Are network indices robust indicators of food web functioning? A Monte Carlo approach

Indices based on network theory are often used to describe food web functioning. These indices take as input food web flows that are estimated based on merging of (scarce) data with linear inverse methods (LIMs). Due to under sampling, most food webs are highly uncertain and can only be quantified within a specific uncertainty range. The linear inverse method (LIM) can estimate food web flows using a variety of techniques, e.g. the parsimonious or minimum norm (MN) solution, which selects one food web, based on a quadratic minimization technique or the Monte Carlo solution where a finitely many random solutions are generated which are then averaged. We use the Monte Carlo approach (MCA) to estimate the values of several indices from four published food webs, the Gulf of Riga for the autumn, summer and spring seasons, and the Takapoto atoll system. We first show that network indices are much better constrained than the uncertain food webs from which they are calculated. Therefore, even in the face of food web uncertainty, they are robust estimators of food web functioning. We then use the MCA-derived network indices to generate cumulative density functions for each index. These serve to compute the probabilities of the MN indices estimates being an extreme solution as compared to the median values. Our findings show that 82% of the MN solutions are smaller than the MCA solutions, and 63% of the network indices are significantly under-estimated.     

On the consequences of aggregation and balancing of networks on system properties derived from ecological network analysis

In the ecological network analysis (ENA) of complex flow food webs the assumption is often made that the models characterizing the flows and stocks of ecosystems occur in a steady state where inflows equals outflows. An assessment of the system indices derived from ENA of six balanced and unbalanced system models, respectively, indicate to differences between indices. The aggregation of highly articulated flow models into models with fewer compartments also has drastic effects on the system metrics, particularly on the information indices.     

An inverse model for the analysis of the Venice lagoon food web

A steady-state model of the Venice lagoon food web was constructed, based on a comprehensive set of data, which were collected in the years 2001-2005. Energy flows were estimated by means of an inverse methodology of constrained optimization based on the Minimum Norm criterion, i.e. on the minimization of both the sum of squares of the residuals and of the sum of squares of energy flows. The solution was constrained by a set inequalities, which were derived from general eco-physiological knowledge and site specific data on energy flows. The trophic network was represented by thirty-two nodes, including single-species compartments for the species of high economical or ecological relevance. Mass balance equations were weighted, in order to obtain meaningful results in presence of large differences, up to 5 orders of magnitude, among biomasses. A perturbation technique was applied, with the purpose of reducing the risk of finding solutions heavily affected by the set of constraints and of obtaining a more robust representation of the energy flows. The main patterns of energy flow are consistent with those obtained in previous attempts at modelling the Venice lagoon food web. Micro- and macro-phytobenthos account for the largest fraction of the primary production. Energy is then transferred towards higher trophic levels by means of two main pathways: the recycling of dead biomass through the detritus compartment and the direct consumption by grazers. The first pathway is the most important and accounts for approximately two/thirds of the energy transferred to the second trophic level.     

Origin of compartmentalization in food webs

The response of an ecosystem to perturbations is mediated by both antagonistic and facilitative interactions between species. It is thought that a community's resilience depends crucially on the food web--the network of trophic interactions--and on the food web's degree of compartmentalization. Despite its ecological importance, compartmentalization and the mechanisms that give rise to it remain poorly understood. Here we investigate several definitions of compartments, propose ways to understand the ecological meaning of these definitions, and quantify the degree of compartmentalization of empirical food webs. We find that the compartmentalization observed in empirical food webs can be accounted for solely by the niche organization of species and their diets. By uncovering connections between compartmentalization and species' diet contiguity, our findings help us understand which perturbations can result in fragmentation of the food web and which can lead to catastrophic effects. Additionally, we show that the composition of compartments can be used to address the long-standing question of what determines the ecological niche of a species.     

