Self-loops in evolutionary graph theory: Friends or foes?
Fig 2
(A) We mostly work with these five graphs throughout the manuscript. (B) The steady-state average fitnesses obtained using the Moran Birth-death mutation-selection dynamics simulations for the self-looped (weighted) star graph, an amplifier of selection, the star graph, a suppressor of fixation, the self-looped directed line, a suppressor of selection, the cycle graph, an isothermal graph, and the complete graph are shown via circles as a function of mutation rates. Solid horizontal lines represent steady-state average fitnesses for different graphs obtained under the low mutation rate approximation, Eq 1. The arrows mark the mutation rates beyond which the low mutation rate approximation is violated for respective graphs. The graphs with higher average fixation time is expected to deviate earlier, see Eq 4. (C) The average fixation time scaling with N at neutrality is shown for different graphs. Solid lines are the analytical results whereas circles represent Moran Bd simulations. For larger N, it gets computationally expensive to work with microscopic Moran Bd simulations, in such cases we use a Gillespie algorithm, shown via triangles. For details on the Gillespie algorithm, refer to App. 5.3.3. (D) The scaling of the average fixation time with population size N for the different graphs. (Parameters: (B) population size, N = 10, uniform mutant fitness distribution, i.e., , (B,C) with 2000 total number of independent realisations used for averaging, fmin = 0.1 and fmax = 10).