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.     

Linking saturation,stability and sustainability in food webs with observed equilibrium structure

Stability of a dynamic equilibrium in a predator-prey system depends both on the type of functional response and on the point of equilibrium on the response curve. Saturation effects from Holling type II responses are known to destabilise prey populations, while a type III (sigmoid) response curve has been shown to provide stability at lower levels of saturation. These effects have also been shown in multi-trophic model systems. However, stability analyses of observed equilibria in real complex ecosystems have as yet not assumed non-linear functional responses. Here, we evaluate the implications of saturation in observed balanced material-flow structures, for system stability and sustainability. We first make the effects of the non-linear functional responses on the interaction strengths in a food web transparent by expressing the elements of Jacobian ‘community’ matrices for type II and III systems as simple functions of their linear (type I) counterparts. We then determine the stability of the systems and distinguish two critical saturation levels: (1) a level where the system is just as stable as a type I system and (2) a level above which the system cannot be stable unless it is subsidised, separating a stable materially sustainable regime from an unsustainable one. We explain the stabilising and destabilising effects in terms of the feedbacks in the systems. The results shed light on the robustness of observed patterns of interaction strengths in complex food webs and suggest the implausibility of saturation playing a significant role in the equilibrium dynamics of sustainable ecosystems.     

The structure of food webs

For nonrandom models of species interaction there is a precipitous decrease in stability as connectance increases. However, the range of stability for different models of the same connectance is large; stability also depends on how the species interactions are organized. Systems with species feeding on more than one trophic level (omnivores) are likely to be unstable, the extent depending on the number and position of the omnivores. For systems of equal connectance, those that are completely compartmentalized are less likely to be stable than those that are not.     

Quantifying the interaction structure and the topological importance of species in food webs: A signed digraph approach

Due to the structural complexity of nature, it is not always easy to identify topologically importance species in an ecosystem. In the past decade, several studies in ecology have developed methods for measuring species importance basing on direct and indirect inter-specific interactions. Here, by extending a previously developed methodology, we present an approach that can quantify the interaction structure of a food web and consequently the topological importance of species when the food web is viewed as a signed digraph. The basic principle behind our approach is to determine the sign and strength of direct and indirect interactions for all pathways up to a predefined number of steps. Our approach mainly differs from the previous methodology in that we are able to quantify the strength of inter-specific interaction as well as in what way species interact with each other, as it can explicitly quantify a wide range of ecological interactions such as cascading effect, indirect food supply effect, apparent and exploitive competitions in the same framework. This then allows us to quantify the topological importance of a species and examine whether it is a predominately positive or negative interactor in a food web. Furthermore, our analysis reveals that positive and negative effects from one species on others eventually cancel each other out for longer pathways resulting in stable interaction structure. Applications of our methodology include providing a more informative index for conservation biologists, and the potential use of interaction structure derived from our approach in food web robustness studies is also discussed.     

Rescaling the trophic structure of marine food webs

Measures of trophic position (TP) are critical for understanding food web interactions and human‐mediated ecosystem disturbance. Nitrogen stable isotopes (δ¹⁵N) provide a powerful tool to estimate TP but are limited by a pragmatic assumption that isotope discrimination is constant (change in δ¹⁵N between predator and prey, Δ¹⁵N = 3.4‰), resulting in an additive framework that omits known Δ¹⁵N variation. Through meta‐analysis, we determine narrowing discrimination from an empirical linear relationship between experimental Δ¹⁵N and δ¹⁵N values of prey consumed. The resulting scaled Δ¹⁵N framework estimated reliable TPs of zooplanktivores to tertiary piscivores congruent with known feeding relationships that radically alters the conventional structure of marine food webs. Apex predator TP estimates were markedly higher than currently assumed by whole‐ecosystem models, indicating perceived food webs have been truncated and species‐interactions over simplified. The scaled Δ¹⁵N framework will greatly improve the accuracy of trophic estimates widely used in ecosystem‐based management.     

