Jennifer A. Dunne

Food-web structure and network theory : the role of connectance and size

Networks from a wide range of physical, biological, and social systems have been recently described as “small-world” and “scale-free.” 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.

Parasites in food webs: the ultimate missing links

Parasitism is the most common consumer strategy among organisms, yet only recently has there been a call for the inclusion of infectious disease agents in food webs. The value of this effort hinges on whether parasites affect food-web properties. Increasing evidence suggests that parasites have the potential to uniquely alter food-web topology in terms of chain length, connectance and robustness. In addition, parasites might affect food-web stability, interaction strength and energy flow. Food-web structure also affects infectious disease dynamics because parasites depend on the ecological networks in which they live. Empirically, incorporating parasites into food webs is straightforward. We may start with existing food webs and add parasites as nodes, or we may try to build food webs around systems for which we already have a good understanding of infectious processes. In the future, perhaps researchers will add parasites while they construct food webs. Less clear is how food-web theory can accommodate parasites. This is a deep and central problem in theoretical biology and applied mathematics. For instance, is representing parasites with complex life cycles as a single node equivalent to representing other species with ontogenetic niche shifts as a single node? Can parasitism fit into fundamental frameworks such as the niche model? Can we integrate infectious disease models into the emerging field of dynamic food-web modelling? Future progress will benefit from interdisciplinary collaborations between ecologists and infectious disease biologists.

Two degrees of separation in complex food webs

Feeding relationships can cause invasions, extirpations, and population fluctuations of a species to dramatically affect other species within a variety of natural habitats. Empirical evidence suggests that such strong effects rarely propagate through food webs more than three links away from the initial perturbation. However, the size of these spheres of potential influence within complex communities is generally unknown. Here, we show for that species within large communities from a variety of aquatic and terrestrial ecosystems are on average two links apart, with >95% of species typically within three links of each other. Species are drawn even closer as network complexity and, more unexpectedly, species richness increase. Our findings are based on seven of the largest and most complex food webs available as well as a food-web model that extends the generality of the empirical results. These results indicate that the dynamics of species within ecosystems may be more highly interconnected and that biodiversity loss and species invasions may affect more species than previously thought.

Food webs: Reconciling the structure and function of biodiversity

The global biodiversity crisis concerns not only unprecedented loss of species within communities, but also related consequences for ecosystem function. Community ecology focuses on patterns of species richness and community composition, whereas ecosystem ecology focuses on fluxes of energy and materials. Food webs provide a quantitative framework to combine these approaches and unify the study of biodiversity and ecosystem function. We summarise the progression of food-web ecology and the challenges in using the food-web approach. We identify five areas of research where these advances can continue, and be applied to global challenges. Finally, we describe what data are needed in the next generation of food-web studies to reconcile the structure and function of biodiversity.

INTEGRATING EXPERIMENTAL AND GRADIENT METHODS IN ECOLOGICAL CLIMATE CHANGE RESEARCH

Field-based research on the responses of ecosystems to anthropogenic climate change has primarily used either natural gradient or experimental methods. Taken separately, each approach faces methodological, spatial, and temporal limitations that potentially constrain the generality of results and predictions. Integration of the two approaches within a single study can overcome some of those limitations and provide ways to distinguish among consistent, dynamic, and context-dependent ecosystem responses to global warming. A simple conceptual model and two case studies that focus on climate change impacts on flowering phenology and carbon cycling in a subalpine meadow ecosystem illustrate the utility of this type of integration.

Cascading extinctions and community collapse in model food webs.

Species loss in ecosystems can lead to secondary extinctions as a result of consumer–resource relationships and other species interactions. We compare levels of secondary extinctions in communities generated by four structural food-web models and a fifth null model in response to sequential primary species removals. We focus on various aspects of food-web structural integrity including robustness, community collapse and threshold periods, and how these features relate to assumptions underlying different models, different species loss sequences and simple measures of diversity and complexity. Hierarchical feeding, a fundamental characteristic of food-web structure, appears to impose a cost in terms of robustness and other aspects of structural integrity. However, exponential-type link distributions, also characteristic of more realistic models, generally confer greater structural robustness than the less skewed link distributions of less realistic models. In most cases for the more realistic models, increased robustness and decreased levels of web collapse are associated with increased diversity, measured as species richness S, and increased complexity, measured as connectance C. These and other results, including a surprising sensitivity of more realistic model food webs to loss of species with few links to other species, are compared with prior work based on empirical food-web data.

