. At temperatures below 0°C microbial food webs are neither energy sinks or links: they are suppressed. Because the underlying mechanism of low-temperature inhibition is not known, we cannot yet generalize about this as a control of food web processes. Microorganisms may operate on several trophic levels simultaneously. Therefore, the realism of the trophic level concept and the reality of the use of ecological efficiency calculations in ecosystem models is questionable.     

Fit, efficiency, and biology: some thoughts on judging food web models

Revealing the processes that determine who eats whom, and thereby the structure of food webs, is a long running challenge in ecological research. Recent advances include development of new methods for measuring fit of models to observed food web data, and thereby testing which are the ‘best’ food web models. The best model could be considered the most efficient with relatively few parameters and high explanatory power. Another recent advance involves adding some additional biology to food web models in the form of foraging theory based on maximisation of energy intake as the predictor of species' diets in food webs. While it is interesting to compare efficiency among food web models, we believe that such comparisons at least should be interpreted with caution, since they do not account for any differences in motivation, formulation, and potential that might also exist among models. Furthermore, we see an important but somewhat neglected role for experimental tests of models of food web structure.     

Body size and food web structure: testing the equiprobability assumption of the cascade model

The cascade model successfuly predicts many patterns in reported food webs. A key assumption of this model is the existence of a predetermined trophic hierarchy; prey are always lower in the hierarchy than their predators. At least three studies have suggested that, in animal food webs, this hierarchy can be explained to a large extent by body size relationships. A second assumption of the standard cascade model is that trophic links not prohibited by the hierarchy occur with equal probability. Using nonparametric contingency table analyses, we tested this ”equiprobability hypothesis” in 16 published animal food webs for which the adult body masses of the species had been estimated. We found that when the hierarchy was based on body size, the equiprobability hypothesis was rejected in favor of an alternative, ”predator-dominance” hypothesis wherein the probability of a trophic link varies with the identity of the predator. Another alternative to equiprobabilty is that the probability of a trophic link depends upon the ratio of the body sizes of the two species. Using nonparametric regression and liklihood ratio tests, we show that a size-ratio based model represents a significant improvement over the cascade model. These results suggest that models with heterogeneous predation probabilities will fit food web data better than the homogeneous cascade model. They also suggest a new way to bridge the gap between static and dynamic food web models. Received: 3 February 1999 / Accepted: 26 October 1999     

The effects of mixotrophy on the stability and dynamics of a simple planktonic food web model

Recognition of the microbial loop as an important part of aquatic ecosystems disrupted the notion of simple linear food chains. However, current research suggests that even the microbial loop paradigm is a gross simplification of microbial interactions due to the presence of mixotrophs-organisms that both photosynthesize and graze. We present a simple food web model with four trophic species, three of them arranged in a food chain (nutrients-autotrophs-herbivores) and the fourth as a mixotroph with links to both the nutrients and the autotrophs. This model is used to study the general implications of inclusion of the mixotrophic link in microbial food webs and the specific predictions for a parameterization that describes open ocean mixed layer plankton dynamics. The analysis indicates that the system parameters reside in a region of the parameter space where the dynamics converge to a stable equilibrium rather than displaying periodic or chaotic solutions. However, convergence requires weeks to months, suggesting that the system would never reach equilibrium in the ocean due to alteration of the physical forcing regime. Most importantly, the mixotrophic grazing link seems to stabilize the system in this region of the parameter space, particularly when nutrient recycling feedback loops are included.     

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.     

Effects of extinction on food web structures on an evolutionary time scale

Extinction affected food web structure in paleoecosystems. Recent theoretical studies that examined the effects of extinction intensity on food web structure on ecological time scales have considered extinction to involve episodic events, with pre-extinction food webs becoming established without dynamics. However, in terms of the paleontological time scale, food web structures are generated from feedback with repeated extinctions, because extinction frequency is affected by food web structure, and food web structure itself is a product of previous extinctions. We constructed a simulation model of changes in tri-trophic-level food webs to examine how continual extinction events affect food webs on an evolutionary time scale. We showed that under high extinction intensity (1) species diversity, especially that of consumer species, decreased; (2) the total population density at each trophic level decreased, while the densities of individual species increased; and (3) the trophic link density of the food web increased. In contrast to previous models, our results were based on an assumption of long-term food web development and are able to explain overall trends posited by empirical investigations based on fossil records.     

