Ricard V. Solé

Ecological networks and their fragility

Darwin used the metaphor of a ‘tangled bank’ to describe the complex interactions between species. Those interactions are varied: they can be antagonistic ones involving predation, herbivory and parasitism, or mutualistic ones, such as those involving the pollination of flowers by insects. Moreover, the metaphor hints that the interactions may be complex to the point of being impossible to understand. All interactions can be visualized as ecological networks, in which species are linked together, either directly or indirectly through intermediate species. Ecological networks, although complex, have well defined patterns that both illuminate the ecological mechanisms underlying them and promise a better understanding of the relationship between complexity and ecological stability.

Complexity and Fragility in Ecological Networks

A detailed analysis of three species–rich ecosystem food webs has shown that they display skewed distributions of connections. Such graphs of interaction are, in fact, shared by a number of biological and technological networks, which have been shown to display a very high homeostasis against random removals of nodes. Here, we analyse the responses of these ecological graphs to both random and selective perturbations (directed against the most–connected species). Our results suggest that ecological networks are very robust against random removals but can be extremely fragile when selective attacks are used. These observations have important consequences for biodiversity dynamics and conservation issues, current estimations of extinction rates and the relevance and definition of keystone species.

Habitat Fragmentation and Extinction Thresholds in Spatially Explicit Models

The incidence of habitat destruction on the survivorship of a single metapopulation is studied by means of a spatially explicit model. As the proportion of destroyed sites increases, the structural properties of the resulting landscape change in a non-linear way, showing the existence of critical thresholds and phase transitions. Such critical thresholds are identified by means of an order parameter, which discriminates a quantitative process, i.e. habitat loss, from a qualitative one, i.e. habitat fragmentation. This difference is only well understood using a spatially explicit framework. We introduce on such a fragmented landscape the dynamics of a metapopulation balanced by local colonization and extinction by means of the cellular automaton formalism. The existence of extinction thresholds when a given fraction of habitat is destroyed is reported. These thresholds are determined both by the critical behaviour of the landscape structural properties, and by the demographic properties of the metapopulation. Some differences between these results and those derived from the study of spatially implicit models are described and explained. In particular, the percentage of patch occupancy is lower for a given value of habitat destruction in the spatially explicit formulation. Extinction threshold also take place for a lower destruction value. Some implications for the management of natural landscapes are discussed.

Evolving protein interaction networks through gene duplication.

The topology of the proteome map revealed by recent large-scale hybridization methods has shown that the distribution of protein-protein interactions is highly heterogeneous, with many proteins having few edges while a few of them are heavily connected. This particular topology is shared by other cellular networks, such as metabolic pathways, and it has been suggested to be responsible for the high mutational homeostasis displayed by the genome of some organisms. In this paper we explore a recent model of proteome evolution that has been shown to reproduce many of the features displayed by its real counterparts. The model is based on gene duplication plus re-wiring of the newly created genes. The statistical features displayed by the proteome of well-known organisms are reproduced and suggest that the overall topology of the protein maps naturally emerges from the two leading mechanisms considered by the model.

Least effort and the origins of scaling in human language

The emergence of a complex language is one of the fundamental events of human evolution, and several remarkable features suggest the presence of fundamental principles of organization. These principles seem to be common to all languages. The best known is the so-called Zipfs law, which states that the frequency of a word decays as a (universal) power law of its rank. The possible origins of this law have been controversial, and its meaningfulness is still an open question. In this article, the early hypothesis of Zipf of a principle of least effort for explaining the law is shown to be sound. Simultaneous minimization in the effort of both hearer and speaker is formalized with a simple optimization process operating on a binary matrix of signal–object associations. Zipfs law is found in the transition between referentially useless systems and indexical reference systems. Our finding strongly suggests that Zipfs law is a hallmark of symbolic reference and not a meaningless feature. The implications for the evolution of language are discussed. We explain how language evolution can take advantage of a communicative phase transition.

Scale-free networks from optimal design

A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being one of them. In this letter we present the first evidence for the emergence of scaling (and the presence of small-world behavior) in software architecture graphs from a well-defined local optimization process. Although the rules that define the strategies involved in software engineering should lead to a tree-like structure, the final net is scale-free, perhaps reflecting the presence of conflicting constraints unavoidable in a multidimensional optimization process. The consequences for other complex networks are outlined.

A MODEL OF LARGE-SCALE PROTEOME EVOLUTION

The next step in the understanding of the genome organization, after the determination of complete sequences, involves proteomics. The proteome includes the whole set of protein-protein interactions, and two recent independent studies have shown that its topology displays a number of surprising features shared by other complex networks, both natural and artificial. In order to understand the origins of this topology and its evolutionary implications, we present a simple model of proteome evolution that is able to reproduce many of the observed statistical regularities reported from the analysis of the yeast proteome. Our results suggest that the observed patterns can be explained by a process of gene duplication and diversification that would evolve proteome networks under a selection pressure, favoring robustness against failure of its individual components.

Distributed biological computation with multicellular engineered networks

Ongoing efforts within synthetic and systems biology have been directed towards the building of artificial computational devices using engineered biological units as basic building blocks. Such efforts, inspired in the standard design of electronic circuits, are limited by the difficulties arising from wiring the basic computational units (logic gates) through the appropriate connections, each one to be implemented by a different molecule. Here, we show that there is a logically different form of implementing complex Boolean logic computations that reduces wiring constraints thanks to a redundant distribution of the desired output among engineered cells. A practical implementation is presented using a library of engineered yeast cells, which can be combined in multiple ways. Each construct defines a logic function and combining cells and their connections allow building more complex synthetic devices. As a proof of principle, we have implemented many logic functions by using just a few engineered cells. Of note, small modifications and combination of those cells allowed for implementing more complex circuits such as a multiplexer or a 1-bit adder with carry, showing the great potential for re-utilization of small parts of the circuit. Our results support the approach of using cellular consortia as an efficient way of engineering complex tasks not easily solvable using single-cell implementations.

TOPOLOGICAL VULNERABILITY OF THE EUROPEAN POWER GRID UNDER ERRORS AND ATTACKS

We present an analysis of the topological structure and static tolerance to errors and attacks of the September 2003 actualization of the Union for the Coordination of Transport of Electricity (UCTE) power grid, involving thirty-three different networks. Though every power grid studied has exponential degree distribution and most of them lack typical small-world topology, they display patterns of reaction to node loss similar to those observed in scale-free networks. We have found that the node removal behavior can be logarithmically related to the power grid size. This logarithmic behavior would suggest that, though size favors fragility, growth can reduce it. We conclude that, with the ever-growing demand for power and reliability, actual planning strategies to increase transmission systems would have to take into account this relative increase in vulnerability with size, in order to facilitate and improve the power grid design and functioning.

Robustness of the European power grids under intentional attack

The power grid defines one of the most important technological networks of our times and sustains our complex society. It has evolved for more than a century into an extremely huge and seemingly robust and well understood system. But it becomes extremely fragile as well, when unexpected, usually minimal, failures turn into unknown dynamical behaviours leading, for example, to sudden and massive blackouts. Here we explore the fragility of the European power grid under the effect of selective node removal. A mean field analysis of fragility against attacks is presented together with the observed patterns. Deviations from the theoretical conditions for network percolation (and fragmentation) under attacks are analysed and correlated with non topological reliability measures.