Fig. 5. Selection and evolution in assembly space.

a, Assembly processes with and without selection. The selection process is defined by a transition from undirected to directed exploration. The parameter $\alpha$ represents the selectivity of the assembly process ($\alpha =1$: undirected/random expansion, $\alpha <1$: directed expansion). Undirected exploration leads to the fast homogeneous expansion of discovered objects in the assembly space, whereas directed exploration leads to a process that is more like a depth-first search. Here, ${\tau }_{\mathrm{d}}$ is the characteristic timescale of discovery, determining the growth of the expansion front, and ${\tau }_{\mathrm{p}}$ is the characteristic timescale of production that determines the rate of formation of objects (increasing copy number). b, Rate of discovery of unique objects at assembly $a+1$ versus number of objects at assembly $a$. The transition of $\alpha =1$ to $\alpha <1$ represents the emergence of selectivity limiting the discovery of new objects. c, Phase space defined by the production (${\tau }_{\mathrm{p}}$) and discovery (${\tau }_{\mathrm{d}}$) timescales. The figure shows three different regimes: (1) ${\tau }_{\mathrm{d}}\ll {\tau }_{\mathrm{p}}$, (2) ${\tau }_{\mathrm{d}}\gg {\tau }_{\mathrm{p}}$, and (3) ${\tau }_{\mathrm{d}}\approx {\tau }_{\mathrm{p}}$. Selection is unlikely to emerge in regimes 1 and 2, and is possible in regime 3.