Evidence for the dominance of indirect effects in 50 trophic ecosystem networks

Indirect effects are powerful influences in ecosystems that may maintain species diversity and alter apparent relationships between species in surprising ways. Here, we applied network environ analysis to 50 empirically-based trophic ecosystem models to test the hypothesis that indirect flows dominate direct flows in ecosystem networks. Further, we used Monte Carlo based perturbations to investigate the robustness of these results to potential error in the underlying data. To explain our findings, we further investigated the importance of the microbial food web in recycling energy-matter using components of the Finn Cycling Index and analysis of environ centrality. We found that indirect flows dominate direct flows in 37/50 (74.0%) models. This increases to 31/35 (88.5%) models when we consider only models that have cycling structure and a representation of the microbial food web. The uncertainty analysis reveals that there is less error in the I/D values than the ±5% error introduced into the models, suggesting the results are robust to uncertainty. Our results show that the microbial food web mediates a substantial percentage of cycling in some systems (median = 30.2%), but its role is highly variable in these models, in agreement with the literature. Our results, combined with previous work, strongly suggest that indirect effects are dominant components of activity in ecosystems.     

The modified niche model: Including detritus in simple structural food web models

Food webs are constructed as structural directed graphs that describe “who eats whom,” but it is common to interpret them as energy flow diagrams where predation represents an energy transfer from the prey to the predator. It is the aim of this work to demonstrate that food webs are incomplete as energy flow diagrams if they ignore passive flows to detritus (dead organic material). While many ecologists do include detritus in conceptual and mathematical models, the detrital omission is still commonly found. Often detritus is either ignored or treated as an unlimited energy source, yet all organisms contribute to the detritus pool, which can be an energy source for other species in the system. This feedback loop is of high importance, since it increases the number of pathways available for energy flows, revealing the significance of indirect effects, and making the functional role of the top predators less clear. In this work we propose the modified niche model by adding a detritus compartment to the niche model. We demonstrate the effect of structural loops that result from feeding on detritus, by comparing empirical data sets to five different assembly models: (1) cascade, (2) constant connectance, (3) niche, (4) modified niche (original in this work), and (5) cyber-ecosystem. Of these models, only the last two explicitly include detritus. We show that when passive flows to detritus are included in the food web structure, the structure becomes more robust to the removal of individual nodes or connections. In addition, we show that food web models that include the detritus feedback loop perform better with respect to several structural network metrics.     

Adaptations in a hierarchical food web of southeastern Lake Michigan

Two issues in ecological network theory are: (1) how to construct an ecological network model and (2) how do entire networks (as opposed to individual species) adapt to changing conditions? We present a novel method for constructing an ecological network model for the food web of southeastern Lake Michigan (USA) and we identify changes in key system properties that are large relative to their uncertainty as this ecological network adapts from one time point to a second time point in response to multiple perturbations. To construct our food web for southeastern Lake Michigan, we followed the list of seven recommendations outlined in Cohen et al. [Cohen, J.E., et al., 1993. Improving food webs. Ecology 74, 252–258] for improving food webs. We explored two inter-related extensions of hierarchical system theory with our food web; the first one was that subsystems react to perturbations independently in the short-term and the second one was that a system's properties change at a slower rate than its subsystems’ properties. We used Shannon's equations to provide quantitative versions of the basic food web properties: number of prey, number of predators, number of feeding links, and connectance (or density). We then compared these properties between the two time-periods by developing distributions of each property for each time period that took uncertainty about the property into account. We compared these distributions, and concluded that non-overlapping distributions indicated changes in these properties that were large relative to their uncertainty. Two subsystems were identified within our food web system structure (p < 0.001). One subsystem had more non-overlapping distributions in food web properties between Time 1 and Time 2 than the other subsystem. The overall system had all overlapping distributions in food web properties between Time 1 and Time 2. These results supported both extensions of hierarchical systems theory. Interestingly, the subsystem with more non-overlapping distributions in food web properties was the subsystem that contained primarily benthic taxa, contrary to expectations that the identified major perturbations (lower phosphorous inputs and invasive species) would more greatly affect the subsystem containing primarily pelagic taxa. Future food-web research should employ rigorous statistical analysis and incorporate uncertainty in food web properties for a better understanding of how ecological networks adapt.     

