{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T15:40:03Z","timestamp":1779896403749,"version":"3.53.1"},"reference-count":50,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T00:00:00Z","timestamp":1725926400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Installations and the Operational Environment Program of the U.S. Army Corps of Engineers"},{"name":"National Science Foundation\u2019s Mathematical Sciences Graduate Internship (NSF-MSGI) program"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Leader\u2013follower modalities and other asymmetric interactions that drive the collective motion of organisms are often quantified using information theory metrics like transfer or causation entropy. These metrics are difficult to accurately evaluate without a much larger number of data than is typically available from a time series of animal trajectories collected in the field or from experiments. In this paper, we use a generalized leader\u2013follower model to argue that the time-separated mutual information between two organism positions can serve as an alternative metric for capturing asymmetric correlations that is much less data intensive and more accurately estimated by popular k-nearest neighbor algorithms than transfer entropy. Our model predicts a local maximum of this mutual information at a time separation value corresponding to the fundamental reaction timescale of the follower organism. We confirm this prediction by analyzing time series trajectories recorded for a pair of golden shiner fish circling an annular tank.<\/jats:p>","DOI":"10.3390\/e26090775","type":"journal-article","created":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T07:33:25Z","timestamp":1725953605000},"page":"775","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Probing Asymmetric Interactions with Time-Separated Mutual Information: A Case Study Using Golden Shiners"],"prefix":"10.3390","volume":"26","author":[{"given":"Katherine","family":"Daftari","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9014-1859","authenticated-orcid":false,"given":"Michael L.","family":"Mayo","sequence":"additional","affiliation":[{"name":"U.S. Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bertrand H.","family":"Lemasson","sequence":"additional","affiliation":[{"name":"U.S. Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James M.","family":"Biedenbach","sequence":"additional","affiliation":[{"name":"U.S. Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3278-2268","authenticated-orcid":false,"given":"Kevin R.","family":"Pilkiewicz","sequence":"additional","affiliation":[{"name":"U.S. Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2123","DOI":"10.1016\/j.cub.2006.08.087","article-title":"From Compromise to Leadership in Pigeon Homing","volume":"16","author":"Biro","year":"2006","journal-title":"Curr. 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