Fitness in time-dependent environments includes a geometric phase contribution

Area of Science:

• Evolutionary biology
• Population dynamics
• Theoretical biology

Background:

• Phenotypic evolution involves the increasing frequency of new genomic sequences.
• The rate of this evolutionary process is influenced by the relative fitness (selection coefficient) of mutants compared to ancestors.
• Understanding fitness in fluctuating environments is crucial for predicting evolutionary trajectories.

Purpose of the Study:

• To investigate how relative fitness is determined in dynamical (changing) environments.
• To explore the relationship between environmental sequences and the speed of evolutionary change.
• To connect evolutionary dynamics to concepts from physical systems.

Main Methods:

• Development and analysis of a simple population dynamics model.
• Mathematical modeling of relative fitness in sequentially varying environments.
• Comparison of dynamic fitness with geometric averages of fitness.

Main Results:

• Relative fitness in dynamical environments is not the geometric average of fitness across environments.
• A novel term in relative fitness explicitly depends on the sequence of environmental changes.
• For slowly varying environments, this term relates to the oriented area enclosed by the environmental trajectory, analogous to geometric phases.

Conclusions:

• Environmental history, not just average conditions, shapes evolutionary speed.
• The findings offer insights into the evolution of complex traits like metabolic functions and stress resistance.
• The study highlights potential parallels between evolutionary dynamics and geometric phases in physics.