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.     

The structure of food webs along river networks

Do changes in the species composition of riverine fish assemblages along river networks lead to predictable changes in food‐web structure? We assembled empirical “fish‐centered” river food webs for three rivers located along a latitudinal gradient in the South Saskatchewan River Basin (SSRB) that differ in land‐use impacts and geomorphology but flow through similar mountain, foothill, and prairie physiographic regions. We then calculated 17 food‐web properties to determine whether the nine river food webs differed according to physiographic region or river sub‐basin. There were no statistically significant differences in the 17 food‐web properties calculated among the rivers. In contrast, fish species richness, connectance, the proportion of herbivores, and the proportion of cannibals changed longitudinally along the river network. Our results suggest that regional changes in river geomorphology and physicochemistry play an important role in determining longitudinal variation in food‐web properties such as fish species richness and connectance. In contrast, the overall structure of river food webs may be relatively similar and insensitive to regional influences such as zoogeography. Further explorations of river and other food webs would greatly illuminate this suggestion.     

Temperature alters food web body-size structure

The increased temperature associated with climate change may have important effects on body size and predator–prey interactions. The consequences of these effects for food web structure are unclear because the relationships between temperature and aspects of food web structure such as predator–prey body-size relationships are unknown. Here, we use the largest reported dataset for marine predator–prey interactions to assess how temperature affects predator–prey body-size relationships among different habitats ranging from the tropics to the poles. We found that prey size selection depends on predator body size, temperature and the interaction between the two. Our results indicate that (i) predator–prey body-size ratios decrease with predator size at below-average temperatures and increase with predator size at above-average temperatures, and (ii) that the effect of temperature on predator–prey body-size structure will be stronger at small and large body sizes and relatively weak at intermediate sizes. This systematic interaction may help to simplify forecasting the potentially complex consequences of warming on interaction strengths and food web stability.     

Emergence of non-random structure in local food webs generated from randomly structured regional webs

Previous studies have shown that high-resolution, empirical food webs possess a non-random network structure, typically characterized by uniform or exponential degree distributions. However, the empirical food webs that have been investigated for their structural properties represent local communities that are only a subset of a larger pool of regionally coexisting species. Here, we use a simple model to investigate the effects of regional food web structure on local food webs that are assembled by two simple processes: random immigration of species from a source web (regional food web), and random extinction of species within the local web. The model shows that local webs with non-random degree distributions can arise from randomly structured source webs. A comparison of local webs assembled from randomly structured source webs with local webs assembled from source webs generated by the niche model shows that the former have higher species richness at equilibrium, but have a nonlinear response to changing extinction rates. These results imply that the network structure of regional food webs can play a significant role in the assembly and dynamics of local webs in natural ecosystems. With natural landscapes becoming increasingly fragmented, understanding such structure may be a necessary key to understanding the maintenance and stability of local species diversity.     

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.     

Omnivory,vertical food‐web structure and system productivity: stable isotope analysis of freshwater planktonic food webs

1. The energetic hypothesis proposes that the vertical structure of food webs should increase in height with increasing system productivity. I measured the trophic positions and extent of trophic separation between the invertebrate planktivores Mysis relicta and Chaoborus spp. and their putative zooplankton prey along a gradient of lake productivity with the use of stable nitrogen isotopes. 2. In lakes of low productivity, these planktivores were found to be herbivorous, becoming omnivorous at intermediate lake productivities, and only able to be truly zooplanktivorous as lakes approached mesotrophy. A subsequent secondary analysis of literature data revealed that the strength of top‐down trophic cascades among these organisms increased with lake productivity as reflected by relationships between the abundance of planktivores and that of phytoplankton. 3. Increased omnivory under conditions of low productivity, effectively shortening the vertical structure of food webs as predicted by the energetic hypothesis, may produce increased community stability.     

