Food web models: a plea for groups
Mercedes Pascual2009
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Abstract
The concept of a group is ubiquitous in biology. It underlies classifications in evolution and ecology, including those used to describe phylogenetic levels, the habitat and functional roles of organisms in ecosystems. Surprisingly, this concept is not explicitly included in simple models for the structure of food webs, the ecological networks formed by consumer-resource interactions. We present here the simplest possible model based on groups, and show that it performs substantially better than current models at predicting the structure of large food webs. Our group-based model can be applied to different types of biological and non-biological networks, and for the first time merges in the same framework two important notions in network theory: that of compartments (sets of highly interacting nodes) and that of roles (sets of nodes that have similar interaction patterns). This model provides a basis to examine the significance of groups in biological networks and to develop more accurate models for ecological network structure. It is especially relevant at a time when a new generation of empirical data is providing increasingly large food webs.
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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.
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Proceedings of The National Academy of Sciences, 2002
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Journal of Animal Ecology, 2009
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Food webs are networks describing who is eating whom in an ecological community. By now it is clear that many aspects of food-web structure are reproducible across diverse habitats, yet little is known about the driving force behind this structure. Evolutionary and population dynamical mechanisms have been considered. We propose a model for the evolutionary dynamics of food-web topology and show that it accurately reproduces observed food-web characteristics in the steady state. It is based on the observation that most consumers are larger than their resource species and the hypothesis that speciation and extinction rates decrease with increasing body mass. Results give strong support to the evolutionary hypothesis.
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PloS one, 2011
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QUANTITATIVE PATTERNS IN THE STRUCTURE OF MODEL AND EMPIRICAL 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.
Ecological networks – beyond food webs
A fundamental goal of ecological network research is to understand how the complexity observed in nature can persist and how this affects ecosystem functioning. This is essential for us to be able to predict, and eventually mitigate, the consequences of increasing environmental perturbations such as habitat loss, climate change, and invasions of exotic species. 2. Ecological networks can be subdivided into three broad types: 'traditional' food webs, mutualistic networks and host-parasitoid networks. There is a recent trend towards cross-comparisons among network types and also to take a more mechanistic, as opposed to phenomenological, perspective. For example, analysis of network configurations, such as compartments, allows us to explore the role of co-evolution in structuring mutualistic networks and host-parasitoid networks, and of body size in food webs. 3. Research into ecological networks has recently undergone a renaissance, leading to the production of a new catalogue of evermore complete, taxonomically resolved, and quantitative data. Novel topological patterns have been unearthed and it is increasingly evident that it is the distribution of interaction strengths and the configuration of complexity, rather than just its magnitude, that governs network stability and structure. 4. Another significant advance is the growing recognition of the importance of individual traits and behaviour: interactions, after all, occur between individuals. The new generation of high-quality networks is now enabling us to move away from describing networks based on species-averaged data and to start exploring patterns based on individuals. Such refinements will enable us to address more general ecological questions relating to foraging theory and the recent metabolic theory of ecology. 5. We conclude by suggesting a number of 'dead ends' and 'fruitful avenues' for future research into ecological networks.
From Small to Large Ecological Networks in a Dynamic World
2005
Food webs are one of the most useful, and challenging, objects of study in ecology. These networks of predator-prey interactions, conjured in Darwin's image of a "tangled bank," provide a paradigmatic example of complex adaptive systems. While it is deceptively easy to throw together simplified caricatures of feeding relationships among a few taxa as can be seen in many basic ecology text books, it is much harder to create detailed descriptions that portray a full range of diversity of species in an ecosystem and the complexity of interactions among them ( ). Difficult to sample, difficult to describe, and difficult to model, food webs are nevertheless of central practical and theoretical importance. The interactions between species on different trophic (feeding) levels underlie the flow of energy and biomass in ecosystems and mediate species' responses to natural and unnatural perturbations such as habitat loss. Understanding the ecology and mathematics of food webs, and more broadly, ecological networks, is central to understanding the fate of biodiversity and ecosystems in response to perturbations.
Using trophic hierarchy to understand food web structure
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).
A General Model for Food Web Structure
Science, 2008
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