Radial Interaction Tomography: Recognizing Non-Transitive Evolutionary Games from One Range-Expansion Image

2026-06-30

AI Summary

This work proposes a radial interaction tomography framework to infer non-transitive evolutionary game dynamics from a single endpoint image of radially expanding microbial colonies and to assess whether these interactions conform to a scalar fitness hierarchy. By applying a log-polar coordinate transform, sector boundaries are converted into geometric signals, enabling the formulation of an inverse problem to reconstruct pairwise boundary flow fields indexed by radius. The approach integrates weighted transitive/cyclic decomposition, exact Gaussian cyclicity tests, and Bonferroni-corrected interval scanning for rigorous analysis. The framework establishes theoretical guarantees on endpoint observability and stability, successfully detects cyclic residuals across four mechanistic classes, and supports downstream applications including reaction–diffusion control, phenotypic front optimization, and protocol synthesis.

Abstract

Colored sectors in a microbial range expansion encode more than lineage survival counts. We formulate a computer-vision inverse problem: from one endpoint image of an accretive multi-type expansion, recover the radius-indexed pairwise boundary-flow field and test whether the visual pattern is compatible with a transitive scalar fitness hierarchy. The observable is a geometric signal extracted from sector-boundary curves in log-polar coordinates. We prove endpoint observability and stability for frozen fronts, weighted transitive/cyclic decomposition, contact-complete circular design, physical-clock and mechanism non-identifiability, exact Gaussian cyclicity testing, and Bonferroni-valid interval scanning. The benchmark is deterministic: analytic endpoint images, blurred/noisy pixel round trips, scalar-null stress tests, public-image tracing, multi-resolution mechanistic endpoints, and a non-learning frozen-front simulator. The implementation recovers pairwise edge-flow histories from endpoint images, detects cyclic residuals in a mechanistic four-type expansion, and uses those residuals as forcing signals for a dimensionless active design-control layer covering reaction-diffusion control, phenotype-frontier optimization, protocol synthesis, Monte Carlo robustness, and a downstream population-state bridge.

Problem

• non-transitive evolutionary games
• range expansion
• sector boundaries
• fitness hierarchy
• inverse problem

Innovation

• Radial Interaction Tomography
• non-transitive evolutionary games
• sector-boundary analysis
• endpoint observability
• cyclicity detection