polymorphism in molecular evolution.

Here, we study the mutual interference of two advantageous mutants that are each initially present in only a single organism. We derive a phenomenological description of the mutants’ fixation probabilities in the interference regime. This phenomenological description, which is in essence an interpolation between limiting cases that can be described with standard theory, agrees very well with numerical simulations. We also find that the expected fitness increase of the population is maximized if the mutant with higher selective advantage arrives earlier, even though this order of appearance leads, on average, to fewer mutants that go to fixation.

Model
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We consider three distinct sequence types: wild type, advantageous mutant 1, and advantageous mutant 2, with fitness values 1, $1+s_1$, and $1+s_2$, respectively. Thus, $s_{1}$ denotes the selective advantage of mutants of type $1$, and $s_{2}$ is the selective advantage of mutants of type $2$. For simplicity, we assume that $s_{2} > s_{1}$. Initially, the population is homogeneous and consists of the wild type only. Then, one randomly chosen wild type individual is replaced by an advantageous mutant of either type, and some $\Delta t$ generations later, another randomly chosen individual of the population (either wild type 