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Higher-Order Competition as a Minimal Mechanism for Spatial Pattern Diversity in Population Dynamics

  • David Pinto-Ramos
  • Anudeep Surendran
  • Ricardo Martinez-Garcia
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Abstract

We show that negative feedback alone generates the diversity of self-organized shapes usually attributed to scale-dependent activation-inhibition. For a broad class of kernels, pairwise competition models only generate hexagonal spot arrays. Higher-order terms eliminate this restriction and promote stripes and gaps. Combining individual-based simulations and nonlinear analysis, we derive the pattern-selection thresholds and construct the full state diagram, including an unusual spots-stripes-spots sequence. Spot patterns are thus not a reliable indicator of proximity to a tipping point.

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Cite

BibTeXRIS
BibTeX
@misc{pintoramos2026higherorder,
  title = {{Higher-Order Competition as a Minimal Mechanism for Spatial Pattern Diversity in Population Dynamics}},
  author = {David Pinto-Ramos and Anudeep Surendran and Ricardo Martinez-Garcia},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29725},
  eprint = {2609.29725},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29725},
}
RIS
TY  - UNPB
TI  - Higher-Order Competition as a Minimal Mechanism for Spatial Pattern Diversity in Population Dynamics
AU  - David Pinto-Ramos
AU  - Anudeep Surendran
AU  - Ricardo Martinez-Garcia
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29725
UR  - https://arxiv.org/abs/2609.29725
AB  - We show that negative feedback alone generates the diversity of self-organized shapes usually attributed to scale-dependent activation-inhibition. For a broad class of kernels, pairwise competition models only generate hexagonal spot arrays. Higher-order terms eliminate this restriction and promote stripes and gaps. Combining individual-based simulations and nonlinear analysis, we derive the pattern-selection thresholds and construct the full state diagram, including an unusual spots-stripes-spots sequence. Spot patterns are thus not a reliable indicator of proximity to a tipping point.
ER  -