Persistence in stochastic food web models

A sufficient condition is given for stochastic boundedness persistence of a top predator in generalized Lotka-Volterra-type stochastic food web models in arbitrary bounded regions of state space. The main result indicates that persistence in the corresponding deterministic system is preserved in the stochastic system if the intensities of the random fluctuations are not too large. This work was supported, in part, by the U. S. Environmental Protection Agency under Grant No. CR 807830.     

Why allometric scaling enhances stability in food web models

It has recently been shown that the incorporation of allometric scaling into the dynamic equations of food web models enhances network stability if predators are assigned a higher body mass than their prey. We investigate the underlying mechanisms leading to this stability increase. The dynamic equations can be written such that allometric scaling influences these equations at three places: the time scales of predator and prey dynamics become separated, the energy outflow to the predators is decreased, and intraspecific competition is increased relative to metabolic rates. For five food web topologies and various network sizes (i.e., species richness), we study the effect of each of these modifications on the percentage of surviving species separately and find that the decreased interaction strengths and the increased intraspecific competition are responsible for the enhanced stability. We also investigate the range of parameter values for which an enhanced stability is observed.     

Positive complexity-stability relations in food web models without foraging adaptation

May's [1972. Will a large complex system be stable? Nature 238, 413-414] local stability analysis of random food web models showed that increasing network complexity leads to decreasing stability, a result that is contradictory to earlier empirical findings. Since this seminal work, research of complexity-stability relations became one of the most challenging issues in theoretical ecology. We investigate conditions for positive complexity-stability relations in the niche, cascade, nested hierarchy, and random models by evaluating the network robustness, i.e., the fraction of surviving species after population dynamics. We find that positive relations between robustness and complexity can be obtained when resources are large, Holling II functional response is used and interaction strengths are weighted with the number of prey species, in order to take foraging efforts into account. In order to obtain these results, no foraging dynamics needs to be included. However, the niche model does not show positive complexity-stability relations under these conditions. By comparing to empirical food web data, we show that the niche model has unrealistic distributions of predator numbers. When this distribution is randomized, positive complexity-stability relations can be found also in the niche model.     

Evolutionary food web models: effects of an additional resource

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

Body sizes,cumulative and allometric degree distributions across natural food webs

The distributions of body masses and degrees (i.e. the number of trophic links) across species are key determinants of food‐web structure and dynamics. In particular, allometric degree distributions combining both aspects in the relationship between degrees and body masses are of critical importance for the stability of these complex ecological networks. They describe decreases in vulnerability (i.e. the number of predators) and increases in generality (i.e. the number of prey) with increasing species’ body masses. We used an entirely new global body‐mass database containing 94 food webs from four different ecosystem types (17 terrestrial, 7 marine, 54 lake, 16 stream ecosystems) to analyze (1) body mass distributions, (2) cumulative degree distributions (vulnerability, generality, linkedness), and (3) allometric degree distributions (e.g. generality – body mass relationships) for significant differences among ecosystem types. Our results demonstrate some general patterns across ecosystems: (1) the body masses are often roughly log‐normally (terrestrial and stream ecosystems) or multi‐modally (lake and marine ecosystems) distributed, and (2) most networks exhibit exponential cumulative degree distributions except stream networks that most often possess uniform degree distributions. Additionally, with increasing species body masses we found significant decreases in vulnerability in 70% of the food webs and significant increases in generality in 80% of the food webs. Surprisingly, the slopes of these allometric degree distributions were roughly three times steeper in streams than in the other ecosystem types, which implies that streams exhibit a more pronounced body mass structure. Overall, our analyses documented some striking generalities in the body‐mass (allometric degree distributions of generality and vulnerability) and degree structure (exponential degree distributions) across ecosystem types as well as surprising exceptions (uniform degree distributions in stream ecosystems). This suggests general constraints of body masses on the link structure of natural food webs irrespective of ecosystem characteristics.     

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.     

