Path-integral calculation for the emergence of rapid evolution from demographic stochasticity

Shih, Hong Yan; Goldenfeld, Nigel

doi:10.1103/physreve.90.050702

“…This approach is complementary to a more traditional description of ecosystem dynamics at or around the steady state solution25928. The emergent cyclic dynamic in our model is entirely collapse-driven and thus distinct from either stable or transient periodic oscillations present in predator-prey ecosystems described by the Lotka-Volterra equations102324282930.…”

Section: Discussionmentioning

confidence: 94%

Population cycles and species diversity in dynamic Kill-the-Winner model of microbial ecosystems

Maslov

¹

,

Sneppen

²

2017

Sci Rep

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Determinants of species diversity in microbial ecosystems remain poorly understood. Bacteriophages are believed to increase the diversity by the virtue of Kill-the-Winner infection bias preventing the fastest growing organism from taking over the community. Phage-bacterial ecosystems are traditionally described in terms of the static equilibrium state of Lotka-Volterra equations in which bacterial growth is exactly balanced by losses due to phage predation. Here we consider a more dynamic scenario in which phage infections give rise to abrupt and severe collapses of bacterial populations whenever they become sufficiently large. As a consequence, each bacterial population in our model follows cyclic dynamics of exponential growth interrupted by sudden declines. The total population of all species fluctuates around the carrying capacity of the environment, making these cycles cryptic. While a subset of the slowest growing species in our model is always driven towards extinction, in general the overall ecosystem diversity remains high. The number of surviving species is inversely proportional to the variation in their growth rates but increases with the frequency and severity of phage-induced collapses. Thus counter-intuitively we predict that microbial communities exposed to more violent perturbations should have higher diversity.

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“…To understand the experimentally observed oscillations of cell-length after subjecting the bacteria to Ag + ions, we developed a model based on the predator-prey argument 45,46 . Briefly, we consider a system composed of nutrients ( N ), positive growing components such as active proteins and other cellular products ( P ), and damaging components such as Ag + ions, protein/DNA damages, and reactive oxygen species ( D ).…”

Section: Resultsmentioning

confidence: 99%

Silver ions cause oscillation of bacterial length of Escherichia coli

Krishnamurthi

¹

,

Chen

²

,

Wang

³

2019

Sci Rep

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Silver (Ag) in various forms have recently gained broad interest and been revisited due to their promising antimicrobial effects. Here we report our study on the morphological dynamics of live bacteria when subjected to Ag + ions. Using time-lapse microscopy, we observed oscillations of cell-length for a large fraction of bacteria exposed to 60 μ M of Ag + ions. In addition, we found that the responses of bacteria to Ag + ions were heterogeneous. We quantified the oscillations of cell-length with power spectral density, which appeared different from that of bacteria growing in the absence of Ag + ions. Furthermore, a model similar to the predator-prey argument was developed to understand the observed oscillations of cell-length upon exposure to Ag + ions. This model not only successfully produced the oscillations but also explained the observed heterogeneity in the bacterial responses to Ag + ions.

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“…Scientific RepoRts | 7:39642 | DOI: 10.1038/srep39642 thus distinct from either stable or transient periodic oscillations present in predator-prey ecosystems described by the Lotka-Volterra equations 10,23,24,[28][29][30] . The key assumption used in our study is that larger populations are more exposed to sudden collapses than the smaller populations.…”

Section: Discussionmentioning

confidence: 99%

Population cycles and species diversity in dynamic Kill-the-Winner model of microbial ecosystems

Maslov

¹

,

snepppen²

2016

Preprint

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Determinants of species diversity in microbial ecosystems remain poorly understood. Bacteriophages are believed to increase the diversity by the virtue of Kill-the-Winner infection bias preventing the fastest growing organism from taking over the community. Phage-bacterial ecosystems are traditionally described in terms of the static equilibrium state of Lotka-Volterra equations in which bacterial growth is exactly balanced by losses due to phage predation. Here we consider a more dynamic scenario in which phage infections give rise to abrupt and severe collapses of bacterial populations whenever they become sufficiently large. As a consequence, each bacterial population in our model follows cyclic dynamics of exponential growth interrupted by sudden declines. The total population of all species fluctuates around the carrying capacity of the environment, making these cycles cryptic. While a subset of the slowest growing species in our model is always driven towards extinction, in general the overall ecosystem diversity remains high. The number of surviving species is inversely proportional to the variation in their growth rates but increases with the frequency and severity of phage-induced collapses. Thus counter-intuitively we predict that microbial communities exposed to more violent perturbations should have higher diversity.An important and largely unsolved question in microbial ecology is what determines the diversity of microbial ecosystems. Indeed, unbridled competition between microbes sharing common resources would eventually limit species diversity not to exceed the number of different nutrient types 1 . Predation by bacteriophages introduces the negative frequency-dependent selection 2-5 which offers the possibility for a dramatically larger species diversity 5 . In the classical Kill-the-Winner (KtW) model of Thingstad 5 virulent phages reduce populations of their susceptible hosts to a low steady state level, which is independent of hosts' growth rate thus allowing multiple species per nutrient type. The number of co-existing bacterial species in the resulting ecosystem is determined exclusively by the parameters of phage predation 5 , the topology of the phage-bacterial infection network [6][7][8] , and the carrying capacity of the environment 4,[7][8][9] . Microbial populations are routinely exposed to more dynamics than assumed in the traditional steady state KtW model and its variants. Extended Lotka-Volterra equations for two layer ecosystems of phages and bacteria could predict persistently varying populations 10 , even without considering mutations. In addition, microbial systems are typically exposed to changes in interaction rules and new invading species. For example, in the lab experiments 11 E. coli population suffered a dramatic collapse by a factor ~10 4 -10 5 caused by a T7 phage infection. Collapse-driven dynamics is common in both natural 12 and man-made 13-16 ecosystems in which bacteria are engaged in the continuous arms race with phages [17][18][19][20][21] . Here we propose and ...

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Path-integral calculation for the emergence of rapid evolution from demographic stochasticity

Cited by 19 publications

References 62 publications

Population cycles and species diversity in dynamic Kill-the-Winner model of microbial ecosystems

Population cycles and species diversity in dynamic Kill-the-Winner model of microbial ecosystems

Silver ions cause oscillation of bacterial length of Escherichia coli

Population cycles and species diversity in dynamic Kill-the-Winner model of microbial ecosystems

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