{
  "abstract": "We study the evolution of cooperation in a finite haploid population whose individuals carry both a strategy and a phenotype on a finite periodic space. Cooperators help with a probability that decays exponentially with phenotypic distance, generating graded phenotype-dependent assortment. Under weak selection and a large-population mutation scaling, we combine coalescent arguments with the spectral representation of a random walk on the discrete torus to derive an explicit benefit-to-cost threshold for cooperation to be favored in stationary abundance. Stronger phenotypic discrimination and higher phenotype-space dimension strictly lower this threshold, whereas strategy mutation raises it. In contrast, phenotype mutation has a nonmonotone effect: the threshold diverges for both very rare and very rapid phenotype mutation and therefore attains at least one minimum at an intermediate rate. The high-mutation inhibition results from mixing on the finite phenotype space and distinguishes the periodic model from its unbounded-lattice counterpart.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phyical Review E (2026)",
  "arxiv": "2608.21872",
  "author_total": 1,
  "authors": [
    {
      "name": "Dhaker Kroumi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aqz430a1pgv5p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.21872",
  "fulltext_url": null,
  "id": "aqz430a1pgv5p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.21872",
  "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",
      "q-bio.PE"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.21872",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aqz430a1pgv5p.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:38Z",
      "native_id": "2608.21872",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.21872"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    }
  ],
  "title": "Phenotypic Assortment and the Evolution of Cooperation in Finite Periodic Phenotype Spaces",
  "title_text": "Phenotypic Assortment and the Evolution of Cooperation in Finite Periodic Phenotype Spaces",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:38Z",
  "url": "https://research.draconitic.com/paper/aqz430a1pgv5p",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/7pzd-gtdv",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}