Food webs aim to provide a thorough representation of the trophic interactions found in an ecosystem. The complexity of empirical food webs, however, is leading many ecologists to focus dynamic ecosystem studies on smaller microcosm or mesocosm studies based upon community modules, which comprise three to five species and the interactions likely to have ecological relevance. We provide here a structural counterpart to community modules. We investigate food-web 'motifs' which are n-species connected subgraphs found within the food web. Remarkably, we find that the over- and under-representation of three-species motifs in empirical food webs can be understood through comparison to a static food-web model, the niche model. Our result conclusively demonstrates that predation upon species with some 'characteristic' niche value is the prey selection mechanism consistent with the structural properties of empirical food webs.
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.
Intervality of a food web is related to the number of trophic dimensions characterizing the niches in a community. We introduce here a mathematically robust measure for food web intervality. It has previously been noted that empirical food webs are not strictly interval; however, upon comparison to suitable null hypotheses, we conclude that empirical food webs actually do exhibit a strong bias toward contiguity of prey, that is, toward intervality. Further, our results strongly suggest that empirically observed species and their diets can be mapped onto a single dimension. This finding validates a critical assumption in the recently proposed static niche model and provides guidance for ongoing efforts to develop dynamic models of ecosystems.niche dimensions ͉ networks ͉ universality ͉ predator-prey D espite their complexity, the structure of natural food webs displays a number of remarkable regularities (1-9). The existence of these empirical regularities has prompted several researchers to develop simple models that aim to identify the mechanisms that underlie food webs. In particular, three recent ''static'' models, the niche model (2), the nested-hierarchy model (7), and the generalized cascade model (9) predict key statistical properties of food webs from a variety of environments, including deserts, rain forests, lakes, and estuaries. Stouffer et al. (9) demonstrated that these three models share two fundamental mechanisms that account for the models' success in reproducing many of the empirical patterns. (i) Species form a totally ordered set in niche space, that is, species can be ordered along a single niche dimension. (ii) Each species has an exponentially decaying probability of preying on a given fraction of the species with equal or lower niche values (9). Despite these similarities, the models exhibit some differences; a crucial distinction concerns how species' prey are organized along the single dimension. In the niche model, species prey on a contiguous range of prey. In the nested-hierarchy and generalized cascade models, in contrast, the diets are not restricted to a contiguous range.The differences in prey selection lead to drastic differences in the intervality of the food web graph § ( Fig. 1 a and b). The significance of intervality in complex food webs was first noted by Cohen (10), who reported, as did subsequent studies (1,(11)(12)(13), that the vast majority of empirical food webs in the literature appeared to be interval graphs. Significantly, these studies also suggested that the probability that a food web is interval strongly depends on the number of species represented in the food web, decreasing from approximately one for very small food webs to close to zero for larger webs (1). The food webs that were analyzed in these studies typically comprised very few species, leaving open the question of whether, or to what degree, larger and more complex food webs are interval (1). More recent studies reported persistent nonintervality of highly resolved empirical food webs (2, 7).Importa...
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