Paper List

期刊: ArXiv Preprint
发布日期: 2026-03-11
Complex SystemsTheoretical Biology

Macroscopic Dominance from Microscopic Extremes: Symmetry Breaking in Spatial Competition

Department of Mathematics, Florida State University | Department of Mathematics and Statistics, Cleveland State University | Institute of Molecular Biophysics, Florida State University

Stuti Guha, Shawn D. Ryan, Bhargav R. Karamched
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IN SHORT: This paper addresses the fundamental question of how microscopic stochastic advantages in spatial exploration translate into macroscopic resource dominance, revealing that initial discovery and final monopolization are governed by distinct physical mechanisms.

核心创新

  • Methodology Introduces a dimensionless scaling parameter χ = (N₂/N₁)8^(d₁-d₂) that completely determines competitive symmetry, showing that a linear spatial disadvantage requires an exponential population advantage to overcome.
  • Theory Demonstrates that extreme first-passage statistics govern initial discovery, while non-reciprocal interaction bias (β) controls the sharpness of the competitive phase transition and stability of the absorbing state.
  • Biology Reveals a strict hierarchy of symmetry-breaking factors: proximity to resource > population size > interaction bias, with β being necessary but not sufficient for dominance.

主要结论

  • Proximity imparts the strongest competitive advantage: a colony with distance d₁ < d₂ requires N₂/N₁ ~ 8^(d₂-d₁) ants to compensate (Equation 3).
  • The interaction bias β acts as a phase transition tuner: for β → 0, outcomes remain probabilistic; for large β, the symmetry-breaking boundary sharpens into a step function (Figure 3).
  • Discovery and monopolization are decoupled: extreme first-passage statistics govern initial finding (⟨T_i⟩ = d_i + (1-p_i)^(N_i)), while β strictly controls stability of the absorbing state.
研究空白： Classical ecological models based on deterministic mass-action kinetics fail to capture the stochastic nature of spatial exploration and the separation between discovery dynamics and resource monopolization.

摘要: How do competing populations convert a spatial advantage into macroscopic dominance? We introduce a stochastic model for resource competition that decouples the transient discovery phase from monopolization. Initial symmetry breaking is governed by extreme value statistics of first-passage times: a linear spatial disadvantage requires an exponentially larger population to overcome. However, transient superiority cannot stabilize dominance. A non-reciprocal interaction bias is strictly necessary to arrest local fluctuations and drive the system into a robust absorbing state.