Nonlethal Fraction of Virus Population in Evolution Models with Lethal Mutations

Journal of the Physical Society of Japan. 2017. Vol. 86. No. 3. P. 1–5.

Якушкина Т. С., Saakian D.

Lethal mutations are very common in asexual evolution, both in RNA viruses and in the clonal evolution of cancer cells. In a special case of lethal mutations (truncated selection), after a critical total number of mutations the replicator (the virus or the cell) has no offspring. We consider the Eigen and Crow–Kimura models with truncated fitness landscapes, and calculate the fraction of viable replicators (that do have offspring) in the population. We derive a formula for the fraction of the population with nonlethal replicators for the case of a uniform distribution of lethal sequences in the sequence space. We assume that our results can be applied to the origin of life and cancer biology.

Ключевые слова: Hamilton-Jacobi equation, уравнение Гамильтона-Якоби, evolutionary model, fitness-function, evolutionary selection, эволюционная модель, lethal mutations, летальные мутации