Selection Dynamics in Transient Compartmentalization

Transient compartments have been recently shown to be able to maintain functional replicators in the context of prebiotic studies. Here, we show that a broad class of selection dynamics is able to achieve this goal. We identify two key parameters, the relative amplification of nonactive replicators (parasites) and the size of compartments. These parameters account for competition and diversity, and the results are relevant to similar multilevel selection problems, such as those found in virus-host ecology and trait group selection.

Figure 1

Contour plots of $\mathrm{\Delta }x$ for four values of $\mathrm{\Lambda }=1$, 2.5, 4, and 1000 in the plane ($x$, $\lambda$), with red (respectively, blue) regions corresponding to $\mathrm{\Delta }x>0$ (respectively, $\mathrm{\Delta }x<0$).

Figure 2

Phase diagram of the transient compartmentalization dynamics with the selection function of Eq. (3) in the ($\lambda$, $\mathrm{\Lambda }$) plane. The phases are $R$, pure ribozyme; $B$, bistable; $C$, coexistence; and $P$, pure parasite.

Figure 3

Evolution of the average ribozyme fraction $x$ as a function of the number of rounds for the three protocols, namely, (i) no compartments (bulk behavior), (ii) compartments with no selection, and (iii) compartments with selection. We choose $\lambda =5$ and $\mathrm{\Lambda }=10$, corresponding to the coexistence region of Fig. 2.

Figure 4

Evolution of the distributions of ribozyme fraction $\overline{x}(n,m)$ before and after selection at different times. The chosen times are shown as red circles in the lower right panel, which represents the evolution of the average fraction $x$ as a function of the number of selection rounds.