Comparative network analysis toward characterization of systemic organization for human–environmental sustainability

A preliminary study in comparative ecological network analysis was conducted to identify key assumptions and methodological challenges, test initial hypotheses and explore systemic and network structural characteristics for environmentally sustainable ecosystems. A nitrogen network for the U.S. beef supply chain – a small sub-network of the industrial food system analyzed as a pilot study – was constructed and compared to four non-human carbon and nitrogen trophic networks for the Chesapeake Bay and the Florida Everglades. These non-human food webs served as sustainable reference systems. Contrary to the main original hypothesis, the “window of vitality” and the number of network roles did not clearly differentiate between a human sub-network and the more complete non-human networks. The effective trophic level of humans (a partial estimate of trophic level based on the single food source of beef) was much higher (8.1) than any non-human species (maximum of 4.88). Network connectance, entropy, total dependency coefficients, trophic efficiencies and the ascendency to capacity ratio also indicated differences that serve as hypotheses for future tests on more comprehensive human food webs. The study elucidated important issues related to (1) the steady state assumption, which is more problematic for industrial human systems, (2) the absence or dearth of data on contributions of dead humans and human wastes to feed other species in an integrated food web, (3) the ambiguity of defining some industrial compartments as living versus non-living, and (4) challenges with constructing compartments and trophic transfers in industrial versus non-human food webs. The two main novel results are (1) the progress made toward adapting ecological network analysis (ENA) methodology for analysis of human food networks in industrial cultures and (2) characterizing the critical aspects of comparative ENA for understanding potential causes of the problems, and providing avenues for solutions, for environmental sustainability. Based on this work, construction and comparative network analysis of a more comprehensive industrial human food network seems warranted and likely to provide valuable insights for modifying structures of industrial food networks to be more like natural networks and more sustainable.     

Linking the brown and green: nutrient transformation and fate in the Sarracenia microecosystem

Linkages between detritus-based ("brown") food webs and producer-based ("green") food webs are critical components of ecosystem functionality, but these linkages are hard to study because it is difficult to measure release of nutrients by brown food webs and their subsequent uptake by plants. In a three-month greenhouse experiment, we examined how the detritus-based food web inhabiting rain-filled leaves of the pitcher plant Sarracenia purpurea affects nitrogen transformation and its subsequent uptake by the plant itself. We used isotopically enriched prey (detritus) and soluble inorganic nitrogen, and manipulated food web structure to determine whether the presence of a complete brown web influences uptake efficiency of nitrogen by the plant. Uptake efficiency of soluble inorganic nitrogen was greater than that of nitrogen derived from mineralized prey. Contrary to expectation, there was no effect of the presence in the food web of macroinvertebrates on uptake efficiency of either form of nitrogen. Further, uptake efficiency of prey-derived nitrogen did not differ significantly among S. purpurea and two congeneric species (S. flava and S. alata) that lack associated food webs. Although upper trophic levels of this brown food web actively process detritus, it is the activity of the microbial component of this web that ultimately determines nitrogen availability for S. purpurea.     

What is hidden behind the concept of ecosystem efficiency in energy transformation?

The number of energy transformation levels in trophic webs is usually below five, but can be extended up to ten when parasites and hyper-parasites are included. Research on the structure and function of food webs is relevant to the complexity–stability–productivity debate. The aim of this theoretical analysis is to link energetic and connectional aspects of ecosystems with information theory. Updating an energetic model reported by Ricklefs [Ecologia, Zanichelli Editore S.p.A., Bologna, Italy, 1993, p. 896], our approach is integrated with a static analysis of food webs. The length of food webs is theoretically associated with the average ecological efficiency which can be empirically correlated with the effective connectance between species. Furthermore, the advantage of greater complexity when applied to a signalling network is qualitatively addressed.The overall efficiency of energy transformation into biomass throughout a trophic web, in an ecosystem with a given number of species, is the resultant of the various ecological efficiencies, η, at the transitions between the trophic levels. However, we propose that an increment in effective connectance and interspecies connectivity based on a superimposed signalling web may increase the η values, despite the fact that signalling per se has an energetic cost. According to this hypothesis, ecosystem stability would not be necessarily reduced by increasing the number of trophic levels, N, whenever stability in terms of persistence is improved by a cost-efficient regulatory network.     

