Return time and vulnerability for a food chain model

Simulation studies have shown that the time it takes for a system of interacting species in a food chain to return to equilibrium after a disturbance increases as the number of trophic levels increase. It has been argued that this effect is important in limiting the length of food chains subject to perturbations of the real world. We show that for an asymptotically stable system a lower bound on the return time is directly proportional to the number of trophic levels in agreement with simulation studies. In addition, the lower bound on the return time is shown to be inversely proportional to the sum of products of the intraspecific competition coefficient and equilibrium population of the species. A new method for directly computing the vulnerability of a system to external perturbations is presented. Using this method we demonstrate that for a food chain where the number of species is equal to the number of trophic levels, the return time alone is not a proper measure of system vulnerability. Indeed, adding an additional trophic level may make the system less vulnerable to disturbances. Interspecific coupling between the trophic levels is shown to be an important factor in determining system vulnerability.     

Top predator persistence in differential equation models of food chains: The effects of omnivory and external forcing of lower trophic levels

Persistence criteria are given for the highest trophic level predator in ordinary differential equation models of food chains exhibiting arbitrary omnivory and external supplementation of food source or an intermediate predator. The results are expressed in terms of inequalities involving the bounds on the intrinsic growth and interaction rates. Whether omnivory or external forcing enhances persistence is discussed, particularly for the examples of three-, four-, and five-link Lotka-Volterra food chains.     

Effects of Enrichment on Three-Level Food Chains with Omnivory

Although omnivory (the consumption of resources from more than one trophic level) is widespread, this fundamental limitation to the applicability of food chain theory to real communities has received only limited treatment. We investigated effects of enrichment (increasing carrying capacity, K, of the resource) on a system consisting of a resource (R), an intermediate consumer (N), and an omnivore (P) using a general mathematical model and tested the relevance of some of its predictions to a laboratory system of mixed bacteria (=R) and the ciliates Tetrahymena (=N) and Blepharisma (=P). The model produced six major predictions. First, N may facilitate or inhibit P. Enrichment may revert the net effect of N on P from facilitation to inhibition. Second, along a gradient of K, up to four regions of invasibility and stable coexistence of N and P may exist. At the lowest K, only R is present. At somewhat higher K, N can coexist with R. At intermediate K, either N and P coexist, or either consumer excludes the other depending on initial conditions. At the highest K, N may be excluded through apparent competition and only R and P can coexist. The pattern of persistence of Tetrahymena and Blepharisma along an enrichment gradient conformed fairly well to the scenario allowing coexistence at intermediate K. Third, for stable equilibria of the omnivory system, R always increases and N always decreases with K. The abundances of bacteria and Tetrahymena were suggestive of such a pattern but did not allow a strict test because coexistence occurred at only one level of enrichment. Fourth, an omnivore can invade an R-N system at a lower K than an otherwise identical specialist predator of N. Fifth, an omnivore can always invade a food chain with such a specialist predator. Sixth, over ranges of K where both omnivory systems and otherwise identical three-level food chains are feasible, N is always less abundant in the omnivory system, whereas the relative abundances of R and P in omnivory systems compared to food chains may change with K. It is thus possible that total community biomass at a given K is lower in an omnivory system than in a food chain. Both the model and the experimental results caution that patterns of trophic-level abundances in response to enrichment predicted by food chain theory are not to be expected in systems with significant omnivory.     

