Scaling relations in food webs

Proceedings of The National Academy of Sciences, 2002

Networks from a wide range of physical, biological, and social systems have been recently described as ''small-world'' and ''scalefree.'' However, studies disagree whether ecological networks called food webs possess the characteristic path lengths, clustering coefficients, and degree distributions required for membership in these classes of networks. Our analysis suggests that the disagreements are based on selective use of relatively few food webs, as well as analytical decisions that obscure important variability in the data. We analyze a broad range of 16 high-quality food webs, with 25-172 nodes, from a variety of aquatic and terrestrial ecosystems. Food webs generally have much higher complexity, measured as connectance (the fraction of all possible links that are realized in a network), and much smaller size than other networks studied, which have important implications for network topology. Our results resolve prior conflicts by demonstrating that although some food webs have small-world and scale-free structure, most do not if they exceed a relatively low level of connectance. Although food-web degree distributions do not display a universal functional form, observed distributions are systematically related to network connectance and size. Also, although food webs often lack small-world structure because of low clustering, we identify a continuum of real-world networks including food webs whose ratios of observed to random clustering coefficients increase as a power-law function of network size over 7 orders of magnitude. Although food webs are generally not small-world, scale-free networks, food-web topology is consistent with patterns found within those classes of networks.

Theoretical Population Biology, 1979

Ecological Modelling, 2009

Energy flow Link distribution Interaction strength Trophic structure Flow diversity a b s t r a c t In the present work we investigate whether the distribution of energy flows in ecosystems responds to criteria of trophic organization. We analyzed weighted and unweighted food webs estimating, for each node, trophic position (TP), Shannon's index of inflow diversity (H) and individual contribution to the whole average mutual information (AMI). Finally, we performed the same analysis on simulated webs that were constructed using the following criteria: (a) preserving topology and varying link strength; (b) modifying position of links and their intensities.

Ecology, 2009

Food webs depict who eats whom in communities. Ecologists have examined statistical metrics and other properties of food webs, but mainly due to the uneven quality of the data, the results have proved controversial. The qualitative data on which those efforts rested treat trophic interactions as present or absent and disregard potentially huge variation in their magnitude, an approach similar to analyzing traffic without differentiating between highways and side roads. More appropriate data are now available and were used here to analyze the relationship between trophic complexity and diversity in 59 quantitative food webs from seven studies (14-202 species) based on recently developed quantitative descriptors. Our results shed new light on food-web structure. First, webs are much simpler when considered quantitatively, and link density exhibits scale invariance or weak dependence on food-web size. Second, the ''constant connectance'' hypothesis is not supported: connectance decreases with web size in both qualitative and quantitative data. Complexity has occupied a central role in the discussion of food-web stability, and we explore the implications for this debate. Our findings indicate that larger webs are more richly endowed with the weak trophic interactions that recent theories show to be responsible for food-web stability.

Oikos, 2002

Advances in Ecological Research, 2010

Oikos, 1995

2008

Oikos, 2009

Link arrangement in food webs is determined by the species' feeding habits. This work investigates whether food web topology is organized in a gradient of trophic positions from producers to consumers. To this end, we analyzed 26 food webs for which the consumption rate of each species was specified. We computed the trophic positions and the link densities of all species in the food webs. Link density measures how much each species contributes to the distribution of energy in the system. It is expressed as the number of links species establish with other nodes, weighted by their magnitude. We computed these two metrics using various formulations developed in the ecological network analysis framework. Results show a positive correlation between trophic position and link density across all the systems, regardless the specific formulas used to measure the two quantities. We performed the same analysis on the corresponding binary matrices (i.e. removing information about rates). In addition, we investigated the relation between trophic position and link density in: a) simulated binary webs with same connectance as the original ones; b) weighted webs with constant topology but randomized link strengths and c) weighted webs with constant connectance where both topology and link strengths are randomized. The correlation between the two indices attenuates, vanishes or becomes negative in the case of binary food webs and simulated data (weighted and unweighted).

Science, 1989

Journal of Theoretical Biology, 2007

Food webs are complex networks describing trophic interactions in ecological communities. Since Robert May's seminal work on random structured food webs, the complexity-stability debate is a central issue in ecology: does network complexity increase or decrease food-web persistence? A multi-species predator-prey model incorporating adaptive predation shows that the action of ecological dynamics on the topology of a food web (whose initial configuration is generated either by the cascade model or by the niche model) render, when a significant fraction of adaptive predators is present, similar hyperbolic complexity-persistence relationships as those observed in empirical food webs. It is also shown that the apparent positive relation between complexity and persistence in food webs generated under the cascade model, which has been pointed out in previous papers, disappears when the final connectance is used instead of the initial one to explain species persistence.

2000

Artificial Life and Robotics, 2009

Journal of Animal Ecology, 2008

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 underestimate severely the fraction of species that are herbivores and exhibit other important failures that need to be addressed in future research.

2008

Large, complex networks of ecological interactions with random structure tend invariably to instability. This mathematical relationship between complexity and local stability ignited a debate that has populated ecological literature for more than three decades. Here we show that, when species interact as predators and prey, systems as complex as the ones observed in nature can still be stable. Moreover, stability is highly robust to perturbations of interaction strength, and is largely a property of structure driven by predator-prey loops with the stability of these small modules cascading into that of the whole network. These results apply to empirical food webs and models that mimic the structure of natural systems as well. These findings are also robust to the inclusion of other types of ecological links, such as mutualism and interference competition, as long as consumer-resource interactions predominate. These considerations underscore the influence of food web structure on ecological dynamics and challenge the current view of interaction strength and long cycles as main drivers of stability in natural communities.