The probabilistic niche model reveals substantial variation in the niche structure of empirical food webs

The structure of food webs, complex networks of interspecies feeding interactions, plays a crucial role in ecosystem resilience and function, and understanding food web structure remains a central problem in ecology. Previous studies have shown that key features of empirical food webs can be reproduced by low-dimensional "niche" models. Here we examine the form and variability of food web niche structure by fitting a probabilistic niche model to 37 empirical food webs, a much larger number of food webs than used in previous studies. The model relaxes previous assumptions about parameter distributions and hierarchy and returns parameter estimates for each species in each web. The model significantly outperforms previous niche model variants and also performs well for several webs where a body-size-based niche model performs poorly, implying that traits other than body size are important in structuring these webs' niche space. Parameter estimates frequently violate previous models' assumptions: in 19 of 37 webs, parameter values are not significantly hierarchical, 32 of 37 webs have nonuniform niche value distributions, and 15 of 37 webs lack a correlation between niche width and niche position. Extending the model to a two-dimensional niche space yields networks with a mixture of one- and two-dimensional niches and provides a significantly better fit for webs with a large number of species and links. These results confirm that food webs are strongly niche-structured but reveal substantial variation in the form of the niche structuring, a result with fundamental implications for ecosystem resilience and function.     

Structuring pelagic trophic networks from the biomass size spectra

The selection and establishment of the structure (number and compartments, aggregation criteria, and trophic links) of the food webs is a critical task in trophic modelling. The present work proposes a systematic method to structure trophic networks in pelagic food webs. The biomass-size spectrum (BSS) is a well-established approach to analyze the structure of pelagic communities, and the body size is especially related to the ecological role of the organisms in the pelagic environment. To structure food webs, this work uses detailed arrangements of the community in size classes with increasing widths (like Sheldon-type BSS) as first aggregation criteria, and BSS theory as a framework to integrate the available knowledge about feeding selectivity in order to obtain a method to identify the trophic links between compartments. Diet composition matrices were estimated through the combination of a probability of encounter for each food type and a specific probability of ingestion related to the food size selectivity and other food quality characteristics (e.g., morphology and nutritional quality). The feasibility of this approach has been illustrated through data of size-structured communities extracted from the literature including different planktonic predator guilds (nanoflagellates, cladoceran-dominated zooplankton and copepod-dominated zooplankton) in a high mountain lake (La Caldera, Spain), two subtropical wetland lakes (meso-oligotrophic Laguna Galarza and eutrophic Laguna Iberá, Argentina) and a marine microcosm (Alborán Sea, Mediterranean). The identification of “who eats whom” and “by how much” also allows for more accurate analyses of the trophic control in the BSS. Extensive analyses of the balance between top-down and bottom-up controls were developed for the feeding interactions of the study cases.     

Quantitative approaches to the analysis of stable isotope food web data

Ecologists use stable isotopes (delta13C, delta15N) to better understand food webs and explore trophic interactions in ecosystems. Traditionally, delta13C vs. delta15N bi-plots have been used to describe food web structure for a single time period or ecosystem. Comparisons of food webs across time and space are increasing, but development of statistical approaches for testing hypotheses regarding food web change has lagged behind. Here we present statistical methodologies for quantitatively comparing stable isotope food web data. We demonstrate the utility of circular statistics and hypothesis tests for quantifying directional food web differences using two case studies: an arthropod salt marsh community across a habitat gradient and a freshwater fish community from Lake Tahoe, USA, over a 120-year time period. We calculated magnitude and mean angle of change (theta) for each species in food web space using mean delta13C and delta15N of each species as the x, y coordinates. In the coastal salt marsh, arthropod consumers exhibited a significant shift toward dependence on Spartina, progressing from a habitat invaded by Phragmites to a restored Spartina habitat. In Lake Tahoe, we found that all species from the freshwater fish community shifted in the same direction in food web space toward more pelagic-based production with the introduction of nonnative Mysis relicta and onset of cultural eutrophication. Using circular statistics to quantitatively analyze stable isotope food web data, we were able to gain significant insight into patterns and changes in food web structure that were not evident from qualitative comparisons. As more ecologists incorporate a food web perspective into ecosystem analysis, these statistical tools can provide a basis for quantifying directional food web differences from standard isotope data.     