Effects of Multi-chain Omnivory on the Strength of Trophic Control in Lakes

Omnivory has been implicated in both diffusing and intensifying the effects of consumer control in food chains. Some have postulated that the strong, community level, top-down control apparent in lakes is not expressed in terrestrial systems because terrestrial food webs are reticulate, with high degrees of omnivory and diverse plant communities. In contrast, lake food webs are depicted as simple linear chains based on phytoplankton-derived energy. Here, we explore the dynamic implications of recent evidence showing that attached algal (periphyton) carbon contributes substantially to lake primary and secondary productivity, including fish production. Periphyton production represents a cryptic energy source in oligotrophic and mesotrophic lakes that is overlooked by previous theoretical treatment of trophic control in lakes. Literature data demonstrate that many fish are multi-chain omnivores, exploiting food chains based on both littoral and pelagic primary producers. Using consumer-resource models, we examine how multiple food chains affect fourth-level trophic control across nutrient gradients in lakes. The models predict that the stabilizing effects of linked food chains are strongest in lakes where both phytoplankton and periphyton contribute substantially to production of higher trophic levels. This stabilization enables a strong and persistent top down control on the pelagic food chain in mesotrophic lakes. The extension of classical trophic cascade theory to incorporate more complex food web structures driven by multi-chain predators provides a conceptual framework for analysis of reticulate food webs in ecosystems.     

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.     

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.

     

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.     

Are high Arctic terrestrial food chains really that simple? – The Bear Island food web revisited

Summerhayes and Elton's (1923) "nitrogen cycle" diagram for Bear Island (Bjørnøya), Svalbard, is widely used to illustrate the organisation of high Arctic food webs. We present a revision of the terrestrial section of this food web based on 12 years work on Spitsbergen, Svalbard. The level of complexity is much greater than Summerhayes and Elton suggested and the implications for ecological theory are discussed. In particular the low level of primary productivity does not appear to restrict the length of ectotherm food chains. This may in part be due to the open nature of the ecosystem, which receives energy/nutrient subsidies in the form of allochthonous wind-blown insects and detritus, particularly from surrounding aquatic environments. Connectivity is also significantly higher. Our data support the increasingly accepted view that many food webs presented in the literature are gross oversimplifications and that analysis of their structure can produce misleading conclusions.     

Intraguild predation,invertebrate predators,and trophic cascades in lake food webs

The top-down and bottom-up properties of model food webs that include intraguild predation and self-limiting factors such as cannibalism are investigated. Intraguild predation can dampen or even reverse the top-down effects predicted by food chain theory. The degree of self-limitation among the intraguild prey is a key factor in determining the direction and strength of the top-down response. Intraguild predation and self-limiting factors can also substantially alter the bottom-up effects of enrichment. These results can help explain the disparate results of trophic cascade experiments in lakes, where cascades are usually seen when large Daphnia are the primary herbivores, but not when smaller-bodied herbivores are dominant. Top-down manipulations should cascade at least modestly to phytoplankton in those lakes whose food web can be reasonably approximated by a chain (typically, those where Daphnia is the dominant herbivore), as predicted by food chain theory. On the other hand, smaller-bodied zooplankton are often preyed upon heavily by invertebrate predators as well as by planktivorous fish, thereby introducing elements of intraguild predation into these food webs. In this case, conventional food chain theory is likely to give incorrect predictions. Very large cascade effects may be due primarily to regime shifts between intraguild predation-dominated food webs and those that more resemble food chains, rather than due to the simple food chain cascade usually considered.