Flood disturbance affects macroinvertebrate food chain length in an alluvial river floodplain

1. Characterising food-web responses to environmental factors could greatly improve our understanding of environment-biota relationships, and especially in floodplains where trophic interactions can be particularly important during phases of hydrological disconnection. The effects of floodplain hydrology and environmental attributes on structural aspects of biotic assemblages have been extensively studied, but responses at the functional level remain largely unknown.
2. Here, we characterised a central aspect of food-web architecture, the food chain length, as the maximum trophic position within 24 macroinvertebrate communities of parafluvial habitats in the Maggia river floodplain, in Switzerland. We investigated how the food chain length changed with different levels of habitat size, primary productivity and disturbance, the three factors potentially affecting food chain length in both theoretical and empirical studies.
3. We found that food chain length was lower in frequently flooded habitats and immediately after a flood. We also showed that trophic omnivory, where predators fed at lower trophic levels after flooding, and in more frequently flooded habitats, may explain these changes.
4. These findings show that trophic omnivory may explain how predators resist disturbance and are maintained in highly dynamic landscapes. More importantly, given that trophic omnivory may overall weaken trophic linkages and thus increase food-web stability, this suggests that it could be a key mechanism in sustaining biodiversity in river floodplains.

     

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.     

Re-evaluating the omnivory–stability relationship in food webs

Under equilibrium conditions, previous theory has shown that the presence of omnivory destabilizes food webs. Correspondingly, omnivory ought to be rare in real food webs. Although, early food web data appeared to verify this, recently many ecologists have found omnivory to be ubiquitous in food web data gathered at a high taxonomic resolution. In this paper, we re-investigate the role of omnivory in food webs using a non-equilibrium perspective. We find that the addition of omnivory to a simple food chain model (thus a simple food web) locally stabilizes the food web in a very complete way. First, non-equilibrium dynamics (e.g. chaos) tend to be eliminated or bounded further away from zero via period-doubling reversals invoked by the omnivorous trophic link. Second, food chains without interior attractors tend to gain a stable interior attractor with moderate amounts of omnivory.     

Trophic niche differences between coexisting omnivores silver carp and bighead carp in a pelagic food web

Understanding how omnivorous consumers are affected by their resources and how this is expressed through the food chain is a fundamental issue in ecology. We used stable isotope analysis of archived scales of two pelagic single-chain omnivorous fish species, bighead carp (Hypophthalmichthys nobilis) and silver carp (H. molitrix), to reconstruct historical trophic interactions patterns along a gradient of resources. We found that, although bighead carp and silver carp utilize the similar resources from the pelagic food chain, they can coexist and persist not only by regulating their trophic position and trophic dissimilarity, but also by regulating trophic niche width. Omnivorous fish often exhibit flexible foraging strategies, which is closely related to the availability of ecologic context. We found a positive relationship between trophic dissimilarity and zooplankton density, which may indicate that the competitive interactions induce strong top-down effects on zooplankton, and/or that high zooplankton availability release the between-population trophic interaction through bottom-up effect. The trophic niche width of bighead carp was positively related with zooplankton availability, probably reflecting that the niche of an omnivore at a higher trophic position is more sensitive to high quality resources. Our results indicate how different aspects of the trophic partitioning of coexisting omnivores may be regulated by different ecological contexts. These alternatives are not mutually exclusive and further theoretical work should include both these mechanisms to re-evaluate the effects of omnivory on food web properties.     

δ15N examination of the Lindeman-Hutchinson-Peters theory of increasin omnivory with trophic height in aquatic foodwebs

The advent of stable nitrogen isotope analysis in ecological research has at last enabled precise identification of trophic position and omnivory due to the differential enrichment of¹⁵N over¹⁴N with progressive assimilation up the foodweb. I compiled literature data on δ¹⁵N values in freshwater and marine foodwebs to search for qeneral patterns in omnivory, specifically the supposition originally proposed by Lindeman (1942) and most recently advanced by Peters (1977), that omnivory should increase with trophic height or position. Omnivory, measured as average intraspecific variability in δ¹⁵N, was indeed found to increase with trophic height, such that species at the top of foodwebs were comprised of animals relying, on average, on energy originating from a mixture of different trophic categories.     

