{
  "abstract": "We extend the ``Brownian bees'' model of Berestycki et al.\\ (2021, 2022) to cooperative reproduction, $kA\\to(k{+}1)A$, of a population of $N$ symmetric random walkers with removal, at each birth event, of the particle farthest from the origin. Working in the limit $N\\to\\infty$, we formulate a hydrodynamic free-boundary problem for this model. Using this formalism, we determine steady state population densities for all~$k$ and prove their linear stability for $k\\le 2$ and instability for $k\\ge 4$. In the marginal case $k=3$, there is a whole continuous family of steady states at a single critical ratio of the reproduction and diffusion rates. Above criticality the population undergoes an asymptotically self-similar finite-time collapse to the origin. Below the criticality the population spreads diffusively, but the reproduction remains quantitatively relevant. For $k\\ge 4$, the unstable steady state separates regimes of a finite-time collapse and diffusive spreading. Here the collapse dynamics is asymptotically self-similar, and the population density exhibits a scale separation requiring a matched-asymptotic description. Our analytical predictions are confirmed by numerical solutions of the hydrodynamic free-boundary problem and by Monte Carlo simulations of the original microscopic model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.29958",
  "author_total": 2,
  "authors": [
    {
      "name": "Ohad Vilk"
    },
    {
      "name": "Baruch Meerson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cwm7nczqja2vs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.29958",
  "fulltext_url": null,
  "id": "cwm7nczqja2vs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.29958",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "nlin.PS"
    ],
    [
      "arxiv",
      "q-bio.PE"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.29958",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cwm7nczqja2vs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2605.29958",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.29958"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Lattice Brownian bees with cooperative reproduction: steady states, collapse, and spreading",
  "title_text": "Lattice Brownian bees with cooperative reproduction: steady states, collapse, and spreading",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/cwm7nczqja2vs",
  "venue": "arXiv",
  "versions": []
}