From Small to Large Ecological Networks in a Dynamic World

2000

2008

Large, complex networks of ecological interactions with random structure tend invariably to instability. This mathematical relationship between complexity and local stability ignited a debate that has populated ecological literature for more than three decades. Here we show that, when species interact as predators and prey, systems as complex as the ones observed in nature can still be stable. Moreover, stability is highly robust to perturbations of interaction strength, and is largely a property of structure driven by predator-prey loops with the stability of these small modules cascading into that of the whole network. These results apply to empirical food webs and models that mimic the structure of natural systems as well. These findings are also robust to the inclusion of other types of ecological links, such as mutualism and interference competition, as long as consumer-resource interactions predominate. These considerations underscore the influence of food web structure on ecological dynamics and challenge the current view of interaction strength and long cycles as main drivers of stability in natural communities.

Theoretical Population Biology, 1979

Proceedings of The National Academy of Sciences, 2002

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.

Trends in Ecology & Evolution, 2012

Glossary Assembly: the set of processes by which a food web is rebuilt after disturbance or the creation of new habitat. Bioenergetics: the flow and transformation of energy in and between living organisms and between living organisms and their environment. Cascade model: a food-web model which assumes hierarchical feeding along a single niche axis, with each species allocated a probability of feeding on taxa below it in the hierarchy. Community web: a food web intended to include all species and trophic links that occur within a defined ecological community. 'Species' in this sense might involve various degrees of aggregation or division of biological species. Compartmentalisation: the property by which one subset of species within a food web operates, to varying degrees, independently of other parts. Ecological stoichiometry: how the balance of multiple chemical elements within organisms influences their interactions in food webs. Ecosystem function: the physical, chemical, and biological processes or attributes that contribute to the self-maintenance of the ecosystem; including energy flow, nutrient cycling, filtering, buffering of contaminants, and regulation of populations. Interaction strength: a measure of how much a predator alters population size, biomass, or production of its prey. In food webs these are associated with energy flows while noting that predators can affect prey non-trophically. Niche model: a food-web model which assigns each consumer a feeding distribution on the niche axis that can overlap with itself (cannibalism) and permits trophic loops but still generates realistic patterns whereby species tend to feed in a linear hierarchy. Quantitative food web: a food web where the interaction strengths or trophic flows are quantified. Scale-independence and/or dependence: the degree to which attributes of a food web change with food-web size. Stability: measures of the ability to and/or speed with which a food web regains its structure following a disturbance (resilience) or resists change in food web structure (resistance).

Nature, 2000

Ecology …, 2010

Species coexistence within ecosystems and the stability of patterns of temporal changes in population sizes are central topics in ecological theory. In the last decade, adaptive behaviour has been proposed as a mechanism of population stabilization. In particular, widely distributed adaptive trophic behaviour (ATB), the fitness-enhancing changes in individualsÕ feeding-related traits due to variation in their trophic environment, may play a key role in modulating the dynamics of feeding relationships within natural communities. In this article, we review and synthesize models and results from theoretical research dealing with the consequences of ATB on the structure and dynamics of complex food webs. We discuss current approaches, point out limitations, and consider questions ripe for future research. In spite of some differences in the modelling and analytic approaches, there are points of convergence: (1) ATB promotes the complex structure of ecological networks, (2) ATB increases the stability of their dynamics, (3) ATB reverses MayÕs negative complexity-stability relationship, and (4) ATB provides resilience and resistance of networks against perturbations. Current knowledge supports ATB as an essential ingredient for models of community dynamics, and future research that incorporates ATB will be well positioned to address questions important for basic ecological research and its applications.

Ecology Letters, 2010

Food web structure plays an important role when determining robustness to cascading secondary extinctions. However, existing food web models do not take into account likely changes in trophic interactions (‘rewiring’) following species loss. We investigated structural dynamics in 12 empirically documented food webs by simulating primary species loss using three realistic removal criteria, and measured robustness in terms of subsequent secondary extinctions. In our model, novel trophic interactions can be established between predators and food items not previously consumed following the loss of competing predator species. By considering the increase in robustness conferred through rewiring, we identify a new category of species – overlap species – which promote robustness as shown by comparing simulations incorporating structural dynamics to those with static topologies. The fraction of overlap species in a food web is highly correlated with this increase in robustness; whereas species richness and connectance are uncorrelated with increased robustness. Our findings underline the importance of compensatory mechanisms that may buffer ecosystems against environmental change, and highlight the likely role of particular species that are expected to facilitate this buffering.

Bulletin of mathematical biology, 2015

We consider a simple food web with commensal relationship, where organisms utilize both external resources and resources produced by other organisms. We show that in such a community with no competition, there is at most one possible equilibrium for each fixed set of surviving species, and develop a natural condition that determines which species survive based on available resource. Our main result shows that among all possible communities described by equilibria, the one which is stable has the largest number of surviving species and largest combined biomass and hence maximizes utilization of available resources.

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.