Omnivory and the stability of simple food webs

Traditional ecological theory predicts that the stability of simple food webs will decline with an increasing number of trophic levels and increasing amounts of omnivory. These ideas have been tested using protozoans in laboratory microcosms. However, the results are equivocal, and contrary to expectation, omnivory is common in natural food webs. Two recent developments lead us to re-evaluate these predictions using food webs assembled from protists and bacteria. First, recent modelling work suggests that omnivory is actually stabilizing, providing that interactions are not too strong. Second, it is difficult to evaluate the degree of omnivory of some protozoan species without explicit experimental tests. This study used seven species of ciliated protozoa and a mixed bacterial flora to assemble four food webs with two trophic levels, and four webs with three trophic levels. Protist species were assigned a rank for their degree of omnivory using information in the literature and the results of experiments that tested whether the starvation rate of predators was influenced by the amount of bacteria on which they may have fed and whether cannibalism (a form of omnivory) occurred. Consistent with recent modelling work, both bacterivorous and predatory species with higher degrees of omnivory showed more stable dynamics, measured using time until extinction and the temporal variability of population density. Systems with two protist species were less persistent than systems with one protist species, supporting the prediction that longer food chains will be less stable dynamically. Received: 28 December 1997 / Accepted: 22 June 1998     

Omnivory and stability of food webs

The role and prevalence of omnivory, defined as feeding on more than one trophic level, are critical to understand food web structure and dynamics. Whether omnivory stabilizes or destabilizes food webs depends on the assumptions of theoretical models. Recently, Tanabe and Namba [Tanabe, K., Namba, T., 2005. Omivory creates chaos in simple food web models. Ecology 86, 3411–3414] found that omnivory can create chaos in a simple food web model with linear functional responses and 12 model parameters. In this paper, first we numerically examined bifurcation diagrams with all the parameters as bifurcation parameters, including self-limitation of the intermediate consumer and predator. Chaos spontaneously appears when the intraguild predator’s consumption rates are low for nutrient-rich intraguild prey and high for nutrient-poor basal resource and the intraguild prey reproduces efficiently feeding on the basal resource. Second, we investigated effects of the addition of a species into the basic model food web which exhibits chaos. The additional species is assumed to consume only one of the basal resource, intermediate consumer, or omnivorous predator. Consequences of the addition greatly depend on the trophic level on which the additional species feeds. While the increased diversity of predators feeding on the intermediate consumer stabilizes the web, the increased diversity of prey feeding on the basal resource induces collapse of the food web through exploitative competition for the basal resource. The food chain with the top predator feeding on the omnivorous predator is highly unstable unless the mortality of the top predator is extremely low. We discuss the possibility of real-world chaos and the reason why stability of food webs strongly depends on the topological structure of the webs. Finally, we consider the implications of our results for food web theory and resource management.     

Structure of tropical river food webs revealed by stable isotope ratios

Fish assemblages in tropical river food webs are characterized by high taxonomic diversity, diverse foraging modes, omnivory, and an abundance of detritivores. Feeding links are complex and modified by hydrologic seasonality and system productivity. These properties make it difficult to generalize about feeding relationships and to identify dominant linkages of energy flow. We analyzed the stable carbon and nitrogen isotope ratios of 276 fishes and other food web components living in four Venezuelan rivers that differed in basal food resources to determine 1) whether fish trophic guilds integrated food resources in a predictable fashion, thereby providing similar trophic resolution as individual species, 2) whether food chain length differed with system productivity, and 3) how omnivory and detritivory influenced trophic structure within these food webs. Fishes were grouped into four trophic guilds (herbivores, detritivores/algivores, omnivores, piscivores) based on literature reports and external morphological characteristics. Results of discriminant function analyses showed that isotope data were effective at reclassifying individual fish into their pre-identified trophic category. Nutrient-poor, black-water rivers showed greater compartmentalization in isotope values than more productive rivers, leading to greater reclassification success. In three out of four food webs, omnivores were more often misclassified than other trophic groups, reflecting the diverse food sources they assimilated. When fish δ¹⁵N values were used to estimate species position in the trophic hierarchy, top piscivores in nutrient-poor rivers had higher trophic positions than those in more productive rivers. This was in contrast to our expectation that productive systems would promote longer food chains. Although isotope ratios could not resolve species-level feeding pathways, they did reveal how top consumers integrate isotopic variability occurring lower in the food web. Top piscivores, regardless of species, had carbon and nitrogen profiles less variable than other trophic groups.     

