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The network structure of food webs
"... Descriptions of foodweb relationships first appeared more than a century ago, and the quantitative analysis of the network structure of food webs dates back several decades. Recent improvements in foodweb data collection and analysis methods, coupled with a resurgence of interdisciplinary resear ..."
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Descriptions of foodweb relationships first appeared more than a century ago, and the quantitative analysis of the network structure of food webs dates back several decades. Recent improvements in foodweb data collection and analysis methods, coupled with a resurgence of interdisciplinary research on the topology of many kinds of “realworld ” networks, have resulted in renewed interest in foodweb structure. This chapter reviews the history of the search for generalities in the structure of complex food webs, and discusses current and future research trends. Analysis of foodweb structure has used empirical and modeling approaches, and has been inspired both by questions from ecology such as “What factors promote stability of complex ecosystems given internal dynamics and external perturbations? ” and questions from network research such as “Do food webs display universal structure similar to other types of networks? ” Recent research has suggested that once variable diversity and connectance are taken into account, there are universal coarsegrained characteristics of how trophic links and species
An explanatory model for foodweb structure and evolution.
 Ecol. Complex.,
, 2005
"... Abstract Food webs are networks describing who is eating whom in an ecological community. By now it is clear that many aspects of foodweb structure are reproducible across diverse habitats, yet little is known about the driving force behind this structure. Evolutionary and population dynamical mec ..."
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Abstract Food webs are networks describing who is eating whom in an ecological community. By now it is clear that many aspects of foodweb 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 foodweb topology and show that it accurately reproduces observed foodweb 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. #
Biodiversity in model ecosystems, II: Species assembly and food web structure
, 2008
"... This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here we consider species assembly models where the population dynamics is kept far from fixed points through the continuous introduction of new species, and generalize to such mo ..."
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This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here we consider species assembly models where the population dynamics is kept far from fixed points through the continuous introduction of new species, and generalize to such models the coexistence condition derived for systems at the fixed point. The ecological overlap between species with shared preys, that we define here, provides a quantitative measure of the effective interspecies competition and of the trophic network topology. We obtain distributions of the overlap from simulations of a new model based both on immigration and speciation, and show that they are in good agreement with those measured for three large natural food webs. As discussed in the first paper, rapid environmental fluctuations, interacting with the condition for coexistence of competing species, limit the maximal biodiversity that a trophic level can host. This horizontal limitation to biodiversity is here combined with either dissipation of energy or growth of fluctuations, which in our model limit the length of food webs in the vertical direction. These ingredients yield an effective model of food webs that produce a biodiversity profile with a maximum at an intermediate trophic level, in agreement with field studies. 1
Critical Critical Systems
 in British Computer Society, Proceedings of Formal Aspects of Security FASEC
, 2003
"... Abstract. I discuss the view of communication networks as selforganised critical systems, the mathematical models that may be needed to describe the emergent properties of such networks, and how certain security hygiene schemes may push a network into a supercritical state, potentially leading to ..."
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Abstract. I discuss the view of communication networks as selforganised critical systems, the mathematical models that may be needed to describe the emergent properties of such networks, and how certain security hygiene schemes may push a network into a supercritical state, potentially leading to large scale security disasters. 1
Designing complex networks
, 2006
"... We suggest a new perspective of research towards understanding the relations between the structure and dynamics of a complex network: can we design a network, e.g. by modifying the features of its units or interactions, such that it exhibits a desired dynamics? Here we present a case study where we ..."
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We suggest a new perspective of research towards understanding the relations between the structure and dynamics of a complex network: can we design a network, e.g. by modifying the features of its units or interactions, such that it exhibits a desired dynamics? Here we present a case study where we positively answer this question analytically for networks of spiking neural oscillators. First, we present a method of finding the set of all networks (defined by all mutual coupling strengths) that exhibit an arbitrary given periodic pattern of spikes as an invariant solution. In such a pattern, all the spike times of all the neurons are exactly predefined. The method is very general, as it covers networks of different types of neurons, excitatory and inhibitory couplings, interaction delays that may be heterogeneously distributed, and arbitrary network connectivities. Second, we show how to design networks if further restrictions are imposed, for instance by predefining the detailed network connectivity. We illustrate the applicability of the method by examples of Erdös–Rényi and powerlaw random networks. Third, the method can be used to design networks that optimize network properties. To illustrate this idea, we design networks that exhibit a predefined pattern dynamics while at the same time minimizing the networks’ wiring costs.
