{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"institution":[{"name":"bioRxiv"}],"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T15:41:33Z","timestamp":1785426093348,"version":"3.56.0"},"posted":{"date-parts":[[2026,3,21]]},"group-title":"Evolutionary Biology","reference-count":55,"publisher":"openRxiv","license":[{"start":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T00:00:00Z","timestamp":1774051200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"award":["DEB-2040347"],"award-info":[{"award-number":["DEB-2040347"]}],"id":[{"id":"https:\/\/ror.org\/021nxhr62","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000061","name":"Fogarty International Center at the National Institutes of Health","doi-asserted-by":"crossref","award":["R01 TW012704"],"award-info":[{"award-number":["R01 TW012704"]}],"id":[{"id":"10.13039\/100000061","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2026,3,21]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                <jats:p>\n                  Ancestral state reconstruction is a classical problem of broad relevance in phylogenetics. Likelihood-based methods for reconstructing ancestral states under discrete character models, such as Markov models, have proven extremely useful, but only work so long as the assumed model yields a tractable likelihood function. Unfortunately, extending a simple but tractable phylogenetic model to possess new, but biologically realistic, properties often results in an intractable likelihood, preventing its use in standard modeling tasks, including ancestral state reconstruction. The rapid advancement of deep learning offers a potential alternative to likelihood-based inference of ancestral states, particularly for models with intractable likelihoods. In this study, we modify the phylogenetic deep learning software\n                  <jats:sc>phyddle<\/jats:sc>\n                  to conduct ancestral state reconstruction. We evaluate\n                  <jats:sc>phyddle<\/jats:sc>\n                  \u2019s performance under various methodological and modeling conditions, while comparing to Bayesian inference when possible. For simple models and small trees, its performance resembles the performance of Bayesian inference, but worsens as tree size increases. While\n                  <jats:sc>phyddle<\/jats:sc>\n                  still performs adequately for more complex models, such as speciation and extinction models, the estimates differ more from Bayesian inference in comparison with simpler models. Lastly, we use\n                  <jats:sc>phyddle<\/jats:sc>\n                  to infer ancestral states for two empirical datasets, one of the ancestral ranges of a subclade of the genus\n                  <jats:italic>Liolaemus<\/jats:italic>\n                  and ancestral locations for sequences from the 2014 Sierra Leone Ebola virus disease outbreak.\n                <\/jats:p>","DOI":"10.64898\/2026.03.19.712918","type":"posted-content","created":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T04:50:12Z","timestamp":1774155012000},"source":"Crossref","is-referenced-by-count":1,"title":["Ancestral state reconstruction with discrete characters using deep learning"],"prefix":"10.64898","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6067-2800","authenticated-orcid":false,"given":"Anna A.","family":"Nagel","sequence":"first","affiliation":[{"name":"One Brookings Drive, Department of Biology, Washington University in St. Louis, St. Louis, MO 63130, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8672-6966","authenticated-orcid":false,"given":"Michael J.","family":"Landis","sequence":"additional","affiliation":[{"name":"One Brookings Drive, Department of Biology, Washington University in St. Louis, St. Louis, MO 63130, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"54368","reference":[{"key":"2026032420500357000_2026.03.19.712918v1.1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1558-5646.2012.01619.x"},{"key":"2026032420500357000_2026.03.19.712918v1.2","doi-asserted-by":"publisher","DOI":"10.1093\/sysbio\/syw022"},{"key":"2026032420500357000_2026.03.19.712918v1.3","doi-asserted-by":"crossref","first-page":"1640","DOI":"10.1111\/2041-210X.13901","article-title":"Deep learning as a tool for ecology and evolution","volume":"13","year":"2022","journal-title":"Methods in Ecology and Evolution"},{"key":"2026032420500357000_2026.03.19.712918v1.4","first-page":"1","article-title":"BEAST 2.5: An advanced software platform for Bayesian evolutionary analysis","volume":"15","year":"2019","journal-title":"PLOS Computational Biology"},{"key":"2026032420500357000_2026.03.19.712918v1.5","doi-asserted-by":"crossref","first-page":"evaf177","DOI":"10.1093\/gbe\/evaf177","article-title":"Phylogenetic methods meet deep learning","volume":"17","year":"2025","journal-title":"Genome Biology and Evolution"},{"key":"2026032420500357000_2026.03.19.712918v1.6","doi-asserted-by":"crossref","first-page":"e0006161","DOI":"10.1371\/journal.pntd.0006161","article-title":"Unreported cases in the 2014-2016 Ebola epidemic: Spatiotemporal variation, and implications for estimating transmission","volume":"12","year":"2018","journal-title":"PLOS Neglected Tropical Diseases"},{"key":"2026032420500357000_2026.03.19.712918v1.7","doi-asserted-by":"publisher","DOI":"10.1038\/nature22040"},{"key":"2026032420500357000_2026.03.19.712918v1.8","doi-asserted-by":"publisher","DOI":"10.1111\/evo.13657"},{"key":"2026032420500357000_2026.03.19.712918v1.9","doi-asserted-by":"publisher","DOI":"10.1093\/ve\/veac045"},{"key":"2026032420500357000_2026.03.19.712918v1.10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01734359"},{"key":"2026032420500357000_2026.03.19.712918v1.11","doi-asserted-by":"crossref","first-page":"1084","DOI":"10.1111\/j.2041-210X.2012.00234.x","article-title":"Diversitree: Comparative phylogenetic analyses of diversification in R","volume":"3","year":"2012","journal-title":"Methods in Ecology and Evolution"},{"key":"2026032420500357000_2026.03.19.712918v1.12","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177011136"},{"key":"2026032420500357000_2026.03.19.712918v1.13","doi-asserted-by":"publisher","DOI":"10.1111\/j.1558-5646.2012.01730.x"},{"key":"2026032420500357000_2026.03.19.712918v1.14","doi-asserted-by":"publisher","DOI":"10.1093\/sysbio\/syr046"},{"key":"2026032420500357000_2026.03.19.712918v1.15","doi-asserted-by":"publisher","DOI":"10.1093\/sysbio\/syw021"},{"key":"2026032420500357000_2026.03.19.712918v1.16","doi-asserted-by":"publisher","DOI":"10.1016\/j.ympev.2024.108168"},{"key":"2026032420500357000_2026.03.19.712918v1.17","first-page":"1","article-title":"Ancestral reconstruction","volume":"12","year":"2016","journal-title":"PLOS Computational Biology"},{"key":"2026032420500357000_2026.03.19.712918v1.18","first-page":"700","article-title":"A contribution to the mathematical theory of epidemics","volume":"115","year":"1927","journal-title":"Proceedings of the Royal Society of London. 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