Scale invariance in food web properties

Oikos, 1995

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).

Advances in Ecological Research, 2005

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.

One of the key measures that have been used to describe the topological properties of complex networks is the "degree distribution", which is a measure that describes the frequency distribution of number of links per node. Food webs are complex ecological networks that describe the trophic relationships among species in a community, and the topological properties of empirical food webs, including degree distributions, have been examined previously. Previously, the "niche model" has been shown to accurately predict degree distributions of empirical food webs, however, the niche model-generated food webs were referenced against empirical food webs that had their species grouped together based on their taxonomic and/or trophic relationships (aggregated food webs). Here, we explore the effects of species aggregation on the ability of the niche model to predict the total-(sum of prey and predator links per node), in-(number of predator links per node), and out-(number of prey links per node) degree distributions of empirical food webs by examining two food webs that can be aggregated at different levels of resolution. The results showed that (1) the cumulative total-and out-degree distributions were consistent with the niche model predictions when the species were aggregated, (2) when the species were disaggregated (i.e., higher resolution), there were mixed conclusions with regards to the niche model's ability to predict total-and out-degree distributions, (3) the model's ability to predict the in-degree distributions of the two food webs was generally inadequate. Although it has been argued that universal functional form based on the niche model could describe the degree distribution patterns of empirical food webs, we believe there are some limitations to the model's ability to accurately predict the structural properties of food webs.

Ecology, 2005

We analyze the properties of model food webs and of fifteen community food webs from a variety of environments -including freshwater, marine-freshwater interfaces and terrestrial environments. We first perform a theoretical analysis of a recently proposed model for food webs-the niche model of Williams and Martinez (2000). We derive analytical expressions for the distributions of species' number of prey, number of predators, and total number of trophic links and find that they follow universal functional forms. We also derive expressions for a number of other biologically relevant parameters which depend on these distributions. These include the fraction of top, intermediate, basal, and cannibal species, the standard deviations of generality and vulnerability, the correlation coefficient between species' number of prey and number of predators, and assortativity. We show that our findings are robust under rather general conditions; a result which could not have been demonstrated without treating the problem analytically. We then use our analytical predictions as a guide to the analysis of fifteen of the most complete empirical food webs available. We uncover quantitative unifying patterns that describe the properties of the model food webs and most of the trophic webs considered. Our results support a strong new hypothesis that the empirical distributions of number of prey and number of predators follow universal functional forms that, without free parameters, match our analytical predictions. Further, we find that the empirically observed correlation coefficient, assortativity, and fraction of cannibal species are consistent with our analytical expressions and simulations of the niche model. Finally, we show that two quantities typically used to characterize complex networks, the average distance between nodes and the average clustering coefficient of the nodes, show a high degree of regularity for both the empirical data and simulations of the niche model. Our findings suggest that statistical physics concepts such as scaling and universality may be useful in the description of natural ecosystems.

Theoretical Population Biology, 1979

Nature, 1984

We have analysed 62 community food webs drawn from published studies and have found a remarkable regularity in ecosystem structure: in biological communities, the proportions-of top, intermediate and basal species are, on average, independent of the total number of species. Hence, there is a direct proportionaliv between the numbers of prey and' predators.

Advances in Ecological Research, 2010

The American Naturalist, 1999