{
  "annotation_id": "f7f3b006-d110-4b9e-b8fe-e2c52ca7c6d4",
  "date_created": "2026-03-02T18:01:35.573000Z",
  "date_modified": "2026-03-02T18:01:35.573000Z",
  "file_hash": "c1e2beeafc6ea58b3698412b544ff6be98d24229af889477297d9b3c51e92348",
  "private": false,
  "record": {
    "abstract": "The FKPP equation with a variable growth rate and advection by an\nincompressible velocity field is considered as a model for plankton dispersed\nby ocean currents. If the average growth rate is negative then the model has a\nsurvival-extinction transition; the location of this transition in the\nparameter space is constrained using variational arguments and delimited by\nsimulations. The statistical steady state reached when the system is in the\nsurvival region of parameter space is characterized by integral constraints and\nupper and lower bounds on the biomass and productivity that follow from\nvariational arguments and direct inequalities. In the limit of\nzero-decorrelation time the velocity field is shown to act as Fickian diffusion\nwith an eddy diffusivity much larger than the molecular diffusivity and this\nallows a one-dimensional model to predict the biomass, productivity and\nextinction transitions. All results are illustrated with a simple growth and\nstirring model.",
    "arxiv_id": "q-bio/0703039",
    "authors": [
      "Daniel A. Birch",
      "Yue-Kin Tsang",
      "William R. Young"
    ],
    "categories": [
      "q-bio.PE",
      "nlin.CD",
      "physics.chem-ph"
    ],
    "doi": "10.1103/PhysRevE.75.066304",
    "journal_ref": "Physical Review E 75, 066304 (2007)",
    "title": "Bounding biomass in the Fisher equation",
    "url": "https://arxiv.org/abs/q-bio/0703039"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "521b8b37-6fda-4db4-915f-768e0dc2ba21",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}