{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T20:14:37Z","timestamp":1767212077695,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,9]],"date-time":"2019-01-09T00:00:00Z","timestamp":1546992000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CMMI-1342176, CMMI-1433670"],"award-info":[{"award-number":["CMMI-1342176, CMMI-1433670"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Social animals exhibit collective behavior whereby they negotiate to reach an agreement, such as the coordination of group motion. Bats are unique among most social animals, since they use active sensory echolocation by emitting ultrasonic waves and sensing echoes to navigate. Bats\u2019 use of active sensing may result in acoustic interference from peers, driving different behavior when they fly together rather than alone. The present study explores quantitative methods that can be used to understand whether bats flying in pairs move independently of each other or interact. The study used field data from bats in flight and is based on the assumption that interactions between two bats are evidenced in their flight patterns. To quantify pairwise interaction, we defined the strength of coupling using model-free methods from dynamical systems and information theory. We used a control condition to eliminate similarities in flight path due to environmental geometry. Our research question is whether these data-driven methods identify directed coupling between bats from their flight paths and, if so, whether the results are consistent between methods. Results demonstrate evidence of information exchange between flying bat pairs, and, in particular, we find significant evidence of rear-to-front coupling in bats\u2019 turning behavior when they fly in the absence of obstacles.<\/jats:p>","DOI":"10.3390\/e21010042","type":"journal-article","created":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T11:36:42Z","timestamp":1547206602000},"page":"42","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Extracting Interactions between Flying Bat Pairs Using Model-Free Methods"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5740-188X","authenticated-orcid":false,"given":"Subhradeep","family":"Roy","sequence":"first","affiliation":[{"name":"Physical Computing Lab., Virginia Tech, Blacksburg, VA 24061, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4724-8081","authenticated-orcid":false,"given":"Kayla","family":"Howes","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering and Mechanics, Virginia Tech, Blacksburg, VA 24061, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8358-4053","authenticated-orcid":false,"given":"Rolf","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA"},{"name":"Shandong University-Virginia Tech International Laboratory, Shandong University, Jinan 250100, China"}]},{"given":"Sachit","family":"Butail","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Northern Illinois University, DeKalb, IL 60115, USA"}]},{"given":"Nicole","family":"Abaid","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering and Mechanics, Virginia Tech, Blacksburg, VA 24061, USA"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Krause, J., and Ruxton, G.D. 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