Subpopulations and stability in microbial communities

Haas, Pierre A.; Oliveira, Nuno M.; Goldstein, Raymond E.

doi:10.1103/physrevresearch.2.022036

Cited by 11 publications

(38 citation statements)

References 33 publications

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“…So far, most studies have consid-ered dynamical systems for which the system constituents interact with either a number of degrees of freedom that increases with system size, see, e.g., Refs. [13,20,22,26,27,[79][80][81][82][83][84], or interact through a one-dimensional chain, see, e.g., Refs. [25,85,86].…”

Section: Discussionmentioning

confidence: 99%

“…Let λ be an eigenvalue of the matrix A and let R be the right eigenvector associated with λ. Equation (27) implies that…”

Section: Recursion Relations For P R In Locally Treelike and Orientedmentioning

confidence: 99%

“…Models like Eq. (1) appear when linearizing a set of nonlinearly coupled differential equations in the vicinity of a fixed point [18][19][20] as occurs, for example, in the study of neural networks [21][22][23][24][25] and ecosystems [13,20,26,27]. The vector y describes then the deviation of the system from its fixed point, which is located at the origin, i.e., y = 0.…”

Section: Introductionmentioning

confidence: 99%

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Linear stability analysis of large dynamical systems on random directed graphs

Neri

Metz

2020

Phys. Rev. Research

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We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random, directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such dynamical systems. First, infinitely large systems on directed graphs can be stable even when the degree distribution has unbounded support; this result is surprising since their counterparts on nondirected graphs are unstable when system size is large enough. Second, we show that the phase transition between the stable and unstable phase is universal in the sense that it depends only on a few parameters, such as, the mean degree and a degree correlation coefficient. In addition, in the unstable regime, we characterize the nature of the destabilizing mode, which also exhibits universal features. These results follow from an exact theory for the leading eigenvalue of infinitely large graphs that are locally treelike and oriented, as well as, the right and left eigenvectors associated with the leading eigenvalue. We corroborate analytical results for infinitely large graphs with numerical experiments on random graphs of finite size. We discuss how the presented theory can be extended to graphs with diagonal disorder and to graphs that contain nondirected links. Finally, we discuss the influence of cycles and how they can destabilize large dynamical systems when they induce strong feedback loops.

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Section: Discussionmentioning

confidence: 99%

“…Let λ be an eigenvalue of the matrix A and let R be the right eigenvector associated with λ. Equation (27) implies that…”

Section: Recursion Relations For P R In Locally Treelike and Orientedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Linear stability analysis of large dynamical systems on random directed graphs

Neri

Metz

2020

Phys. Rev. Research

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“…In this Section, we introduce a model, which builds upon that of Ref. [15], for the competition of N species that switch, both responsively and stochastically, between two phenotypes. We show that its statistical stability properties are generically different from those of the corresponding model with stochastic switching only.…”

Section: Statistical Stability Of Responsive Phenotypic Switchingmentioning

confidence: 99%

Stabilization of Microbial Communities by Responsive Phenotypic Switching

Haas

Gutierrez

Oliveira

et al. 2021

Preprint

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Clonal microbes can switch between different phenotypes and recent theoretical work has shown that stochastic switching between these subpopulations can stabilize microbial communities. This phenotypic switching need not be stochastic, however, but can also be in response to environmental factors, both biotic and abiotic. Here, motivated by the bacterial persistence phenotype, we explore the ecological effects of such responsive switching by analyzing phenotypic switching in response to competing species. We show how the stability of microbial communities with responsive switching differs generically from that of communities with stochastic switching only. To understand this effect, we go on to analyse simple two-species models. Combining exact results and numerical simulations, we extend the classical stability results for models of two competing species without phenotypic variation to the case where one of the two species switches, stochastically and responsively, between two phenotypes. In particular, we show that responsive switching can stabilize coexistence even when stochastic switching on its own does not affect the stability of the community.

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“…There is of course no more reason to expect the kinetic parameters to be independent or uniformly distributed than there is reason to expect the linearized population dynamics in May's analysis [25] to be independent or normally distributed. Yet, in the absence of experimental understanding of what the distributions of these parameters should be (in reaction-diffusion systems and in population dynamics), the potential of the random matrix approach to reveal stability principles has been amply demonstrated in population dynamics [29][30][31][32][33][34][35][36][37].…”

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confidence: 99%

Turing’s diffusive threshold in random reaction-diffusion systems

Haas

Goldstein

2020

Preprint

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Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in generic systems with N = 2 diffusing species, forcing experimental realizations of the instability to rely on fluctuations or additional non-diffusing species. Here we ask whether this diffusive threshold lowers for N > 2 to allow “true” Turing instabilities. Inspired by May’s analysis of the stability of random ecological communities, we analyze the threshold for reactiondiffusion systems whose linearized dynamics near a homogeneous fixed point are given by a random matrix. In the numerically tractable cases of N ⩽ 6, we find that the diffusive threshold generically decreases as N increases and that these many-species instabilities generally require all species to be diffusing.

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Subpopulations and stability in microbial communities

Cited by 11 publications

References 33 publications

Linear stability analysis of large dynamical systems on random directed graphs

Linear stability analysis of large dynamical systems on random directed graphs

Stabilization of Microbial Communities by Responsive Phenotypic Switching

Turing’s diffusive threshold in random reaction-diffusion systems

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