Evolution models with lethal mutations on symmetric or random fitness landscapes

Area of Science:

• Evolutionary Biology
• Population Genetics
• Mathematical Biology

Background:

• Understanding mean fitness is crucial for modeling evolutionary processes.
• Existing models often simplify fitness landscapes, necessitating more nuanced approaches.
• The behavior of fitness in biological systems, particularly for RNA viruses, can be complex.

Purpose of the Study:

• To calculate the mean fitness for specific evolution models.
• To analyze models where fitness is a function of Hamming distance and subject to probabilistic nullification or divergence to negative infinity.
• To compute mean fitness for random fitness landscapes described by a log-normal distribution.

Main Methods:

• Analytical calculation of mean fitness.
• Modeling fitness as a function of Hamming distance from a reference sequence.
• Incorporating probabilistic fitness nullification (Eigen model) and tending to negative infinity (Crow-Kimura model).
• Applying log-normal distribution to model random fitnesses.

Main Results:

• Derived mean fitness values for the specified Eigen and Crow-Kimura model cases.
• Calculated mean fitness for random fitness landscapes with log-normal distribution.
• Quantified evolutionary dynamics under different fitness function assumptions.

Conclusions:

• The study provides a quantitative framework for mean fitness in complex evolutionary scenarios.
• The findings are applicable to understanding the evolution of RNA viruses and other systems with non-uniform fitness landscapes.
• This work contributes to theoretical population genetics by extending mean fitness calculations to diverse models.