Fig. 3

Steady state evolutionary outcomes of TF duplication. a Left: evolutionary macrostates (see text) depicted graphically as network phenotypes with solid (dashed) lines indicating strong (weak) TF–BS interactions. Red and green squares in the TFs represent the corresponding signal sensing domains. Right: input–output table, where columns represent the presence of either (red or green) external signal and rows represent the resulting gene activation for each phenotype. b (Top) Distribution of fitness values across genotypes in each macrostate (color-coded as in a), shown as violin plots, for two values of signal correlation, ρ. Black dots = median fitness in the macrostate. (Bottom) The number of genotypes in each macrostate (logarithmic scale). c Most probable outcome of gene duplication in steady state (color-coded as in a), as a function of selection strength, Ns, and the correlation between two external signals, ρ. d Free fitness \(\hat F\) (at Ns = 25) for different macrostates as a function of correlation between signals, ρ: for most macrostates, free fitness increases with signal correlation, except for ‘No regulation’, which is naturally unaffected by it, and ‘Specialize Both’, which dominates for low correlation values. e The dominant macrostate (as in c), as a function of the signal frequencies, f ₁, f ₂, and the signal correlation, ρ, at fixed Ns = 25. For simplicity we plot only cases where f ₁ = f ₂. Signals in the hashed region are mathematically impossible. f Steady state distributions for mismatches (P _SS(k _ij | σ ₁ = 10, σ ₂ = 01), upper row) and the match between the two TF consensus sequences (P _SS(M | σ ₁ = 10, σ ₂ = 01), lower left), under strong selection (red; at baseline parameters denoted by the red cross in c) and neutrality (blue; Bernoulli distributions). Comparison between analytical calculation and 400 replicates of the stochastic simulation (lower right). Here and in subsequent figures, baseline parameter values are L = 5, \(\epsilon \) = 3, r _S = r _TF = 1