The dynamics of multispecies, multi-life-stage models of aquatic food webs

We investigated the dynamics of models of aquatic food webs using stability analysis methods previously applied to other types of food web models. Our models expanded traditional Lotka-Volterra models of predator-prey interactions in several ways. We added life history structure to these models in order to investigate its effects. Life history omnivory is different life history stages of a species feeding in trophically different positions in a food web. Such a species might appear omnivorous, integrating across all stages, but the individual stage might not be. Other important additions to the basic models included stock-recruitment relationships between adults and young and food-dependent maturation rates for early life history stages. Complex models of multispecies interactions were built from basic ones by adding new features sequentially. Our analysis revealed five major features of our multispecies, multi-life-stage models. Omnivory reduces stability, as it does in food web models without life history structure. However, life history omnivory reduces stability much less than single life stage omnivory does. Stock recruitment relationships affect the likelihood of finding stable models. If the maturation rate of young varies with their food supply, the chance of finding stable models decreases. Finally, predation loops of the type A eats B, B eats A, or A eats B, B eats C, C eats A greatly reduce model stability. We present both biological and mathematical explanations for these findings. We also discuss their implications for management of marine resources.     

Stability and feedback levels in food web models

Neutel & Thorne (Ecology Letters, 17:651–661, June 2014) provide an approximation for the leading eigenvalue of a food web community matrix involving coefficients of its characteristic polynomial. Though valuably incorporating three‐way species interactions, two critical problems emerge when one considers the dimensions of the system, calling the approach's accuracy and precision into question.     

Synergism between research and simulation models of estuarine microbial food webs

Construction of mathematical simulation models helps to organize current information and extend inferences from available data. During the past two decades, microbial ecology has undergone rapid developments in both quantity and quality of available data. In particular, considerable advances have been made in our knowledge of microbial food web dynamics in the Duplin River watershed at Sapelo Island, Georgia. Here we provide examples of how modeling and microbial ecology have interfaced. In the early 1970s, construction of a 14-compartment model of carbon flow through a salt marsh ecosystem aided in directing method development and field experiments on the sediment microbial community. In turn, the results of field experiments corroborated the model's postulated controls on the community. Also, during the past 12 years we have developed a series of simulation models reflecting the growing information on the aquatic microbial food web. Early models provided evidence for the microbial loop but illustrated the paucity of knowledge concerning controls for bacterial growth on detritus. Results from newer methods in microbial ecology and studies from the Duplin River have allowed us to construct a model which provides realistic simulations but is also highly sensitive to certain parameter value changes (e.g., in organic matter availability and grazing by protozoans). Thus improvements in model structure and corroboration of the models with extant data have been closely tied to methodological and conceptual advances in microbial ecology. The relationship is viewed as synergistic, as needs for model parameter values and equation forms have directed further development of methods, experimentation, and field observations.     

Success and its limits among structural models of complex food webs

1. Following the development of the relatively successful niche model, several other simple structural food web models have been proposed. These models predict the detailed structure of complex food webs given only two input parameters, the numbers of species and the number of feeding links among them. 2. The models claim different degrees of success but have not been compared consistently with each other or with the empirical data. We compared the performance of five structural models rigorously against 10 empirical food webs from a variety of aquatic and terrestrial habitats containing 25-92 species and 68-997 links. 3. All models include near-hierarchical ordering of species' consumption and have identical distributions of the number of prey of each consumer species, but differ in the extent to which species' diets are required to be contiguous and the rules used to assign feeding links. 4. The models perform similarly on a range of food-web properties, including the fraction of top, intermediate and basal species, the standard deviations of generality and connectivity and the fraction of herbivores and omnivores. 5. For other properties, including the standard deviation of vulnerability, the fraction of cannibals and species in loops, mean trophic level, path length, clustering coefficient, maximum similarity and diet discontinuity, there are significant differences in the performance of the different models. 6. While the empirical data do not support the niche model's assumption of diet contiguity, models which relax this assumption all have worse overall performance than the niche model. All the models under-estimate severely the fraction of species that are herbivores and exhibit other important failures that need to be addressed in future research.