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

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.