Multiple definitions of food web statistics: An unnecessary problem for food web research

Three of the statistics that are regularly used to describe food web structure have been defined in two different ways. The use of these statistics by several authors illustrates some of the problems caused by the existence of two different definitions for what is, at least in name, the same statistic.     

Modeling the microbial food web

Models of the microbial food web have their origin in the debate over the importance of bacteria as an energetic subsidy for higher trophic levels leading to harvestable fisheries. Conceptualization of the microbial food web preceded numerical models by 10–15 years. Pomeroy's work was central to both efforts. Elements necessary for informative and comprehensive models of microbial loops in plankton communities include coupled carbon and nitrogen flows utilizing a size-based approach to structuring and parameterizing the food web. Realistic formulation of nitrogen flows requires recognition that both nitrogenous and nonnitrogenous organic matter are important substrates for bacteria. Nitrogen regeneration driven by simple mass-specific excretion constants seems to overestimate the role of bacteria in the regeneration process. Quantitative assessment of the link-sink question, in which the original loop models are grounded, requires sophisticated analysis of size-based trophic structures. The effects of recycling complicate calculation of the link between bacteria or dissolved organic matter and mesozooplankton, and indirect effects show that the link might be much stronger than simple analyses have suggested. Examples drawn from a series of oceanic mixed layer plankton models are used to illustrate some of these points. Single-size class models related to traditional P-Z-N approaches are incapable of simulating bacterial biomass cycles in some locations (e.g., Bermuda) but appear to be adequate for more strongly seasonal regimes at higher latitudes.     

Phytoplankton food quality control of planktonic food web processes

We developed a mechanistic model of nutrient, phytoplankton, zooplankton and fish interactions to test the effects of phytoplankton food quality for herbivorous zooplankton on planktonic food web processes. When phytoplankton food quality is high strong trophic cascades suppress phytoplankton biomass, the zooplankton can withstand intense zooplanktivory, and energy is efficiently transferred through the food web sustaining higher trophic level production. Low food quality results in trophic decoupling at the plant-animal interface, with phytoplankton biomass determined primarily by nutrient availability, zooplankton easily eliminated by fish predation, and poor energy transfer through the food web. At a given nutrient availability, food quality and zooplanktivory interact to determine zooplankton biomass which in turn determines algal biomass. High food quality resulted in intense zooplankton grazing which favored fast-growing phytoplankton taxa, whereas fish predation favored slow-growing phytoplankton. These results suggest algal food quality for herbivorous zooplankton can strongly influence the nature of aquatic food web dynamics, and can have profound effects on water quality and fisheries production. Handling editor: D. Hamilton     

Field biology, food web models, and management: challenges of context and scale

Managers are increasingly aware of the need for science to inform the stewardship of natural lands and resources. If ecologists are to address this need, we must increase the scope of our inferences, while maintaining sufficient resolution and realism to predict trajectories of specific populations or ecosystem variables. Food chain and simple food web models, used either as core or component hypotheses, can help us to meet this challenge. The simple mass balance logic of dynamic food chain or food web models can organize our thinking about a range of applied problems, such as evaluating controls over populations of concern, or of biotic assemblages that affect important ecosystem properties. In other applications, a food chain or web may be incorporated as one element in models of regional mass balances affecting resources or environments. Specific predictions of food web models will often fail because of inadequate resolution (e.g., of functionally significant differences among taxa within "trophic levels") or insufficient scope (e.g., of spatio-temporal variation over scales relevant to management). Increasing use of tracers to delimit spatial scales of food web interactions will reduce, but not eliminate, this limitation. If used with skepticism and vigilance to local natural history, however, food chain or simple food web models can promote the iterative feedback between prediction, falsification by observation, and new prediction central to hypothetico-deductive science and adaptive management. Experience argues that this stepwise path is the fastest towards better understanding and control of our impacts on nature.     

