New versions of evolutionary models with lethal mutations

In this paper, the impact of lethal mutations on evolutionary dynamics of asexual populations is analyzed. We suggest distinguishing different definitions of lethality, which lead to different mathematical formalizations of the microscopic model. Most of the studies focus on polyphasic lethality, meaning that individuals carrying lethal mutations have no offspring but consume common resources. In an alternative problem setting, monophasic lethal mutants die without giving offspring on the first stage of development. In the third case, semi-lethal mutations are considered when the lethal mutants survive with some probability. We suggest and investigate mathematical models for these cases, deriving the evolutionary characteristics of the steady state. We found that the peak sequence probability drastically depends on the version of lethality. The results obtained here can be used to solve the error threshold paradox at the origin of life.