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Dimensionality-induced critical phase transition in stochastic Lotka-Volterra equation: From statistical averaging to systemic tipping point

  • Xiu-deng Zheng
  • Cong Li
  • Hui Zhang
  • Hui-jie Qiao
  • Shao-peng Wang
  • Yi Tao
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Abstract

By analyzing a stochastic Lotka-Volterra (LV) equation, we show that the underlying logic behind the diversity-stability debate in ecology can be framed as a dimensionality-induced critical phase transition, that is, a transition separating the regime dominated by statistical averaging and a systemic tipping point. This phase transition framework unifies the opposing ecological predictions in the diversity-stability debate and sets an intrinsic diversity ceiling for stochastic ecological communities.

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Cite

BibTeXRIS
BibTeX
@misc{zheng2026dimensionalityinduced,
  title = {{Dimensionality-induced critical phase transition in stochastic Lotka-Volterra equation: From statistical averaging to systemic tipping point}},
  author = {Xiu-deng Zheng and Cong Li and Hui Zhang and Hui-jie Qiao and Shao-peng Wang and Yi Tao},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30655},
  eprint = {2608.30655},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30655},
}
RIS
TY  - UNPB
TI  - Dimensionality-induced critical phase transition in stochastic Lotka-Volterra equation: From statistical averaging to systemic tipping point
AU  - Xiu-deng Zheng
AU  - Cong Li
AU  - Hui Zhang
AU  - Hui-jie Qiao
AU  - Shao-peng Wang
AU  - Yi Tao
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30655
UR  - https://arxiv.org/abs/2608.30655
AB  - By analyzing a stochastic Lotka-Volterra (LV) equation, we show that the underlying logic behind the diversity-stability debate in ecology can be framed as a dimensionality-induced critical phase transition, that is, a transition separating the regime dominated by statistical averaging and a systemic tipping point. This phase transition framework unifies the opposing ecological predictions in the diversity-stability debate and sets an intrinsic diversity ceiling for stochastic ecological communities.
ER  -