Relative ascendency predicts food web robustness

Threats to ecosystems globally from anthropogenic disturbance and climate change requires us to urgently identify the most sensitive biological communities to ensure they are effectively preserved. It is for this reason that understanding and predicting food web stability has been topical within ecology. Food web stability is a multi-faceted concept that represents the ability of a food web to maintain its integrity following disturbance, it includes resistance, resilience and fragility. In this study, we examine the ability of four food web metrics to predict the fragility to random species extinctions in 120 qualitative food webs. We show that three information-based indices out performed food web connectance in predicting fragility, with relative ascendency having the strongest relationship. Relative ascendency was a much stronger predictor of fragility than MacArthur’s stability metric, Average Mutual Information and connectance as it accounted for both the distribution and number of links between species. We also find that most qualitative food webs persist around a central tendency of relative ascendency.     

Community assembly and food web stability

The ecological assembly of food web is considered as a process of predator colonizations and extinctions. The results of computer simulations using predator-prey equations allow us to identify three types of food web stability and examine how they may change through development of food webs. Species turnover stability increases, stability to extensive species extinction remains constant, and local stability to population fluctuations decreases as food web assembly proceeds.     

Size-based predictions of food web patterns

We employ size-based theoretical arguments to derive simple analytic predictions of ecological patterns and properties of natural communities: size-spectrum exponent, maximum trophic level, and susceptibility to invasive species. The predictions are brought about by assuming that an infinite number of species are continuously distributed on a size–trait axis. It is, however, an open question whether such predictions are valid for a food web with a finite number of species embedded in a network structure. We address this question by comparing the size-based predictions to results from dynamic food web simulations with varying species richness. To this end, we develop a new size- and trait-based food web model that can be simplified into an analytically solvable size-based model. We confirm existing solutions for the size distribution and derive novel predictions for maximum trophic level and invasion resistance. Our results show that the predicted size-spectrum exponent is borne out in the simulated food webs even with few species, albeit with a systematic bias. The predicted maximum trophic level turns out to be an upper limit since simulated food webs may have a lower number of trophic levels, especially for low species richness, due to structural constraints. The size-based model possesses an evolutionary stable state and is therefore un-invadable. In contrast, the food web simulations show that all communities, irrespective of number of species, are equally open to invasions. We use these results to discuss the validity of size-based predictions in the light of the structural constraints imposed by food webs.     

A patch-dynamic framework for food web metacommunities

The metacommunity concept has proved to be a valuable tool for studying how space can affect the properties and assembly of competitive communities. However, the concept has not been as extensively applied to the study of food webs or trophically structured communities. Here, we demonstrate how to develop a modelling framework that permits food webs to be considered from a spatial perspective. We do this by broadening the classic metapopulation patch-dynamic framework so that it can also account for trophic interactions between many species and patches. Unlike previous metacommunity models, we argue that this requires a system of equations to track the changing patch occupancy of the various species interactions, not the patch occupancy of individual species. We then suggest how this general theoretical framework can be used to study complex and spatially extended food web metacommunities.     

The microbial food web along salinity gradients

The microbial food web was studied along a gradient of salinity in two solar salterns used for the commercial production of salt. The different ponds in the salterns provide a wide range of ecosystems with food webs of different complexities. Abundance of prokaryotes, cell volume, prokaryotic heterotrophic production, chlorophyll a, abundance of heterotrophic flagellates, ciliates and phytoplankton were determined in several ponds in each saltern. Increases in salinity resulted in a progressive reduction in the abundance and number of different groups of eukaryotic microorganisms present, but an increase in biomass of prokaryotes. Maximal activity of both phyto- and bacterioplankton was found at a salinity of around 100 per thousand, where there was also a maximum in chlorophyll a concentration. Growth rates of heterotrophic prokaryotes decreased with increasing salinity. Bacterivory disappeared above 250 per thousand salinity, whereas other loss factors such as viral lysis appeared to be of minor importance throughout the gradient [Guixa-Boixereu et al. (1996) Aquat. Microb. Ecol. 11, 215-227].     