Diversity Evolution
, 2002
"... Bedau has developed a general set of evolutionary statistics that quantify the adaptive component of evolutionary processes. On the basis of these measures, he has proposed a set of 4 classes of evolutionary system. All artificial life sytems so far looked at fall into the first 3 classes, wher ..."
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Bedau has developed a general set of evolutionary statistics that quantify the adaptive component of evolutionary processes. On the basis of these measures, he has proposed a set of 4 classes of evolutionary system. All artificial life sytems so far looked at fall into the first 3 classes, whereas the biosphere, and possibly the human economy belongs to the 4th class. The challenge to the artificial life community is to identify exactly what is difference between these natural evolutionary systems, and existing artificial life systems. At ALife
Network Evolution: Exploring the Change and Adaptation of Complex Ecological Systems Over Deep Time
, 2005
"... One of the most exciting new directions in research on food webs and ecological networks is network evolution or, in other words, the development of the structure and function of ecological networks over time scales long enough for node ..."
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One of the most exciting new directions in research on food webs and ecological networks is network evolution or, in other words, the development of the structure and function of ecological networks over time scales long enough for node
Modelling Selforganization and Innovation Processes in Networks
, 2004
"... Abstract. In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a nonlinear system. We refer to the theory of comple ..."
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Abstract. In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a nonlinear system. We refer to the theory of complex networks and introduce the notion of sensitive networks. Sensitive networks are networks in which the introduction or the removal of a node/vertex dramatically changes the dynamic structure of the system. As an application we consider interaction networks of firms and technologies and describe technological innovation as a specific dynamic process. Random graph theory, percolation, master equation formalism and the theory of birth and death processes are the mathematical instruments used in this paper. 1
Biological Network Modelling Relating Structure and Dynamics to Function in Food Webs and Neural Networks
, 2007
"... Halnes, G. 2007. Biological network modelling: Relating structure and dynamics to function in food webs and neural networks. ISSN 16526880, ISBN 9789185913121 This study takes a network approach to understanding complex biological systems. The overall objective is to explore how the stability a ..."
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Halnes, G. 2007. Biological network modelling: Relating structure and dynamics to function in food webs and neural networks. ISSN 16526880, ISBN 9789185913121 This study takes a network approach to understanding complex biological systems. The overall objective is to explore how the stability and flexibility of biological networks emerge from underlying structural and dynamical characteristics. The thesis is arranged as a journey into the complexity of biological network models. The starting point is qualitative structural network descriptions. The level of detail in the dynamical description of node properties is then gradually increased. Along this journey, new features, both structural and dynamical, are revealed as crucial for the function of biological networks. A set of constructional properties are defined: structural principles, structural complexity, interaction diversity, node diversity and network density. These constructional properties capture important aspects of the structural organization and dynamic mechanisms in biological networks. A set of functional properties are defined: structural robustness, structural cyclicity, dynamic stability and dynamic flexibility. These functional properties are
Abstract Physica D 224 (2006) 182–201 Designing complex networks
, 2006
"... www.elsevier.com/locate/physd We suggest a new perspective of research towards understanding the relations between the structure and dynamics of a complex network: can we design a network, e.g. by modifying the features of its units or interactions, such that it exhibits a desired dynamics? Here we ..."
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www.elsevier.com/locate/physd We suggest a new perspective of research towards understanding the relations between the structure and dynamics of a complex network: can we design a network, e.g. by modifying the features of its units or interactions, such that it exhibits a desired dynamics? Here we present a case study where we positively answer this question analytically for networks of spiking neural oscillators. First, we present a method of finding the set of all networks (defined by all mutual coupling strengths) that exhibit an arbitrary given periodic pattern of spikes as an invariant solution. In such a pattern, all the spike times of all the neurons are exactly predefined. The method is very general, as it covers networks of different types of neurons, excitatory and inhibitory couplings, interaction delays that may be heterogeneously distributed, and arbitrary network connectivities. Second, we show how to design networks if further restrictions are imposed, for instance by predefining the detailed network connectivity. We illustrate the applicability of the method by examples of Erdös–Rényi and powerlaw random networks. Third, the method can be used to design networks that optimize network properties. To illustrate this idea, we design networks that exhibit a predefined pattern dynamics while at the same time minimizing the networks ’ wiring costs. c ○ 2006 Elsevier B.V. All rights reserved.