Some properties of the speciation model for food-web structure-mechanisms for degree distributions and intervality

Biology, methodology or chance? The degree distributions of bipartite ecological networks

The distribution of the number of links per species, or degree distribution, is widely used as a summary of the topology of complex networks. Degree distributions have been studied in a range of ecological networks, including both mutualistic bipartite networks of plants and pollinators or seed dispersers and antagonistic bipartite networks of plants and their consumers. The shape of a degree distribution, for example whether it follows an exponential or power-law form, is typically taken to be indicative of the processes structuring the network. The skewed degree distributions of bipartite mutualistic and antagonistic networks are usually assumed to show that ecological or co-evolutionary processes constrain the relative numbers of specialists and generalists in the network. I show that a simple null model based on the principle of maximum entropy cannot be rejected as a model for the degree distributions in most of the 115 bipartite ecological networks tested here. The model requires knowledge of the number of nodes and links in the network, but needs no other ecological information. The model cannot be rejected for 159 (69%) of the 230 degree distributions of the 115 networks tested. It performed equally well on the plant and animal degree distributions, and cannot be rejected for 81 (70%) of the 115 plant distributions and 78 (68%) of the animal distributions. There are consistent differences between the degree distributions of mutualistic and antagonistic networks, suggesting that different processes are constraining these two classes of networks. Fit to the MaxEnt null model is consistently poor among the largest mutualistic networks. Potential ecological and methodological explanations for deviations from the model suggest that spatial and temporal heterogeneity are important drivers of the structure of these large networks.

Universal power-law diet partitioning by marine fish and squid with surprising stability-diversity implications

A central question in community ecology is how the number of trophic links relates to community species richness. For simple dynamical food-web models, link density (the ratio of links to species) is bounded from above as the number of species increases; but empirical data suggest that it increases without bounds. We found a new empirical upper bound on link density in large marine communities with emphasis on fish and squid, using novel methods that avoid known sources of bias in traditional approaches. Bounds are expressed in terms of the diet-partitioning function (DPF): the average number of resources contributing more than a fraction f to a consumer's diet, as a function of f. All observed DPF follow a functional form closely related to a power law, with power-law exponents independent of species richness at the measurement accuracy. Results imply universal upper bounds on link density across the oceans. However, the inherently scale-free nature of power-law diet partitioning suggests that the DPF itself is a better defined characterization of network structure than link density.

Food-web structure in low- and high-dimensional trophic niche spaces

A question central to modelling and, ultimately, managing food webs concerns the dimensionality of trophic niche space, that is, the number of independent traits relevant for determining consumer-resource links. Food-web topologies can often be interpreted by assuming resource traits to be specified by points along a line and each consumer's diet to be given by resources contained in an interval on this line. This phenomenon, called intervality, has been known for 30 years and is widely acknowledged to indicate that trophic niche space is close to one-dimensional. We show that the degrees of intervality observed in nature can be reproduced in arbitrary-dimensional trophic niche spaces, provided that the processes of evolutionary diversification and adaptation are taken into account. Contrary to expectations, intervality is least pronounced at intermediate dimensions and steadily improves towards lower- and higher-dimensional trophic niche spaces.

Linking biodiversity and ecosystems: towards a unifying ecological theory

Community ecology and ecosystem ecology provide two perspectives on complex ecological systems that have largely complementary strengths and weaknesses. Merging the two perspectives is necessary both to ensure continued scientific progress and to provide society with the scientific means to face growing environmental challenges. Recent research on biodiversity and ecosystem functioning has contributed to this goal in several ways. By addressing a new question of high relevance for both science and society, by challenging existing paradigms, by tightly linking theory and experiments, by building scientific consensus beyond differences in opinion, by integrating fragmented disciplines and research fields, by connecting itself to other disciplines and management issues, it has helped transform ecology not only in content, but also in form. Creating a genuine evolutionary ecosystem ecology that links the evolution of species traits at the individual level, the dynamics of species interactions, and the overall functioning of ecosystems would give new impetus to this much-needed process of unification across ecological disciplines. Recent community evolution models are a promising step in that direction.

Quantitative analysis of the local structure of food webs

We analyze the local structure of model and empirical food webs through the statistics of three-node subgraphs. We study analytically and numerically the number of appearances of each subgraph for a simple model of food web topology, the so-called generalized cascade model, and compare them with 17 empirical community food webs from a variety of environments, including aquatic, estuarine, and terrestrial ecosystems. We obtain analytical expressions for the probability of appearances of each subgraph in the model, and also for randomizations of the model that preserve species' numbers of prey and number of predators; their difference allows us to quantify which subgraphs are over- or under-represented in both the model and the empirical food webs. We find agreement between the model predictions and the empirical results. These results indicate that simple models such as the generalized cascade can provide a good description not only of the global topology of food webs, as recently shown, but also of its local structure.

Individual-based predator-prey model for biological coevolution: fluctuations, stability, and community structure

We study an individual-based predator-prey model of biological coevolution, using linear stability analysis and large-scale kinetic Monte Carlo simulations. The model exhibits approximate 1/f noise in diversity and population-size fluctuations, and it generates a sequence of quasisteady communities in the form of simple food webs. These communities are quite resilient toward the loss of one or a few species, which is reflected in different power-law exponents for the durations of communities and the lifetimes of species. The exponent for the former is near -1 , while the latter is close to -2 . Statistical characteristics of the evolving communities, including degree (predator and prey) distributions and proportions of basal, intermediate, and top species, compare reasonably with data for real food webs.

Food webs: Experts consuming families of experts

Food webs of habitats as diverse as lakes or desert valleys are known to exhibit common "food-web patterns", but the detailed mechanisms generating these structures have remained unclear. By employing a stochastic, dynamical model, we show that many aspects of the structure of predatory food webs can be understood as the traces of an evolutionary history where newly evolving species avoid direct competition with their relatives. The tendency to avoid sharing natural enemies (apparent competition) with related species is considerably weaker. Thus, "experts consuming families of experts" can be identified as the main underlying food-web pattern. We report the results of a systematic, quantitative model validation showing that the model is surprisingly accurate.

Estimating trophic link density from quantitative but incomplete diet data

The trophic link density and the stability of food webs are thought to be related, but the nature of this relation is controversial. This article introduces a method for estimating the link density from diet tables which do not cover the complete food web and do not resolve all diet items to species level. A simple formula for the error of this estimate is derived. Link density is determined as a function of a threshold diet fraction below which diet items are ignored ("diet partitioning function"). Furthermore, analytic relationships between this threshold-dependent link density and the generality distribution of food webs are established. A preliminary application of the method to field data suggests that empirical results relating link density to diversity might need to be revisited.