An intermediate synthesis about the occurrence of the different possible scenari in clonal interference with non-necessarily transitive fitness

We investigate the probability to observe the different scenari when there are two mutations occurring in a resident populations, and when the second mutations occurs during the first phase, i.e. \(\alpha<1/\S_{10}\). We explore the effect of the two sets of parameters, \(\rho_i=\beta_i-\delta_i\) the net individuals reproductive rate of type \(i\), and \(\tilde{C_{ij}}=\frac{C_{ij}}{C_{jj}}\) the ratio between the intra- and inter-type competitive interactions. We assumed the parameters follow different specific distributions, and we drew \(10^6\) different sets of parameters in these distributions. We give hereafter some intermediate results obtained among the \(10^6\) simulations for every cases we investigated, focusing on cases where type 1 and type 2 mutations are favored compared to type 0 mutation when rare (i.e. \(S_{10}>0\) and \(S_{20}>0\)). Results are presented with three different figures. First, we give the proportion of the different scenari we observed among the \(10^6\) simulations. Second, we give the proportion of the cases where we observe either the fixation of type 1 mutation, or type 2 mutation, or the maintenance of polymorphism with types 0 and 1, 0 and 2, 1 and 2 or 0, 1 and 2. Note that in those figures, the “total” curves correspond to the proportion of cases among the \(10^6\) simulations for which type 1 and type 2 mutations are favored compared to type 0 mutation when rare (i.e. \(S_{10}>0\) and \(S_{20}>0\)). Third, we focused on the cases where the type 2 mutations are fixed, and we give the proportion of cases when clonal interference effectively slows down the fixation of type 2 mutation.

\(\rho_{i}\) are drawn in an approximation of the Fisher’s geometrical model and the \(\tilde{C_{ij}}\) are drawn in an uniform distribution

We assumed that \(\rho_0=2\) and that \(\rho_i=\rho_0 + x_i\) with \(x_i\) drawn in a shifted negative Gamma distribution, which is an approximation of a Fisher’s geometric model for adaptation (Martin 2006). We also assumed that \(\tilde{C_{ij}}\) are drawn in a Uniform distribution with parameters \(1-a\) and \(1+a\). When \(a=0\) all \(\tilde{C_{ij}}=1\), and we expect that there are only transitive fitness interactions. We investigated the effect of \(a\). We begin with the case where \(\rho_0\) is supposed to be half the way to optimum in the adaptative landscape.

Proportion of the different scenari as a function of the range of the uniform distribution \(a\)