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.     

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.     

The effects of stochastic population dynamics on food web structure

We develop a stochastic, individual-based model for food web simulation which in the large-population limit reduces to the well-studied Webworld model, which has been used to successfully construct model food webs with several realistic features. We demonstrate that an almost exact match is found between the population dynamics in fixed food webs, and that the demographic fluctuations have systematic effects when the new model is used to construct food webs due to the presence of species with small populations.     

Persistence in three-species food chain models with group defense.

Gause-type models of a three-species food web with group defense are analyzed. Persistence criteria are derived for both the case of no mutual interference and the case when there is mutual interference of predators.     

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.     

Persistence and extinction for stochastic ecological models with internal and external variables

Journal of Mathematical Biology - The dynamics of species’ densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different...     

Persistence in discrete age-structured population models

Survival analyses of populations are developed in dicrete growth processes. Persistence and extinction attributes of age-structured discrete population models are explored on both a finite and infinite time horizon. Conditions for persistence and extinction are found. Decompositions of the initial population size axes into intervals where populations are persistent at timeN and intervals leading to extinction at timen, wheren≤N, are given for two age class discrete population models.     

Persistence in seasonally forced epidemiological models

In this paper we address the persistence of a class of seasonally forced epidemiological models. We use an abstract theorem about persistence by Fonda. Five different examples of application are given.     

The relative importance of herbivory and carnivory on the distribution of energy in a stochastic tri-trophic food web

A three-state, discrete-time Markov chain is used to model the dynamics of energy flow in a tri-trophic food web. The distribution of energy in the three trophic levels is related to the rates of flow between the trophic levels and calculated for the entire range of possible flow values. These distributions are then analysed for stability and used to test the idea that plants are resource-limited and herbivores are predation-limited. Low rates of death and decomposition, when coupled with low rates of herbivory and carnivory, tend to destabilize this food web. Food webs with higher rates of death and decomposition are relatively more stable regardless of rates of herbivory and carnivory. Plants are more prone to resource-limitation and herbivores are, in general, limited by their predators, which supports Hairston et al. (Am. Nat. 94 (1960) 421). The rate of decomposition often mediates the roles of top-down and bottom-up control of energy flow in the food web.     

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.     

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.

     

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.     

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     

Persistence and extinction in single-species reaction-diffusion models

Single-species reaction-diffusion models are analyzed to determine the effect of various diffusion mechanisms on species persistence or extinction.     

Persistence in population models with demographic fluctuations

A persistence and extinction theory is developed through analytical studies of deterministic population models. Under hypotheses that require demographic parameters to fluctuate temporally, the populations may or may not oscillaate. Extinction, when it occurs, is asymptotic. An hierarchy of persistence criteria, based upon fluctuations measured by time average means, is derived. In some situations a threshold value is found to separate persistent population models from those that tend to extinction. Application of the persistence-extinction theory is to the problem of assessing effects of a toxic substance on a population when toxicant inputs to the environment and to resources are oscillatory.