Relationship between Stability and Connectedness of Non-linear Systems

Somorjai, R. L.; Goswami, Dipendra Narayan

doi:10.1038/236466a0

Cited by 19 publications

(6 citation statements)

References 2 publications

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“…Hence, it is natural to ask what is the link between a ii and J ii . In general, a negative sign in J ii does not imply a constant direct self‐regulation ( a ii < 0), and vice versa (Somorjai and Goswami 1972, Haydon 1994). This property can be easily illustrated using the logistic population dynamics of a single species,

…”

Section: The Translucent Mirror Between Measuresmentioning

confidence: 99%

Bridging parametric and nonparametric measures of species interactions unveils new insights of non‐equilibrium dynamics

Song

Saavedra

2021

Oikos

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A central theme in ecological research is to understand how species interactions contribute to community dynamics. Species interactions are the basis of parametric (model‐driven) and nonparametric (model‐free) approaches in theoretical and empirical work. However, despite their different interpretations across these approaches, these measures have occasionally been used interchangeably, limiting our opportunity to use their differences to gain new insights about ecological systems. Here, we revisit two of the most used measures across these approaches: species interactions measured as constant direct effects (typically used in parametric approaches) and local aggregated effects (typically used in nonparametric approaches). We show two fundamental properties of species interactions that cannot be revealed without bridging these definitions. First, we show that the local aggregated intraspecific effect summarizes all potential pathways through which one species impacts itself, which are likely to be negative even without any constant direct self‐regulation mechanism. This property has implications for the long‐held debate on how communities can be stabilized when little evidence of self‐regulation has been found among higher‐trophic species. Second, we show that a local aggregated interspecific effect between two species is correlated with the constant direct interspecific effect if and only if the population dynamics do not have any higher‐order direct effects. This other property provides a rigorous methodology to detect direct higher‐order effects in the field and experimental data. Overall, our findings illustrate a practical route to gain further insights about non‐equilibrium ecological dynamics and species interactions.

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…”

Section: The Translucent Mirror Between Measuresmentioning

confidence: 99%

Bridging parametric and nonparametric measures of species interactions unveils new insights of non‐equilibrium dynamics

Song

Saavedra

2021

Oikos

View full text Add to dashboard Cite

show abstract

“…Hence, it is natural to ask what is the link between a ii and J ii . In general, a negative sign in J ii does not imply a constant direct self-regulation (a ii < 0), and vice versa (Somorjai & Goswami, 1972;Haydon, 1994). This property can be easily illustrated using the logistic population dynamics of a single species,…”

Section: Intra-specific Interactionsmentioning

confidence: 99%

Bridging parametric and nonparametric measures of species interactions unveils new insights of non-equilibrium dynamics

Song

Saavedra

2020

Preprint

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A central theme in ecological research is to understand how species interactions contribute to community dynamics. Indeed, species interactions are the basis of parametric (model-driven) and nonparametric (model-free) approaches in theoretical and empirical work. However, despite their different interpretation across these approaches, these measures have occasionally been used interchangeably, limiting our opportunity to use their differences to gain new insights about ecological systems. Here, we revisit two of the most used measures across these approaches: species interactions measured as constant direct effects (typically used in parametric approaches) and local aggregated effects (typically used in nonparametric approaches). We study these measures of species interactions under three categories: intra-specific, interspecific, and higherorder interactions. We show that these measures can be linked if and only if all species interactions are pairwise, demonstrate fundamental differences between inter and intra-specific interactions, and illustrate how and when these measures can be combined to gain further insights about non-equilibrium ecological dynamics and higher-order interactions.

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“…The connectedness (or connectance ) [ 56 ] in a directed graph is equal to C = | E |/| V | 2 and, in an undirected graph without loops, to C = 2| E |/[| V | ( | V | - 1 )] . Gardner and Ashby [ 4 ] have studied the relation between the probability of stability and the connectedness of large linear dynamical systems observed in biology [ 57 , 58 ]. We can notice that the connectivity in the Kauffman’s sense [ 41 ] is the average indegree, which is also equal in directed graphs to c = C | V |; c is set to a constant, however, it is possible to let it be random, chosen under various distributions [ 50 , 51 ], with average connectivity c .…”

Section: Preliminary: Notations and Definitionsmentioning

confidence: 99%

Robustness in Regulatory Interaction Networks. A Generic Approach with Applications at Different Levels: Physiologic, Metabolic and Genetic

Demongeot

Amor

Elena

et al. 2009

IJMS

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Regulatory interaction networks are often studied on their dynamical side (existence of attractors, study of their stability). We focus here also on their robustness, that is their ability to offer the same spatiotemporal patterns and to resist to external perturbations such as losses of nodes or edges in the networks interactions architecture, changes in their environmental boundary conditions as well as changes in the update schedule (or updating mode) of the states of their elements (e.g., if these elements are genes, their synchronous coexpression mode versus their sequential expression). We define the generic notions of boundary, core, and critical vertex or edge of the underlying interaction graph of the regulatory network, whose disappearance causes dramatic changes in the number and nature of attractors (e.g., passage from a bistable behaviour to a unique periodic regime) or in the range of their basins of stability. The dynamic transition of states will be presented in the framework of threshold Boolean automata rules. A panorama of applications at different levels will be given: brain and plant morphogenesis, bulbar cardio-respiratory regulation, glycolytic/oxidative metabolic coupling, and eventually cell cycle and feather morphogenesis genetic control.

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Relationship between Stability and Connectedness of Non-linear Systems

Cited by 19 publications

References 2 publications

Bridging parametric and nonparametric measures of species interactions unveils new insights of non‐equilibrium dynamics

Bridging parametric and nonparametric measures of species interactions unveils new insights of non‐equilibrium dynamics

Bridging parametric and nonparametric measures of species interactions unveils new insights of non-equilibrium dynamics

Robustness in Regulatory Interaction Networks. A Generic Approach with Applications at Different Levels: Physiologic, Metabolic and Genetic

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