{
  "abstract": "Single-cell time-lapse microscopy now provides high-resolution size trajectories for thousands of individual cells, yet principled methods for simultaneously learning the functional form of growth laws and the distribution of cell-to-cell physiological variability remain limited. We present a data-driven framework based on the recent Weak-form Estimation of Nonlinear Dynamics (WENDy) algorithm to (i) select the best supported growth law from a set of candidate laws, and (ii) recover individual-level growth parameters via empirical Bayes shrinkage within a random-effects model. We demonstrate the approach on both synthetic individual size data incorporating commonly found growth laws and recorded real size trajectories, showing that the method accurately recovers both growth-law structure and parameter heterogeneity at reasonable noise levels. We finally end with a discussion on how the results obtained by the method here can be upscaled to the population level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31955",
  "author_total": 3,
  "authors": [
    {
      "name": "Rainey Lyons"
    },
    {
      "name": "Vanja Dukic"
    },
    {
      "name": "David M Bortz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/99hyhjdevy60g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31955",
  "fulltext_url": null,
  "id": "99hyhjdevy60g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31955",
  "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",
      "1312|Gene Regulatory Network Analysis"
    ]
  ],
  "openalex": "W7214714594",
  "pdf_url": "https://arxiv.org/pdf/2609.31955",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/99hyhjdevy60g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:21Z",
      "native_id": "2609.31955",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31955"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    }
  ],
  "title": "From Individual Trajectories to Population Densities: Weak-Form Inference of Heterogeneous Growth Laws",
  "title_text": "From Individual Trajectories to Population Densities: Weak-Form Inference of Heterogeneous Growth Laws",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:21Z",
  "url": "https://research.draconitic.com/paper/99hyhjdevy60g",
  "venue": "arXiv",
  "versions": []
}