Coexistence and chaos in complex ecologies

Sprott, J. C.; Vano, J. A.; Wildenberg, Joseph C.; Anderson, M. B.; Noel, Jimmy

doi:10.1016/j.physleta.2004.12.068

Cited by 42 publications

(30 citation statements)

References 22 publications

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“…that systems at 'the edge of chaos' exhibit selforganization and other features that can actually promote successful function in the presence of modest disturbances (Sprott et al, 2005). Third, we predict that observations of instability in nitrification will foreshadow similar observations in other microbial mutualisms that are fragile with high mutual benefit; the obvious example being methanogenesis.…”

Section: Lyapunov Exponentmentioning

confidence: 68%

Experimental demonstration of chaotic instability in biological nitrification

et al. 2007

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Biological nitrification (that is, NH 3 -NO 2 À -NO 3 À ) is a key reaction in the global nitrogen cycle (Ncycle); however, it is also known anecdotally to be unpredictable and sometimes fails inexplicably. Understanding the basis of unpredictability in nitrification is critical because the loss or impairment of this function might influence the balance of nitrogen in the environment and also has biotechnological implications. One explanation for unpredictability is the presence of chaotic behavior; however, proving such behavior from experimental data is not trivial, especially in a complex microbial community. Here, we show that chaotic behavior is central to stability in nitrification because of a fragile mutualistic relationship between ammonia-oxidizing bacteria (AOB) and nitrite-oxidizing bacteria (NOB), the two major guilds in nitrification. Three parallel chemostats containing mixed microbial communities were fed complex media for 207 days, and nitrification performance, and abundances of AOB, NOB, total bacteria and protozoa were quantified over time. Lyapunov exponent calculations, supported by surrogate data and other tests, showed that all guilds were sensitive to initial conditions, suggesting broad chaotic behavior. However, NOB were most unstable among guilds and displayed a different general pattern of instability. Further, NOB variability was maximized when AOB were most unstable, which resulted in erratic nitrification including significant NO 2 À accumulation. We conclude that nitrification is prone to chaotic behavior because of a fragile AOB-NOB mutualism, which must be considered in all systems that depend on this critical reaction.

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Section: Lyapunov Exponentmentioning

confidence: 68%

Experimental demonstration of chaotic instability in biological nitrification

et al. 2007

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“…However, this impression is wrong, and LV models can represent the most complicated nonlinearities 6 ISRN Biomathematics [21,134], including deterministic chaos. For instance, the graph in Figure 3 is the output of an LV system with just four variables [71,137,138].…”

Section: Types Of Nonlinear Canonical Modelsmentioning

confidence: 99%

“…e Lotka-Volterra format looks deceiving restrictive, but even an LV system with only four variables is capable of exhibiting deterministic chaos. See [71,137,138] for further details. divergence and the accuracy of the approximation are seldom practically helpful, even though they can be formulated.…”

Section: Bst Modelsmentioning

confidence: 99%

Biochemical Systems Theory: A Review

Voit

2013

ISRN Biomathematics

144

154

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Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. is paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. e paper is intended as a guide for investigators entering the fascinating �eld of biological systems analysis and as a resource for practitioners and experts. PreambleBiochemical systems theory (BST) is a mathematical and computational framework for analyzing and simulating systems. It was originally developed for biochemical pathways but by now has become much more widely applied to systems throughout biology and beyond. BST is called "canonical, " which means that model construction, diagnosis, and analysis follow stringent rules, which will be discussed throughout this paper. e key ingredient of BST is the power-law representation of all processes in a system.BST has been the focus of a number of books [1-6], including some in Chinese and Japanese [7][8][9]. e most detailed modern text dedicated speci�cally to BST is [3]. Moreover, since its inception, numerous reviews have portrayed the evolving state of the art in BST. Most of these reviews summarized methodological advances for the analysis of biochemical pathway systems . Others compared BST models with alternative modeling frameworks [32,[51][52][53][54][55][56][57][58][59][60][61][62][63]; some of these comparisons will be discussed later. Yet other reviews focused on specialty areas, such as customized methods for optimizing BST models (e.g., [64][65][66][67]) or estimating their parameters (e.g., [68][69][70][71][72]), strategies for discovering design and operating principles in natural system (e.g., [73][74][75][76][77][78]), and even the use of BST models in statistics [79][80][81]. A historical account of the �rst twenty years of BST was presented in [82].Supporting the methodological developments in the �eld, several soware packages were developed for different aspects of BST analysis. e earliest was ESSYNS [83][84][85], which supported all standard steady-state analyses and also contained a numerical solver that, at the time, was many times faster than any off-the-shelf soware [86,87]; see also [88]. Utilizing advances in computing and an extension of the solver from ESSYNS, Ferreira created the very user-friendly package PLAS, which is openly available and still very widely used [89] (see also [3]). Yamada and colleagues developed soware to translate E-cell models into BST models in PLAS format [90]. Okamoto's group created the soware BestKit, which permits the graphical design and translation of models, along with their analysis [91][92][93]. Vera and colleagues developed the soware tool PLMaddon for analyzing BST models within SBML [94]; see also [95]. It expands the Matlab SBToolbox with speci�c functionalities for power-law repr...

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“…It is very reasonable to assume that Nature does not choose randomly from all possible ecologies, but that instead individual species adapt to their environment so as to enhance their own survival. Many models have attempted to include such adaptation [14,15,18,75]. These models often assume that the population goes extinct if its abundance drops below a critical threshold.…”

Section: Ubiquity Of Adaptive Network Across Disciplinesmentioning

confidence: 99%

Dynamic and Topological Interplay in Adaptive Networks

Blasius

Groß

2009

Reviews of Nonlinear Dynamics and Complexity

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Theory and applications of complex networks pervade nonlinear sciences. This chapter is devoted to adaptive networks which combine topological evolution of the network with dynamics in the network nodes -a property which yields a rich dynamical interplay between the state and the topology of the network. Recently, the dynamics of adaptive networks has been investigated in a number of parallel studies from different fields, ranging from genomics to game theory. Here we review these recent developments and show that they can be viewed from a unique angle. We demonstrate that all these studies are characterized by common themes -most prominently: complex dynamics and robust topological self-organization based on simple local rules. With our review we aim to provide an overview of these central properties of adaptive networks, to outline the different perspectives from which they have been considered and finally to set an agenda for future research.

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Coexistence and chaos in complex ecologies

Cited by 42 publications

References 22 publications

Experimental demonstration of chaotic instability in biological nitrification

Experimental demonstration of chaotic instability in biological nitrification

Biochemical Systems Theory: A Review

Dynamic and Topological Interplay in Adaptive Networks

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