Ecological subsystems via graph theory: the role of strongly connected components

Allesina, Stefano; Bodini, Antonio; Bondavalli, Cristina

doi:10.1111/j.0030-1299.2005.13082.x

Cited by 57 publications

(41 citation statements)

References 37 publications

(33 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Their TðGÞ > 0 values indicate a certain degree of pyramidal structure and the low OðGÞs are consistent with an important role played by loops. The special status of these networks (not shared by other webs) is consistent with the well-known picture of a trophic pyramid combined with the presence of recycling (16,54).…”

Section: Null Models and Real Network Analysissupporting

confidence: 84%

On the origins of hierarchy in complex networks

Corominas-Murtra

Goñi

Solé

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

139

147

View full text Add to dashboard Cite

Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting from the convergence of theoretical morphology and network theory that allows constructing a 3D morphospace of hierarchies and hence comparing the hierarchical organization of ecological, cellular, technological, and social networks. Embedded within large voids in the morphospace of all possible hierarchies, four major groups are identified. Two of them match the expected from random networks with similar connectivity, thus suggesting that nonadaptive factors are at work. Ecological and gene networks define the other two, indicating that their topological order is the result of functional constraints. These results are consistent with an exploration of the morphospace, using in silico evolved networks. modularity | evolution F ifty years ago (1), Herbert Simon defined complex systems as nested hierarchical networks of components organized as interconnected modules. Hierarchy seems a pervasive feature of the organization of natural and artificial systems (2, 3). The examples span from social interactions (4, 5), urban growth (6, 7), and allometric scaling (8) to cell function (9-13), development (14), ecosystem flows (15, 16), river networks (17), brain organization (18), and macroevolution (19,20). It also seems to pervade a coherent form of organization that allows reducing the costs associated to reliable information transmission (21) and to support efficient genetic and metabolic control in cellular networks (22). However, hierarchy is a polysemous word, involving order, levels, inclusion, or control as possible descriptors (23), none of which captures either its complexity or the problem of its measure and origins. Although previous work using complex networks theory has quantitatively tackled the problem (4, 24-34), some questions remain: Is hierarchy a widespread feature of complex systems organization? What types of hierarchies do exist? Are hierarchies the result of selection pressures or, conversely, do they arise as a by-product of structural constraints?A well-established concept where such questions are addressed involves the use of a morphospace (35-40), namely a phenotype space where a small set of quantitative traits can be defined as the axes. Here we take a step in this direction by combining morphospace and network theories, taking the intuitive idea of hierarchy as the starting point: a pattern of relations where there is no ambiguity in who controls whom with a pyramidal structure in which the few control the many. Formally, the picture of hierarchy matches a tree of relations (41), ideally represented by a directed graph. As shown in Fig. 1 A-D, the elements of the system are represented by nodes connected by arrows establishing the map of relations of who affects whom. Accordingly, a measure of hierarchy should account for the deviations from this ideal ...

show abstract

Section: Null Models and Real Network Analysissupporting

confidence: 84%

On the origins of hierarchy in complex networks

Corominas-Murtra

Goñi

Solé

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

139

147

View full text Add to dashboard Cite

show abstract

“…Computer programs can iteratively solve secondary extinctions, but this can be inefficient for large networks. A more sophisticated approach from graph theory is to use a depth-first search of the rooted network (Allesina et al 2005). Rooting a network involves assigning a basal species as a root node as a resource (Allesina et al 2009).…”

Section: Model Structurementioning

confidence: 99%

Stochastic ecological network occupancy (SENO) models: a new tool for modeling ecological networks across spatial scales

Lafferty

Dunne

2010

Theor Ecol

View full text Add to dashboard Cite

Stochastic ecological network occupancy (SENO) models predict the probability that species will occur in a sample of an ecological network. In this review, we introduce SENO models as a means to fill a gap in the theoretical toolkit of ecologists. As input, SENO models use a topological interaction network and rates of colonization and extinction (including consumer effects) for each species. A SENO model then simulates the ecological network over time, resulting in a series of sub-networks that can be used to identify commonly encountered community modules. The proportion of time a species is present in a patch gives its expected probability of occurrence, whose sum across species gives expected species richness. To illustrate their utility, we provide simple examples of how SENO models can be used to investigate how topological complexity, species interactions, species traits, and spatial scale affect communities in space and time. They can categorize species as biodiversity facilitators, contributors, or inhibitors, making this approach promising for ecosystem-based management of invasive, threatened, or exploited species.

show abstract

“…This measures the presence and strength of cyclic pathways in a strongly connected component (SCC) of a network. There has not been much application of SCC to ecosystems, but Allesina et al (2005a) recently demonstrated how one could decompose food webs into SCC to determine possible compartments. For an irreducible matrix, max is bounded by n. For a reducable matrix (several SCCs), max is bounded by the number of nodes in the largest subcomponent, and is the dominant eigenvalue for the subcomponent with the strongest degree of structural cycling.…”

Section: Structural Cyclingmentioning

confidence: 99%

Cyclic energy pathways in ecological food webs

Fath

Halnes

2007

Ecological Modelling

View full text Add to dashboard Cite

Detritus Energy flowFood webs Network analysisTrophic dynamics a b s t r a c t Standard ecology textbooks typically maintain that nutrients cycle, but energy flows in unidirectional chains. However, here we use a new metric that allows for the identification and quantification of cyclic energy pathways. Some of these important pathways occur due to the contribution of dead organic matter to detrital pools and those organisms that feed on them, reintroducing some of that energy back into the food web. Recognition of these cyclic energy pathways profoundly impacts many aspects of ecology such as trophic levels, control, and the importance of indirect effects. Network analysis, specifically the maximum eigenvalue of the connectance matrix, is used to identify both the presence and strength of these structural cycles.

show abstract

Ecological subsystems via graph theory: the role of strongly connected components

Cited by 57 publications

References 37 publications

On the origins of hierarchy in complex networks

On the origins of hierarchy in complex networks

Stochastic ecological network occupancy (SENO) models: a new tool for modeling ecological networks across spatial scales

Cyclic energy pathways in ecological food webs

Contact Info

Product

Resources

About