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Environmental spatial and temporal variability and its role in non-favoured mutant dynamics.

Suzan Farhang-Sardroodi1, Amir H Darooneh2,3, Mohammad Kohandel3

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Environmental variability impacts evolution. Temporal randomness can boost or hinder mutant fixation depending on whether division or death rates are affected, while spatial variability consistently increases fixation probability across different models.

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Area of Science:

  • Evolutionary biology
  • Population genetics
  • Mathematical modeling

Background:

  • Environmental variability is crucial for understanding evolutionary dynamics.
  • Population competition is significantly influenced by temporal and spatial heterogeneity.
  • Previous models often simplified environmental conditions, limiting insights into complex evolutionary scenarios.

Purpose of the Study:

  • To investigate the distinct effects of temporal and spatial environmental variability on mutant fixation probability and timing.
  • To analyze these effects across different population structures (circular and complete graphs) and update rules (birth-death and death-birth Moran processes).
  • To explore how variability in division and death rates influences evolutionary outcomes.

Main Methods:

  • Simulations of birth-death (BD) and death-birth (DB) Moran processes on circular and complete graphs.
  • Modeling of temporal and spatial variability in division and/or death rates.
  • Analysis of mutant fixation probability and mean conditional fixation time under varying environmental conditions.

Main Results:

  • Temporal variability shows contrasting effects: randomness in division rates increases fixation probability and time, while randomness in death rates decreases them in well-mixed populations.
  • Spatial restrictions eliminate these effects in some cases, leading to neutral dynamics.
  • Spatial variability consistently increases mutant fixation probability across all considered models (BD/DB, circular/complete graphs, division/death rates).
  • Fixation time is increased by spatial randomness on circular graphs but decreased on complete graphs when division rates are random.

Conclusions:

  • Temporal and spatial environmental variability have fundamentally different impacts on evolutionary dynamics.
  • Spatial variability generally favors mutant expansion, increasing fixation probability.
  • The interplay between population structure, update rules, and the type of environmental variability dictates evolutionary outcomes, with implications for fields like cancer and biofilm research.