The structure of a plant-pollinator food web

The pollination biology literature is dominated by examples of specialization between plants and their pollinators. However, a recent review shows that it is generalization that prevails in the field, with most plants having a number of pollinators and most pollinators visiting a number of plants. Consequently, the vast majority of plant–pollinator interactions are embedded in a complex web of plant–pollinator interactions. These plant-pollinator webs can be studied in the manner of conventional food webs and the aim of this paper is to illustrate how contemporary methods of web construction and analysis can be applied to plant-pollinator communities.     

The food web in the pelagic environment

Summary 1. The study of grazing along ecological successions helps in understanding how the mechanisms of transfer of energy evolve and provides a measure of its effectiveness in the different situations. Phytoplankton populations show regular changes along succession. Average size of cells and relative abundance of mobile organisms increase, and productivity or rate of multiplication slows down; there are also changes in the chemical composition, exemplified in the plant pigments by an absolute and relative decrease of chlorophyll a.2. Along a succession, animals are offered different kinds of food, and the resulting selection produces a shift in the composition of zooplankton populations. The speed at which phytoplankton succession proceeds is a very important factor, and grazing may be effective in the regulation of such speed. In a general way, along usual successions, food in the form of small particles, richly suspended in a more or less turbulent environment, is replaced by scarcer food concentrated in bigger units and dispersed in a more organized (stratified) environment.3. Indiscriminate filter feeders are at an advantage in the first stages of succession, but it can be shown that, given the usual properties of food organisms in later stages, it pays to adopt a more selective and hunting behaviour and to concentrate more and more on bigger prey. The effectiveness of such adaptation depends on the distribution of food in size classes and also on its mobility or other clues that prey organisms can offer, and, in general, on the predictability of their distribution. Divergence between microphagous passive filterers and macrophagous hunters must be rapid. Distribution of populations of copepods along time and in relation with phytoplankton distribution sustain such views.4. In general, in later stages of succession, total transfer of energy may be lower, buts its efficiency seems to be regularly improved. Similar considerations could be extended to the discussion of energy transfer between other, superior, trophic levels.

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Das Nahrungsnetz in der pelagischen Umwelt

Kurzfassung Vergleichende Studien über die Organisation des Nahrungsnetzes während verschiedener Stadien von Planktonsukzessionen können Aufschlüsse liefern über Gesetzmäßigkeiten der Energietransformation. Von dieser Annahme ausgehend, werden zunächst verschiedene Stadien von Phytoplanktonsukzessionen beschrieben und dann an Hand von Beispielen aus der Literatur und theoretischen Erwägungen allgemeinere Gesetzmäßigkeiten abgeleitet. Phytoplanktonpopulationen verändern sich im Verlaufe von Sukzessionen in ganz bestimmter Weise: Die Durchschnittgröße der Zellen und die relative Häufigkeit von Organismen mit Eigenbewegung nehmen zu, während Produktivität oder Zellteilungsrate abnehmen; ferner kommt es zu Veränderungen in der chemischen Zusammensetzung, etwa zu einer Abnahme der Menge an Chlorophyll. Im Verlauf der Sukzessionen verändert sich das Nahrungsangebot für die Zooplankter; dieser Umstand führt zu Verschiebungen in der Komposition der Zooplanktonpopulationen. Die Geschwindigkeit, mit welcher Phytoplanktonsukzessionen fortschreiten, ist ein sehr wichtiger Faktor; grazing ist hier möglicherweise als Geschwindigkeitsregulativ wirksam. Ganz allgemein wird im Verlauf gewöhnlicher Sukzessionen Nahrung, welche in Form von kleinen dispers suspendierten Partikeln in einem mehr oder minder turbulenten Wasserkörper vorliegt, ersetzt durch geringere Nahrungsmengen, welche in größeren Partikeln konzentriert sind und in einer stärker organisierten (stratifizierten) Umwelt vorkommen. In den ersten Sukzessionsstadien sind unspezifische Filtrierer im Vorteil; in späteren Stadien werden jedoch räuberische Formen und solche, die sich auf immer größere Nahrungsorganismen konzentrieren, bevorzugt. In den späteren Sukzessiontadien ist die Gesamtmenge der transferierten Energie möglicherweise geringer, aber der Nutzeffekt scheint größer zu sein.

