{"publication_status":"published","doi":"10.1086/734083","pmid":1,"day":"01","year":"2025","issue":"4","_id":"20056","abstract":[{"lang":"eng","text":"Theoretical studies have shown that stochasticity can affect the dynamics of ecosystems in counterintuitive ways. However, without knowing the equations governing the dynamics of populations or ecosystems, it is difficult to ascertain the role of stochasticity in real datasets. Therefore, the inverse problem of inferring the governing stochastic equations from datasets is important. Here, we present an equation discovery methodology that takes time series data of state variables as input and outputs a stochastic differential equation. We achieve this by combining traditional approaches from stochastic calculus with the equation discovery techniques. We demonstrate the generality of the method via several applications. First, we deliberately choose various stochastic models with fundamentally different governing equations, yet they produce nearly identical steady-state distributions. We show that we can recover the correct underlying equations, and thus infer the structure of their stability, accurately from the analysis of time series data alone. We demonstrate our method on two real-world datasets—fish schooling and single-cell migration—that have vastly different spatiotemporal scales and dynamics. We illustrate various limitations and potential pitfalls of the method and how to overcome them via diagnostic measures. Finally, we provide our open-source code via a package named PyDaDDy (Python Library for Data-Driven Dynamics)."}],"acknowledgement":"V.G. acknowledges support from the Science and Engi-neering Research Board, Department of Biotechnology,and the Indo-French Centre for the Promotion of Ad-vanced Research (64T4-1). D.R.M. acknowledges supportfrom a Department of Science and Technology (DST) In-novation in Science Pursuit for Inspired Research (IN-SPIRE) Faculty Award. J.J. acknowledges support froma Humboldt postdoctoral fellowship and the Heidelber-ger Akademie der Wissenschaften, Heidelberg, Germany.D.B.B. acknowledges support from the NOMIS Founda-tion and an European Molecular Biology Organization(EMBO) postdoctoral fellowship (ALTF 343-2022). A.N.and S.P. acknowledge support from Ministry of Educa-tion (MoE) PhD fellowships. We thank Ashrit Mangal-wedhekar, Vivek Jadhav, Shikhara Bhat, Cassandre Aimon,and Harishankar Muppirala for comments on the manu-script and code. We thank Kollegala Sharma for his inputon the Kannada translation of the title and abstract.Data-Driven Model Discovery E115","publisher":"University of Chicago Press","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2205.02645","open_access":"1"}],"status":"public","date_updated":"2025-08-05T07:06:30Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","volume":205,"date_created":"2025-07-21T08:37:27Z","intvolume":"       205","OA_place":"repository","OA_type":"green","arxiv":1,"citation":{"ieee":"A. Nabeel <i>et al.</i>, “Discovering stochastic dynamical equations from ecological time series data,” <i>The American Naturalist</i>, vol. 205, no. 4. University of Chicago Press, pp. E100–E117, 2025.","ama":"Nabeel A, Karichannavar A, Palathingal S, et al. Discovering stochastic dynamical equations from ecological time series data. <i>The American Naturalist</i>. 2025;205(4):E100-E117. doi:<a href=\"https://doi.org/10.1086/734083\">10.1086/734083</a>","chicago":"Nabeel, Arshed, Ashwin Karichannavar, Shuaib Palathingal, Jitesh Jhawar, David Brückner, Danny Raj M, and Vishwesha Guttal. “Discovering Stochastic Dynamical Equations from Ecological Time Series Data.” <i>The American Naturalist</i>. University of Chicago Press, 2025. <a href=\"https://doi.org/10.1086/734083\">https://doi.org/10.1086/734083</a>.","mla":"Nabeel, Arshed, et al. “Discovering Stochastic Dynamical Equations from Ecological Time Series Data.” <i>The American Naturalist</i>, vol. 205, no. 4, University of Chicago Press, 2025, pp. E100–17, doi:<a href=\"https://doi.org/10.1086/734083\">10.1086/734083</a>.","apa":"Nabeel, A., Karichannavar, A., Palathingal, S., Jhawar, J., Brückner, D., Raj M, D., &#38; Guttal, V. (2025). Discovering stochastic dynamical equations from ecological time series data. <i>The American Naturalist</i>. University of Chicago Press. <a href=\"https://doi.org/10.1086/734083\">https://doi.org/10.1086/734083</a>","short":"A. Nabeel, A. Karichannavar, S. Palathingal, J. Jhawar, D. Brückner, D. Raj M, V. Guttal, The American Naturalist 205 (2025) E100–E117.","ista":"Nabeel A, Karichannavar A, Palathingal S, Jhawar J, Brückner D, Raj M D, Guttal V. 2025. Discovering stochastic dynamical equations from ecological time series data. The American Naturalist. 205(4), E100–E117."},"publication":"The American Naturalist","date_published":"2025-04-01T00:00:00Z","language":[{"iso":"eng"}],"department":[{"_id":"EdHa"}],"page":"E100-E117","type":"journal_article","project":[{"name":"A mechano-chemical theory for stem cell fate decisions in organoid development","_id":"34e2a5b5-11ca-11ed-8bc3-b2265616ef0b","grant_number":"ALTF 343-2022"}],"month":"04","quality_controlled":"1","oa":1,"oa_version":"Preprint","title":"Discovering stochastic dynamical equations from ecological time series data","related_material":{"record":[{"status":"public","relation":"software","id":"20121"}]},"author":[{"first_name":"Arshed","full_name":"Nabeel, Arshed","last_name":"Nabeel"},{"last_name":"Karichannavar","first_name":"Ashwin","full_name":"Karichannavar, Ashwin"},{"full_name":"Palathingal, Shuaib","first_name":"Shuaib","last_name":"Palathingal"},{"last_name":"Jhawar","full_name":"Jhawar, Jitesh","first_name":"Jitesh"},{"id":"e1e86031-6537-11eb-953a-f7ab92be508d","full_name":"Brückner, David","first_name":"David","orcid":"0000-0001-7205-2975","last_name":"Brückner"},{"last_name":"Raj M","first_name":"Danny","full_name":"Raj M, Danny"},{"last_name":"Guttal","first_name":"Vishwesha","full_name":"Guttal, Vishwesha"}],"external_id":{"arxiv":["2205.02645"],"pmid":["40179429"]},"article_type":"original","publication_identifier":{"issn":["0003-0147"],"eissn":["1537-5323"]}}