Omnivory and the stability of food webs

The ecological concept of omnivory, feeding at more than a single trophic level, is formulated as an intermediate stage between any two of three classical three-dimensional species interaction systems-tritrophic chain, competition, and polyphagy. It is shown that omnivory may be either stabilizing or destabilizing, depending, in part, on the conditions of the parent systems from which it derives. It is further conjectured that the tritrophic to competition gradient cannot be entirely stable, that there must be an instability at some level of intermediate omnivory.     

Omnivory as a stabilizing feature of natural communities

Abstract Omnivory-defined broadly as feeding on more than one trophic level-occupies a prominent position in discussions of food web architecture and dynamics, due in large part to an enduring conflict regarding omnivory's role in community dynamics. According to classical results from mathematical food web theory, omnivory destabilizes ecological communities, whereas more recent conceptual syntheses suggest that omnivory should be a strongly stabilizing factor in food webs. Working with an arthropod assemblage at Mount Saint Helens, I experimentally addressed this controversy using a two-way factorial design that crossed a manipulation of the degree of omnivory with another "disturbance" manipulation that targeted a specific component of the assemblage. In this statistical design, significant interaction effects (i.e., how the community impacts of the disturbance varied with the degree of omnivory) identified key stabilizing or destabilizing influences of omnivory. Overall, my experimental results indicated that increasing the degree of omnivory stabilized community dynamics, in keeping with recent conceptual syntheses.     

Towards a mechanistic understanding of temperature and enrichment effects on species interaction strength,omnivory and food‐web structure

Revealing the links between species functional traits, interaction strength and food‐web structure is of paramount importance for understanding and predicting the relationships between food‐web diversity and stability in a rapidly changing world. However, little is known about the interactive effects of environmental perturbations on individual species, trophic interactions and ecosystem functioning. Here, we combined modelling and laboratory experiments to investigate the effects of warming and enrichment on a terrestrial tritrophic system. We found that the food‐web structure is highly variable and switches between exploitative competition and omnivory depending on the effects of temperature and enrichment on foraging behaviour and species interaction strength. Our model contributes to identifying the mechanisms that explain how environmental effects cascade through the food web and influence its topology. We conclude that considering environmental factors and flexible food‐web structure is crucial to improve our ability to predict the impacts of global changes on ecosystem diversity and stability.     

Niche‐dependent trophic position distributions among primary,secondary and tertiary consumers

Many consumers display flexible feeding strategies that vary among individuals or populations, through life‐history, or spatiotemporally. Despite the recognized influence of flexible feeding on the structure and dynamics of food webs, the consequences of these feeding strategies on the actual shape and characteristics of trophic position distributions have received less attention. We proposed and tested several a priori hypotheses to predict the likely effect of niche‐dependent (e.g. herbivore, secondary consumer) foraging on the shape and statistical properties of consumer trophic position distributions using natural abundance stable isotope data from a diverse dataset of consumers. We found evidence that the structural characteristics of consumer trophic position distributions varied as a function of trophic niche. Herbivores and tertiary consumers tended to be ‘packed’ closely near their mean trophic position, with few individuals realizing trophic positions markedly higher or lower than the mean. Conversely, secondary consumers often displayed broad trophic position distributions with many individuals dispersed away from the center of the distribution. We examined the effect of applying constant versus dynamic isotope trophic fractionation models and found that both models yielded similar although not identical results. Our findings suggest that trophic level omnivory supports a larger fraction of consumer diet at intermediate trophic positions than at either the lowest or the highest positions in aquatic food webs. These results suggest that vertical trophic niche declines among higher order consumers despite general evidence that the range of potential foraging options (i.e. horizontal trophic niche) tends to increase at higher trophic positions. Although further work is needed to test the generality of these patterns in other ecosystems, proactively examining trophic position distributions and reporting appropriate measures of central tendency (e.g. arithmetic versus geometric means) will increase the accuracy of individual trophic studies as well as the applicability of results for meta‐analytical food web models.     

