{
  "annotation_id": "8688fc59-aad3-4411-88a3-f0faf072974f",
  "date_created": "2026-03-02T18:01:35.765000Z",
  "date_modified": "2026-03-02T18:01:35.765000Z",
  "file_hash": "f151c4bb3a65c81b52f659e4312ee9e9d1053703d56a895fed9ff45cd61e7f55",
  "private": false,
  "record": {
    "abstract": "Mathematical theory of selection systems is developed for a wide class of\ndynamical models of inhomogeneous populations with discrete time. The Price\nequation and its particular case, the Fisher Fundamental theorem of natural\nselection (FTNS), are well known general results of the theory. It is known\nthat the Price equation being a mathematical identity is not dynamically\nsufficient, i.e., it does not allow one to predict changes in the mean of a\ntrait beyond the immediate response if only the value of covariance of the\ntrait and fitness at this moment is known. We show that the problem of\ndynamically insufficiency for the Price equations and for the FTNS can be\ncorrectly overcome if to study these equations subject to given initial\ndistribution in framework of exact models of the population dynamics. The\nknowledge of the entire distribution at any given instant allows making the\nexact prediction for indefinite time and this prediction dramatically depends\non the initial distribution. For these models, the current trait distribution\nand hence all statistical characteristics of interest, such as mean values of\nthe fitness or any trait could be computed effectively at any time moment.",
    "arxiv_id": "q-bio/0606001",
    "authors": [
      "Georgy P. Karev"
    ],
    "categories": [
      "q-bio.PE",
      "q-bio.QM"
    ],
    "title": "On Mathematical Theory of Selection: Discrete-Time Models",
    "url": "https://arxiv.org/abs/q-bio/0606001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "df4600b5-26fb-4f45-9ce4-c8252201c4c6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}