Analysis of ecosystem structure and function: extended path and flow analysis of a steady-state oyster reef model

An analysis of the extended path and flow structure of a six compartment steady-state oyster reef model was conducted. The extended path and flow structure were analyzed in the context of a refined canonical path classification system based on the systems theory methods of environ and network unfolding analyses. A computer implementation of an operational path classification system facilitated investigation of a finite portion (path length ≤17 arcs) of the direct and indirect path structure of the oyster reef model. Important results of the path structure analysis include: (1) few simple paths and large numbers of compound paths enumerated; (2) dominance of path numbers by subsequent passage terminal cycle paths; (3) structural evidence in support of feedback control in ecosystems; (4) results provide evidence by analogy to support the hypothesis of network homogenization first described using the systems analysis methods of environ analysis and network unfolding; (5) constancy of the pattern of origin–destination path counts with increasing path length; (6) importance of nonliving compartments in the extended path structure of ecosystems. Simultaneous path and flow analysis of the oyster reef model assessed the flow contributions of the fundamental path categories for this model using a modification of a path-based network unfolding method. First passage paths contribute most of the flow; however, multiple passage cyclic paths also provide a large (22%) flow contribution. Because of cycling in the system, the numerous long paths in the extended path structure of this ecosystem model are significant in its function as represented by the flows. These results provide microscopic evidence for the macroscopic results of environ analysis that implicate cycling as a key ecosystem attribute in the mechanisms of holistic system determination. The principles enunciated here for a model with a low cycling index (11%) carry over to, and would be even more significant for, models with high cycling indexes. These results also serve to form a link between the extended structure of food webs and their functioning as represented by energy-matter flows. The present analysis demonstrates that extended path structure, and the component articulation from which it is generated, have significant consequences for ecosystem function.     

Evidence supporting the importance of terrestrial carbon in a large-river food web

Algal carbon has been increasingly recognized as the primary carbon source supporting large-river food webs; however, many of the studies that support this contention have focused on lotic main channels during low-flow periods. The flow variability and habitat-heterogeneity characteristic of these systems has the potential to significantly influence food web structure and must be integrated into models of large-river webs. We used stable-isotope analysis and IsoSource software to model terrestrial and algal sources of organic carbon supporting consumer taxa in the main channel and oxbow lakes of the Brazos River, Texas, USA, during a period of frequent hydrologic connectivity between these habitat types. Standardized sampling was conducted monthly to collect production sources and consumer species used in isotopic analysis. Predictability of hydrologic connections between habitat types was based on the previous 30 years of flow data. IsoSource mixing models identified terrestrial C3 macrophytes (riparian origin) as the primary carbon source supporting virtually all consumers in the main channel and most consumers in oxbow lakes. Small-bodied consumers (<100 mm) in oxbow lakes assimilated large fractions of algal carbon whereas this pattern was not apparent in the main channel. Estimates of detritivore trophic positions based on delta15N values indicated that terrestrial material was likely assimilated via invertebrates rather than directly from detritus. High flows in the river channel influenced algal standing stock, and differences in the importance of terrestrial and algal production sources among consumers in channel vs. oxbow habitats were associated with patterns of flooding. The importance of terrestrial material contradicts the findings of recent studies of large-river food webs that have emphasized the importance of algal carbon and indicates that there can be significant spatial, temporal, and taxonomic variation in carbon sources supporting consumers in large rivers.     

