Selection Rules for Species Coexistence in a Hierarchical May-Leonard Model

Abstract

One of the central challenges in evolutionary dynamics is understanding why some species combinations persist while others disappear. Although cyclic-interaction models have provided fundamental insights into biodiversity maintenance, much less is known about how hierarchical competitive interactions shape long-term community organization. Here, we investigate a hierarchical extension of the May-Leonard model, in which species interact through a directed predation chain while undergoing reproduction and mortality. Combining mean-field analysis with Monte Carlo simulations, we show that the fully coexisting state is generically unstable, causing the dynamics to evolve toward lower-dimensional coexistence states. The simulations further reveal stochastic extinctions dominating small populations with the dynamics progressively approaching the mean-field predictions as the system size increases. Rather than permitting arbitrary species combinations, the hierarchical-interaction structure dynamically constrains coexistence by selecting only specific subsets of species for long-term persistence. We show that these admissible coexistence states have a natural graph-theoretic interpretation as independent sets in the hierarchical interaction network, thereby providing general constraints on coexistence in hierarchical communities. Together, these results establish a theoretical framework linking hierarchical interactions, dynamical selection, graph topology, and biodiversity organization, extending the classical May-Leonard model beyond cyclic competition.

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BibTeX RIS

BibTeX

@misc{samanta2026selection,
  title = {{Selection Rules for Species Coexistence in a Hierarchical May-Leonard Model}},
  author = {Rakesh Samanta and Shraosi Dawn and Sk Jahiruddin and Sirshendu Bhattacharyya and Chittaranjan Hens and Sayantan Nag Chowdhury},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09027},
  eprint = {2609.09027},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09027},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Selection Rules for Species Coexistence in a Hierarchical May-Leonard Model
AU  - Rakesh Samanta
AU  - Shraosi Dawn
AU  - Sk Jahiruddin
AU  - Sirshendu Bhattacharyya
AU  - Chittaranjan Hens
AU  - Sayantan Nag Chowdhury
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09027
UR  - https://arxiv.org/abs/2609.09027
AB  - One of the central challenges in evolutionary dynamics is understanding why some species combinations persist while others disappear. Although cyclic-interaction models have provided fundamental insights into biodiversity maintenance, much less is known about how hierarchical competitive interactions shape long-term community organization. Here, we investigate a hierarchical extension of the May-Leonard model, in which species interact through a directed predation chain while undergoing reproduction and mortality. Combining mean-field analysis with Monte Carlo simulations, we show that the fully coexisting state is generically unstable, causing the dynamics to evolve toward lower-dimensional coexistence states. The simulations further reveal stochastic extinctions dominating small populations with the dynamics progressively approaching the mean-field predictions as the system size increases. Rather than permitting arbitrary species combinations, the hierarchical-interaction structure dynamically constrains coexistence by selecting only specific subsets of species for long-term persistence. We show that these admissible coexistence states have a natural graph-theoretic interpretation as independent sets in the hierarchical interaction network, thereby providing general constraints on coexistence in hierarchical communities. Together, these results establish a theoretical framework linking hierarchical interactions, dynamical selection, graph topology, and biodiversity organization, extending the classical May-Leonard model beyond cyclic competition.
ER  -

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