{
  "annotation_id": "19ebe9d1-4fcb-48ba-bc4e-0f69a2e9f56f",
  "date_created": "2026-02-17T05:53:24.169000Z",
  "date_modified": "2026-02-17T05:53:24.169000Z",
  "file_hash": "cd1fc0cc32dbab1aa9a3740c2f2a8e800f0983a416c79b79e48e90e1f24fe3f3",
  "private": false,
  "record": {
    "abstract": "In this paper, we study the absorption and fixation times for evolutionary processes on graphs, under different updating rules. While in Moran process a single neighbour is randomly chosen to be replaced, in proliferation processes other neighbours can be replaced using Bernoulli or binomial draws depending on $0 \u003c p \\leq 1$. There is a critical value $p_c$ such that the proliferation is advantageous or disadvantageous in terms of fixation probability depending on whether $p \u003e p_c$ or $p \u003c p_c$.\n  We clarify the role of symmetries for computing the fixation time in Moran process. We show that the Maruyama-Kimura symmetry depend on the graph structure induced in each state, implying asymmetry for all graphs except cliques and cycles. There is a fitness value, not necessarily $1$, beyond which the fixation time decreases monotonically.\n  We apply Harris\u0027 graphical method to prove that the fixation time decreases monotonically depending on $p$. Thus there exists another value $p_t$ for which the proliferation is advantageous or disadvantageous in terms of time. However, at the critical level $p=p_c$, the proliferation is highly advantageous when $r \\to +\\infty$.",
    "arxiv_id": "2601.09737",
    "authors": [
      "Fernando Alcalde Cuesta",
      "Gustavo Guerberoff",
      "\u00c1lvaro Lozano Rojo"
    ],
    "categories": [
      "q-bio.PE",
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Absorption and fixation times for evolutionary processes on graphs",
    "url": "https://arxiv.org/abs/2601.09737",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f61ce034-6d01-405e-8975-d364bbcd07e9",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}