Cascade of Complexity in Evolving Predator-Prey Dynamics

We simulate an individual-based model that represents both the phenotype and genome of digital organisms with predator-prey interactions. We show how open-ended growth of complexity arises from the invariance of genetic evolution operators with respect to changes in the complexity, and that the dynamics which emerges is controlled by a non-equilibrium critical point. The mechanism is analogous to the development of the cascade in fluid turbulence.

💡 Research Summary

The paper presents a novel individual‑based simulation that simultaneously models the phenotype and genome of digital organisms engaged in predator‑prey interactions. Its central claim is that open‑ended growth of complexity can be achieved when the genetic operators—mutation and crossover—are invariant with respect to the current level of complexity. In other words, the probability and effect of these operators do not change as genomes become longer or more intricate. This “complexity invariance” eliminates the usual “complexity trap” that halts evolutionary progress in many artificial life models.

The simulated ecosystem consists of two species, predators and prey, moving on a two‑dimensional lattice. Each agent consumes energy, gains it by hunting (predators) or foraging (prey), and reproduces when its energy exceeds a threshold. Reproduction copies the parent’s genome while applying the invariant genetic operators. Because the operators are blind to genome size, offspring can acquire new functional modules without a penalty that would otherwise bias the system toward shorter, simpler genomes.

A key discovery is that when interaction parameters (predator efficiency, resource regeneration rate, mutation rate, etc.) are tuned so that the system hovers near a non‑equilibrium critical point, the distribution of organismal complexity follows a power‑law. This indicates scale‑free behavior: there is no characteristic size of complexity, and structures at all scales coexist. The authors draw a direct analogy to the energy cascade in fluid turbulence, where large eddies transfer kinetic energy to smaller ones. Here, high‑complexity organisms impose selective pressures on lower‑complexity ones, effectively “cascading” informational and energetic advantages down the complexity spectrum.

The dynamics are driven by a feedback loop. As complexity increases, organisms can develop more sophisticated hunting strategies, defensive mechanisms, or sensory processing modules. These capabilities confer a competitive edge, intensifying selection pressure on the opposite species. The heightened pressure, in turn, favors further elaboration of complexity in the responding population. This mutual reinforcement pushes the system toward a state of critical self‑organization, where the evolutionary process remains poised at the edge of chaos and continues to generate novel, increasingly intricate traits indefinitely.

The authors validate the robustness of the mechanism through extensive parameter sweeps. Raising the mutation rate excessively breaks the invariance assumption, leading to a flood of deleterious changes that collapse the cascade. Lowering the mutation rate too much stalls evolution, causing complexity to plateau. Adjusting predator‑prey interaction strength shifts the location of the critical point, confirming that the cascade is contingent on the system being near this non‑equilibrium transition.

In conclusion, the study demonstrates that a combination of complexity‑invariant genetic operators and a predator‑prey driven selection pressure can produce a turbulence‑like cascade of complexity, enabling open‑ended evolution in digital organisms. This framework not only resolves a long‑standing limitation of artificial life simulations but also establishes a conceptual bridge between evolutionary dynamics and physical theories of critical phenomena. The authors suggest future work to compare the model with empirical biological data, incorporate richer environmental variables, and explore applications in designing adaptive artificial intelligence systems.