Table 1.

Reactions for the various metabolisms used in this work.

Metabolism	Birth reactions
Replicase R1	$A\stackrel{s+\beta }{\to }2A$, $\left(A+A\right)\stackrel{s+\beta }{\to }3A$, $B\stackrel{s}{\to }2B$, $\left(A+B\right)\stackrel{s+\beta }{\to }A+2B$
Replicase R2	$A\stackrel{s}{\to }2A$, $\left(A+A\right)\stackrel{s+\beta }{\to }3A$, $B\stackrel{s}{\to }2B$, $\left(A+B\right)\stackrel{s+\beta }{\to }A+2B$
Hypercycle	$A\stackrel{s}{\to }2A$, $\left(A+B\right)\stackrel{s+\beta }{\to }2A+B$, $B\stackrel{s}{\to }2B$, $\left(A+B\right)\stackrel{s+\beta }{\to }A+2B$

While all particles die at the same rate d, birth rates (s in absence of catalyzation) increase under catalyzation (s → s + β), which occurs when a catalyzing particle is within a distance ($\ell$) less than the interaction radius R_int of another particle it has the ability to catalyze. In the replicase models, particle A can catalyze both A and B, but B cannot catalyze A—the difference between R1 and R2 is whether a single A particle can (R1) or cannot (R2) catalyze itself. In the two-member hypercycle shown here, A can catalyze B and B can catalyze A, but A particles cannot catalyze other A particles, nor can B particles catalyze other B particles. In the n-member hypercycle, A particles can only catalyze B particles, B particles can only catalyze C particles, and so on, with the nth member only being able to catalyze A particles.