Compilation and Network Analyses of Cambrian Food Webs

A rich body of empirically grounded theory has developed about food webs—the networks of feeding relationships among species within habitats. However, detailed food-web data and analyses are lacking for ancient ecosystems, largely because of the low resolution of taxa coupled with uncertain and incomplete information about feeding interactions. These impediments appear insurmountable for most fossil assemblages; however, a few assemblages with excellent soft-body preservation across trophic levels are candidates for food-web data compilation and topological analysis. Here we present plausible, detailed food webs for the Chengjiang and Burgess Shale assemblages from the Cambrian Period. Analyses of degree distributions and other structural network properties, including sensitivity analyses of the effects of uncertainty associated with Cambrian diet designations, suggest that these early Paleozoic communities share remarkably similar topology with modern food webs. Observed regularities reflect a systematic dependence of structure on the numbers of taxa and links in a web. Most aspects of Cambrian food-web structure are well-characterized by a simple “niche model,” which was developed for modern food webs and takes into account this scale dependence. However, a few aspects of topology differ between the ancient and recent webs: longer path lengths between species and more species in feeding loops in the earlier Chengjiang web, and higher variability in the number of links per species for both Cambrian webs. Our results are relatively insensitive to the exclusion of low-certainty or random links. The many similarities between Cambrian and recent food webs point toward surprisingly strong and enduring constraints on the organization of complex feeding interactions among metazoan species. The few differences could reflect a transition to more strongly integrated and constrained trophic organization within ecosystems following the rapid diversification of species, body plans, and trophic roles during the Cambrian radiation. More research is needed to explore the generality of food-web structure through deep time and across habitats, especially to investigate potential mechanisms that could give rise to similar structure, as well as any differences.

Complexity in Ecology and Conservation: Mathematical, Statistical, and Computational Challenges

Abstract Creative approaches at the interface of ecology, statistics, mathematics, informatics, and computational science are essential for improving our understanding of complex ecological systems. For example, new information technologies, including powerful computers, spatially embedded sensor networks, and Semantic Web tools, are emerging as potentially revolutionary tools for studying ecological phenomena. These technologies can play an important role in developing and testing detailed models that describe real-world systems at multiple scales. Key challenges include choosing the appropriate level of model complexity necessary for understanding biological patterns across space and time, and applying this understanding to solve problems in conservation biology and resource management. Meeting these challenges requires novel statistical and mathematical techniques for distinguishing among alternative ecological theories and hypotheses. Examples from a wide array of research areas in population biology and community ecology highlight the importance of fostering synergistic ties across disciplines for current and future research and application.

Parasites Affect Food Web Structure Primarily through Increased Diversity and Complexity

Parasites primarily affect food web structure through changes to diversity and complexity. However, compared to free-living species, their life-history traits lead to more complex feeding niches and altered motifs.

Climate change in size-structured ecosystems

One important aspect of climate change is the increase in average temperature, which will not only have direct physiological effects on all species but also indirectly modifies abundances, interaction strengths, food-web topologies, community stability and functioning. In this theme issue, we highlight a novel pathway through which warming indirectly affects ecological communities: by changing their size structure (i.e. the body-size distributions). Warming can shift these distributions towards dominance of small- over large-bodied species. The conceptual, theoretical and empirical research described in this issue, in sum, suggests that effects of temperature may be dominated by changes in size structure, with relatively weak direct effects. For example, temperature effects via size structure have implications for top-down and bottom-up control in ecosystems and may ultimately yield novel communities. Moreover, scaling up effects of temperature and body size from physiology to the levels of populations, communities and ecosystems may provide a crucially important mechanistic approach for forecasting future consequences of global warming.