{
  "abstract": "Phylogenetic comparative methods for continuous traits, such as phylogenetic generalised least squares, Brownian motion and Ornstein–Uhlenbeck models, Pagel's tree transformations, early-burst and multi-rate models, phylogenetic mixed models and ancestral-state reconstruction, can all be regarded as Gaussian processes on a phylogeny that differ only in their covariance function, or kernel. This link has been noted before, but it has not been developed into a working framework. In the present study, I use it to build, check and compare models of trait evolution. Most classical models share a single branch-wise form of the kernel, which makes it possible to compute likelihoods, leave-one-out and leave-clade-out predictive densities, and predictions at tips and internal nodes in a time that grows linearly with the number of species. A generic implementation in Stan reproduced standard software to numerical precision on 99.6% of simulated data sets, on ultrametric trees, trees with fossil tips and trees with polytomies. To check models, I collect the conditions under which kernels defined on patristic distances are valid. Any non-increasing function is valid on ultrametric trees; however, when fossil tips are included only completely monotone functions (e.g. the exponential) are guaranteed to be valid, and the squared-exponential and Matérn kernels can fail. I also provide a numerical test of whether two kernels imply the same distribution for the tips, which recovers the known equivalence between single-optimum Ornstein–Uhlenbeck and accelerating-rate models on ultrametric trees. To build models, I write four extensions as kernels (i.e. autocorrelated rates, smooth rate-through-time functions, joint phylogenetic and spatial structure, and phylogenetically varying regression slopes), all of which have close precedents in the literature, and I assess their bias, interval coverage, power and false-positive rates by simulation on pure-birth trees and on subtrees of an empirical phylogeny. As an empirical example, I applied the framework to brain–body allometry in 1,349 mammal species, where kernel extensions were compared with simpler explanations (e.g. heavy-tailed residuals and a curved allometric relationship) and validated by leaving out whole orders. All methods are implemented in the R package phylogp. Overall, treating comparative methods as Gaussian processes offers a common and extensible basis both for developing new models of trait evolution and for testing them.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas A Püschel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dwevehevmamek.bib",
  "cited_by": 0,
  "doi": "10.32942/x2d99v",
  "fulltext_url": null,
  "id": "dwevehevmamek",
  "issns": [],
  "landing_url": "https://ecoevorxiv.org/repository/view/15619/",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/legalcode",
  "metadata_licence": null,
  "native_subjects": [
    [
      "bepress",
      "Gaussian process"
    ],
    [
      "bepress",
      "Life Sciences"
    ],
    [
      "bepress",
      "Ornstein–Uhlenbeck"
    ],
    [
      "bepress",
      "brownian motion"
    ],
    [
      "bepress",
      "kernel"
    ],
    [
      "bepress",
      "phylogenetic comparative methods"
    ],
    [
      "openalex",
      "1911|Evolution and Paleontology Studies"
    ]
  ],
  "openalex": "W7223198518",
  "pdf_url": "https://ecoevorxiv.org/repository/object/15619/download/27064/",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dwevehevmamek.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:40Z",
      "native_id": "15619",
      "source": "ecoevorxiv",
      "url": "https://ecoevorxiv.org/repository/view/15619/"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "openalex:1911|Evolution and Paleontology Studies",
      "subfield": "evolutionary-biology"
    }
  ],
  "title": "Gaussian processes on phylogenies: a kernel framework for building, checking and comparing models of trait evolution",
  "title_text": "Gaussian processes on phylogenies: a kernel framework for building, checking and comparing models of trait evolution",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:40Z",
  "url": "https://research.draconitic.com/paper/dwevehevmamek",
  "venue": "EcoEvoRxiv",
  "versions": []
}