Introduce ecological interactions into the non-spatial Hash Chemistry model

Develop a mechanism that introduces nontrivial ecological interactions among multisets (higher-order entities) within the non-spatial Hash Chemistry model, which represents evolution as a well-mixed population of multisets undergoing pairwise competitions with hash-based fitness evaluation, so that evolving entities interact ecologically rather than remaining mutually independent.

Background

The paper proposes a non-spatial variant of Hash Chemistry, representing spatial proximity explicitly via multisets of individual entities and modeling evolution through pairwise competitions determined by a hash-based fitness function. This non-spatial model achieves significant speed-ups and exhibits clear unbounded growth in the size of replicating higher-order entities.

However, compared to the original spatial Hash Chemistry, the non-spatial model loses important features: context dependence of fitness and multiscale adaptation. Because evolving entities in the non-spatial model do not interact ecologically, evolution reduces to independent refinement of fitness values of multisets. The authors explicitly identify the introduction of nontrivial ecological interactions into this non-spatial framework as an open question.