Ancestral Lineages in Mutation Selection Equilibria with Moving Optimum.

Area of Science:

• Evolutionary biology
• Population genetics
• Theoretical ecology

Background:

• Populations must adapt to rapid environmental changes for survival.
• Understanding fast evolution requires analyzing individual genealogy and population dynamics.
• Deterministic models are crucial for studying phenotypic density under shifting selection pressures.

Purpose of the Study:

• To investigate the genealogy of individuals in populations adapting to environmental change.
• To model phenotypic density and population dynamics when the fitness optimum moves at a constant speed.
• To analyze ancestral phenotypic lineages and their properties.

Main Methods:

• Utilizing a deterministic model for phenotypic density under a moving fitness optimum.
• Employing the neutral fractions approach to study population dynamics.
• Defining a Markov process for ancestral phenotypic lineage distribution.
• Investigating the asymptotic regime of small mutation effects.

Main Results:

• Demonstrated that typical ancestors in asexual populations possessed traits closer to the fitness optimum than most individuals alive at the same time.
• Derived an explicit formula for typical ancestral lineages in the small mutation effect regime.
• Characterized qualitative and quantitative properties of typical ancestor phenotypes.
• Compared deterministic lineage results with stochastic model lineages.

Conclusions:

• Ancestral lineages provide critical insights into rapid adaptation mechanisms.
• The study offers a framework for understanding evolutionary trajectories under changing environments.
• Deterministic modeling, particularly with Hamilton-Jacobi equations, effectively describes evolutionary dynamics and ancestral properties.