     

Forest fragmentation leads to food web contraction

Fragmentation and loss of habitat are critical components of the global change currently threatening biodiversity and ecosystem functioning. We studied the effects of habitat loss through fragmentation on food web structure, by constructing and analyzing plant‐herbivore and host‐parasitoid food webs including more than 400 species and over 120 000 feeding records, in 19 Chaco Serrano remnants of differing areas. Food web structure was altered by habitat fragmentation, with different metrics being affected depending on interaction type, and with all changes being driven by the reduced size of networks in smaller fragments. Only connectance varied in both quantitative and qualitative analyses, being negatively related to area. In addition, the interactions were represented by proper successive subsets, modulated mainly by resource availability (plant–herbivore) or consumer specialization (host–parasitoid), as forest size decreased. The results suggest that habitat loss has led to food web contraction around a central core of highly‐connected species, for plant–herbivore as well as for host–parasitoid systems. The study provides new insights into the effects of human perturbations on complex biological systems.     

Consequences of symbiosis for food web dynamics

Basic Lotka-Volterra type models in which mutualism (a type of symbiosis where the two populations benefit both) is taken into account, may give unbounded solutions. We exclude such behaviour using explicit mass balances and study the consequences of symbiosis for the long-term dynamic behaviour of a three species system, two prey and one predator species in the chemostat. We compose a theoretical food web where a predator feeds on two prey species that have a symbiotic relationships. In addition to a species-specific resource, the two prey populations consume the products of the partner population as well. In turn, a common predator forages on these prey populations. The temporal change in the biomass and the nutrient densities in the reactor is described by ordinary differential equations (ODE). Since products are recycled, the dynamics of these abiotic materials must be taken into account as well, and they are described by odes in a similar way as the abiotic nutrients. We use numerical bifurcation analysis to assess the long-term dynamic behaviour for varying degrees of symbiosis. Attractors can be equilibria, limit cycles and chaotic attractors depending on the control parameters of the chemostat reactor. These control parameters that can be experimentally manipulated are the nutrient density of the inflow medium and the dilution rate. Bifurcation diagrams for the three species web with a facultative symbiotic association between the two prey populations, are similar to that of a bi-trophic food chain; nutrient enrichment leads to oscillatory behaviour. Predation combined with obligatory symbiotic prey-interactions has a stabilizing effect, that is, there is stable coexistence in a larger part of the parameter space than for a bi-trophic food chain. However, combined with a large growth rate of the predator, the food web can persist only in a relatively small region of the parameter space. Then, two zero-pair bifurcation points are the organizing centers. In each of these points, in addition to a tangent, transcritical and Hopf bifurcation a global heteroclinic bifurcation is emanating. This heteroclinic cycle connects two saddle equilibria where the predator is absent. Under parameter variation the period of the stable limit cycle goes to infinity and the cycle tends to the heteroclinic cycle. At this global bifurcation point this cycle breaks and the boundary of the basin of attraction disappears abruptly because the separatrix disappears together with the cycle. As a result, it becomes possible that a stable two-nutrient–two-prey population system becomes unstable by invasion of a predator and eventually the predator goes extinct together with the two prey populations, that is, the complete food web is destroyed. This is a form of over-exploitation by the predator population of the two symbiotic prey populations. When obligatory symbiotic prey-interactions are modelled with Liebigs minimum law, where growth is limited by the most limiting resource, more complicated types of bifurcations are found. This results from the fact that the Jacobian matrix changes discontinuously with respect to a varying parameter when another resource becomes most limiting.Revised version: 21 July 2003