Figure 1.
Modularity increases after selection for a new additional gene activity pattern.
(A) Activity patterns I and II share the activity state of genes 0–4 and differ in that of genes 5–9. Black and white squares represent inactive and active genes, respectively. (B,C) The horizontal axes indicate mean modularity after selection for I. The vertical axes show modularity in networks after selection for both I and II. Specifically, (B) shows modularity of the network with highest fitness, and (C) shows mean population modularity. Points above the identity line (solid diagonal) show populations in which modularity increases after selection for the second activity pattern. The length of bars indicates one standard deviation. Plots show results for 200 evolving populations. (D,E) Nodes filled with the same color represent genes that lie in the same module. Black edges represent interactions between genes in different modules. (D) Network with the highest fitness in a population after selection for I. The Newman algorithm [33] partitions this network into sets in which genes 0–4 and 5–9 are intermingled. This network has a non-normalized modularity of 0.18, and a normalized modularity equal to −0.1. (E) Network with the highest fitness in a population after selection for I and II. This network is partitioned into modules in which genes with shared (genes 0–4) and different (genes 5–9) activity states in I and II lie apart. This network has a non-normalized modularity of 0.39, and a normalized modularity equal to 0.7.
Figure 2.
Modularity increase is not transient when selecting for a second additional gene activity pattern.
Modularity in the best adapted networks reaches a plateau that is maintained for, at least, 10,000 generations when selected to attain gene activity patterns I and II. Such plateau is significantly higher than that of networks selected to attain only activity pattern I. The length of bars represents one standard error. The plot shows results for 100 evolving populations in each selection regime.
Figure 3.
Networks become partitioned according to genes with shared and non-shared activity states.
(A) represents the frequency at which two specific genes whose activity is the same in I and II occur within the same module.
stands for the frequency at which two specific genes with non-shared activity states that change in a concerted manner occur within the same module.
represents the frequency with which two genes, one with a shared activity state and the other with a different activity state in I and II, are in the same module. (B) As selection for activity patterns I and II starts,
and
increase but
decreases. The plot shows results for 300 evolving populations.
Figure 4.
Modularity increases further after selection for a third activity pattern III.
(A) Gene activity patterns I, II and III. White squares represent active genes and black squares represent inactive genes. Background color distinguishes genes that change their activity state in a concerted manner across all selected patterns. Notice that, in this case, the inclusion of additional activity patterns results in more and smaller groups of genes whose activity changes concertedly. (B) The horizontal axis indicates modularity of the best adapted networks after selection for I and II. The vertical axis shows modularity of the best adapted networks after an additional 3000 generations of selection for I, II and III. Wilcoxon signed-rank test; ;
. The plot shows results for 100 evolving populations.
Figure 5.
Maximal fitness increases faster when co-option of existing gene activity states is possible.
(A,B) Black and white squares represent inactive and active genes, respectively. (A) Networks first attained activity patterns I, II and III after 3,000 generations of evolution. The selection regime promotes the evolution of modules containing genes 0–4 on one hand, and genes 5–9 on the other. (B) After 3,000 generations, selection favored gene activity pattern IV, which is a combination of activity patterns matching those of previously evolved modules, as indicated by the background colors. (C) Networks selected to attain a fourth activity pattern increase their fitness much faster if this pattern is IV, than if it is a randomly chosen activity pattern. The length of bars indicates one standard error.