Persistence in Stochastic Lotka–Volterra Food Chains with Intraspecific Competition

This paper is devoted to the analysis of a simple Lotka–Volterra food chain evolving in a stochastic environment. It can be seen as the companion paper of Hening and Nguyen (J Math Biol 76:697–754, 2018b) where we have characterized the persistence and extinction of such a food chain under the assumption that there is no intraspecific competition among predators. In the current paper, we focus on the case when all the species experience intracompetition. The food chain we analyze consists of one prey and \(n-1\) predators. The jth predator eats the \(j-1\)st species and is eaten by the \(j+1\)st predator; this way each species only interacts with at most two other species—the ones that are immediately above or below it in the trophic chain. We show that one can classify, based on the invasion rates of the predators (which we can determine from the interaction coefficients of the system via an algorithm), which species go extinct and which converge to their unique invariant probability measure. We obtain stronger results than in the case with no intraspecific competition because in this setting we can make use of the general results of Hening and Nguyen (Ann Appl Probab 28:1893–1942, 2018a). Unlike most of the results available in the literature, we provide an in-depth analysis for both non-degenerate and degenerate noise. We exhibit our general results by analyzing trophic cascades in a plant–herbivore–predator system and providing persistence/extinction criteria for food chains of length \(n\le 4\).     

Multiple sources of isotopic variation in a terrestrial arthropod community: challenges for disentangling food webs

Documenting trophic links in a food web has traditionally required complex exclusion experiments coupled with extraordinarily labor-intensive direct observations of predator foraging. Newer techniques such as stable isotope analysis (SIA) may facilitate relatively quick and accurate assessments of consumer feeding behavior. Ratios of N and C isotopes are thought to be useful for determining species' trophic position (e.g., 1 degrees consumer, 2 degrees consumer, or omnivore) and their original carbon source (e.g., C3 or C4 plants; terrestrial or marine nutrients). Thus far, however, applications of stable isotopes to terrestrial arthropod food webs have suggested that high taxon-specific variation may undermine the effectiveness of this method. We applied stable isotope analysis to a pear orchard food web, in which biological control of a dominant pest, pear psylla (Cacopsylla pyricola), involves primarily generalist arthropod predators with a high frequency of omnivory. We found multiple sources of isotopic variation in this food web, including differences among plant tissues; time, stage, and taxon-specific differences among herbivores (despite similar feeding modes); and high taxon-specific variation among predators (with no clear evidence of omnivory). Collectively, these multiple sources of isotopic variation blur our view of the structure of this food web. Idiosyncrasies in consumer trophic shifts make ad hoc application of SIA to even moderately complex food webs intractable. SIA may not be a generally applicable "quick and dirty" method for delineating terrestrial food web structure-not without calibration of specific consumer food trophic shifts.     

Persistence in food webs—I Lotka-Volterra food chains

Persistence-extinction in simple food chains modelled by Lotka-Volterra dynamics is governed by a single parameter which depends upon the interspecific interaction coefficients, the intraspecific interaction coefficients, and the length of the food chain. In persistent systems with nonzero carrying capacity, two new features predominate. Trophic level influence factors relate persistence on different trophic levels and determine, in conjunction with the persistence parameter, the magnitude of persistence. Equilibrium component ordering, which results in persistent systems, mandates once again that systems need to be studied on the complete ecosystem level; static field measurements reflect species location in the food chain, the total length of the food chain and assume characteristics according to these factors.