Nutrient enrichment reduces constraints on material flows in a detritus-based food web

Most aquatic and terrestrial ecosystems are experiencing increased nutrient availability, which is affecting their structure and function. By altering community composition and productivity of consumers, enrichment can indirectly cause changes in the pathways and magnitude of material flows in food webs. These changes, in turn, have major consequences for material storage and cycling in the ecosystem. Understanding mechanisms and predicting consequences of nutrient-induced changes in material flows requires a quantitative food web approach that combines information on consumer energetics and consumer-resource stoichiometry. We examined effects of a whole-system experimental nutrient enrichment on the trophic basis of production and the magnitude and pathways of carbon (C), nitrogen (N), and phosphorus (P) flows in a detritus-based stream food web. We compared the response of the treated stream to an adjacent reference stream throughout the study. Dietary composition and elemental flows varied considerably among invertebrate functional feeding groups. During nutrient enrichment, increased flows of leaf litter and amorphous detritus to shredders and gatherers accounted for most of the altered flows of C from basal resources to consumers. Nutrient enrichment had little effect on patterns of material flows but had large positive effects on the magnitude of C, N, and P flows to consumers (mean increase of 97% for all elements). Nutrient-specific food webs revealed similar flows of N and P to multiple functional groups despite an order of magnitude difference among groups in consumption of C. Secondary production was more strongly related to consumption of nutrients than C, and increased material flows were positively related to the degree of consumer-resource C:P and C:N imbalances. Nutrient enrichment resulted in an increased proportion of detrital C inputs consumed by primary consumers (from -15% to 35%) and a decreased proportion of invertebrate prey consumed by predators (from -80% to 55%). Our results demonstrate that nutrient enrichment of detritus-based systems may reduce stoichiometric constraints on material flows, increase the contribution of consumers to C, N, and P cycling, alter the proportion of C inputs metabolized by consumers, and potentially lead to reduced ecosystem-level storage of C.     

Food web model of the Upper Paraná River Floodplain: description and aggregation effects

To describe the Upper Paraná River Floodplain (the last non-dammed stretch of the Paraná River, Brazil) a food web model was quantified using ECOPATH. The modeled ecosystem showed maturity because of the total primary production/total respiration ratio (close to 2), Finn’s cycling index (7%) and overhead (65%). The first model elaborated had 40 compartments/groups, but its transfer efficiencies among trophic levels did not reduce in despite the trophic level increasing. To solve this, the effect of two grouping methods on system-level information and other ecosystem attributes was investigated. The first series tested, named “classic” (researcher intuitive way and by food preferences) also did not reduce transfer efficiencies. In the second series, named “by pathways”, the first species grouping were those with higher number of input pathways and longest mean length of pathways. Thereby, the news groups from aggregation decreased the number of components and system’s richness, but stability (measured by overhead) did not change, including the model with only eight compartments. The great number of the ten compartments that showed these characteristics was piscivores, increasing the redundancy within highest trophic level. The use of pathways (number and length) can be useful to lumping species since it reduces compartments and do compromise neither maturity nor stability, diminishing grouping subjectivity.     

Potential trophic biomasses and trace-substance concentrations in unstructured marine food webs

It is proposed that unstructured food webs may more closely resemble real marine food webs than does the conventional, structured model. An unstructured food-web model leads to a set of very simple expressions for the potential partition of matter in the food web in steady state, including the potential fluxes of material and biomasses of trophic types and the concentration of trace substances in the members and materials of such a food web. The approach may explain some anomalies of relative predator-prey biomasses and of trace-element distribution, and may be of further use for analyzing and predicting (a) the tropho-dynamic parameters of marine systems, (b) the trophic positions, and the steadystate fluxes and biomasses of marine organisms, (c) the distribution of trace materials in marine biota; and for relating findings among these areas. Other matters, such as limitations of food conversion, indicated by concentration factors of trace substances, the possibilities of non-causal association of anomalously high levels of trace substances (including pollutants) with diseased or otherwise abnormal marine creatures, and an inverse relationship of early concentrations of newly introduced trace substances and their eventual concentrations in various organisms, are also developed in this approach.