Evolutionary Selection on Transient Dynamical Retention Time in Energy-Coupled Chemical Oscillators

Fourth paper in a series on dynamical rigidity in autocatalytic chemical networks. Papers 1–3 showed that network growth dilutes the activation ratio, that feedback-aligned growth preserves oscillatory viability without increasing attractor dimension, and that timescale separation between fast oscillatory cores and a slow shared energy reservoir transiently inflates the correlation dimension D₂ before phase-locking restores rigidity.

Here we test whether evolutionary selection can act on the duration of that transient exploratory phase. Using the enzyme-complex coupled Brusselator model from Paper 3 with fixed reaction topology, we subject the energy dissipation rate γ to tournament selection for transient retention time τ_{>1.2}, defined as the number of sliding windows with D₂ > 1.2.

With population size 20, 40 generations, and 10 selection plus 10 neutral replicates, forward selection drives mean τ_{>1.2} from 1.22 to 3.39, while neutral drift yields 1.08 (Cohen’s d = 3.7, Mann–Whitney p < 0.0001, Wilcoxon p = 0.001).

The mechanism is a convergent 5.6× reduction in γ, extending slow–fast timescale separation; complete separation between conditions is observed (minimum selection τ_{>1.2} = 2.65, maximum neutral τ_{>1.2} = 2.28).

These results show that simple evolutionary pressure acting on a purely dynamical phenotype can prolong high-dimensional state-space exploration in a prebiotic chemical network without genetic encoding or structural change.

This publication reports the confirmed V2 run (n = 10); the earlier V1 pilot (n = 3, d = 4.9) was published separately.

All simulation scripts, raw data (JSONL), and publication figures are available in the paper4/ directory of the accompanying GitHub repository.