Self-loops in evolutionary graph theory: Friends or foes?
Fig 3
Reference graph: Complete graph with self-loops.
Here, the mutation-selection dynamics is studied for the self-looped complete graph with μ → 1. We find a very good agreement for the steady-state statistics between the analytics and the simulations. The thick line represents the analytical average fitness, while the shaded grey area represents the standard deviation around the average. Symbols and error bars show simulations. In the steady-state, on average the self-looped complete graph attains the midpoint of the fitness domain, as the fitness dynamics for each individual node of the population becomes uncorrelated in the fitness space and time. The steady-state average fitness is also independent of the population size. The fluctuations in the steady-state however depends on the population size and decreases with the increase in population size as (Parameters: fmin = 0.1, fmax = 10, number of independent realisations is equal to 2000, mutant fitness distribution, ζ(f′, f) = 1/(fmax − fmin)).