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Population and Single-Cell Analysis of Antibiotic Persistence in Escherichia coli
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Persistence probabilities for stream populations.

Yasmine Samia1, Frithjof Lutscher

  • 1Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N6N5, Canada.

Bulletin of Mathematical Biology
|April 25, 2012
PubMed
Summary
This summary is machine-generated.

Populations in rivers face washout risks. A new stochastic model shows a smooth transition to extinction with increasing flow, unlike deterministic models, and explores how flow variations impact persistence.

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Area of Science:

  • Ecology and Evolutionary Biology
  • Mathematical Biology
  • Environmental Science

Background:

  • Organisms in flowing waters (streams, rivers) are susceptible to downstream displacement and population loss.
  • Previous modeling efforts often used deterministic approaches to study population persistence in advective environments.
  • Deterministic models predict a critical flow velocity threshold beyond which populations cannot survive.

Purpose of the Study:

  • To develop and analyze a stochastic model for population persistence in riverine environments.
  • To investigate the transition from population persistence to extinction under varying advection velocities.
  • To examine the influence of temporal variations in environmental parameters on population persistence probability.

Main Methods:

  • Employed a stochastic approach using the dominant eigenvalue of the advection-diffusion operator.
  • Transformed a spatially explicit model into a spatially implicit birth-death process.
  • Incorporated individual washout as an additional death term within the birth-death process.

Main Results:

  • The study identified a smooth transition from near-certain persistence to extinction as advection velocity increases, replacing the sharp threshold predicted by deterministic models.
  • Temporal variations in flow rate and other parameters were found to generally decrease population persistence probability.
  • Specific scenarios were identified where temporal variation can paradoxically enhance population persistence.

Conclusions:

  • Stochastic modeling provides a more nuanced understanding of population dynamics in advective environments compared to deterministic approaches.
  • Flow variability plays a critical role in population persistence, with both detrimental and potentially beneficial effects.
  • The findings have implications for conservation and management strategies for riverine ecosystems.