{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T00:37:39Z","timestamp":1760488659362,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2015,10,23]],"date-time":"2015-10-23T00:00:00Z","timestamp":1445558400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Accessing information efficiently is vital for animals to make the optimal decisions, and it is particularly important when they are facing predators. Yet until now, very few quantitative conclusions have been drawn about the information dynamics in the interaction between animals due to the lack of appropriate theoretic measures. Here, we employ transfer entropy (TE), a new information-theoretic and model-free measure, to explore the information dynamics in the interaction between a predator and a prey fish. We conduct experiments in which a predator and a prey fish are confined in separate parts of an arena, but can communicate with each other visually and tactilely. TE is calculated on the pair\u2019s coarse-grained state of the trajectories. We find that the prey\u2019s TE is generally significantly bigger than the predator\u2019s during trials, which indicates that the dominant information is transmitted from predator to prey. We then demonstrate that the direction of information flow is irrelevant to the parameters used in the coarse-grained procedures. We further calculate the prey\u2019s TE at different distances between it and the predator. The resulted figure shows that there is a high plateau in the mid-range of the distance and that drops quickly at both the near and the far ends. This result reflects that there is a sensitive space zone where the prey is highly vigilant of the predator\u2019s position.<\/jats:p>","DOI":"10.3390\/e17107230","type":"journal-article","created":{"date-parts":[[2015,10,24]],"date-time":"2015-10-24T08:27:06Z","timestamp":1445675226000},"page":"7230-7241","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Information Dynamics in the Interaction between a Prey and a Predator Fish"],"prefix":"10.3390","volume":"17","author":[{"given":"Feng","family":"Hu","sequence":"first","affiliation":[{"name":"College of physics and electronic engineering, Chongqing Normal University, Chongqing 400047, China"},{"name":"Laboratory of Evolutionary Physiology and Behavior, Chongqing Key Laboratory of Animal Biology, Chongqing Normal University, Chongqing 400047, China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li-Juan","family":"Nie","sequence":"additional","affiliation":[{"name":"Laboratory of Evolutionary Physiology and Behavior, Chongqing Key Laboratory of Animal Biology, Chongqing Normal University, Chongqing 400047, China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7665-9037","authenticated-orcid":false,"given":"Shi-Jian","family":"Fu","sequence":"additional","affiliation":[{"name":"Laboratory of Evolutionary Physiology and Behavior, Chongqing Key Laboratory of Animal Biology, Chongqing Normal University, Chongqing 400047, China."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.tree.2005.01.010","article-title":"Information and its use by animals in evolutionary ecology","volume":"20","author":"Dall","year":"2005","journal-title":"Trends Ecol. Evol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1098\/rstb.2008.0204","article-title":"Quorum responses and consensus decision making","volume":"364","author":"Sumpter","year":"2009","journal-title":"Philos. Trans. R. Soc. Lond. B. Biol. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"11865","DOI":"10.1073\/pnas.1005766107","article-title":"Scale-free correlations in starling flocks","volume":"107","author":"Cavagna","year":"2010","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1145\/37402.37406","article-title":"Flocks, herds, and schools: A distributed behavioral model","volume":"21","author":"Reynolds","year":"1987","journal-title":"ACM SIGGRAPH Comput. Graph."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1226","DOI":"10.1103\/PhysRevLett.75.1226","article-title":"Novel type of phase transition of self-driven particles","volume":"75","author":"Vicsek","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Couzin, I.D., Krause, J., James, R., Ruxton, G.D., and Franks, N.R. (2002). Collective Memory and Spatial Sorting in Animal Groups. J. Theor. Biol., 218.","DOI":"10.1006\/jtbi.2002.3065"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Wang, X.R., Miller, J.M., Lizier, J.T., Prokopenko, M., and Rossi, L.F. (2012). Quantifying and Tracing Information Cascades in Swarms. PLoS one, 7.","DOI":"10.1371\/journal.pone.0040084"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Radakov, D.V., and Mills, H. (1974). Schooling in the ecology of fish. Q. Rev. Biol., 49.","DOI":"10.1086\/408260"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1111\/j.1469-185X.1989.tb00636.x","article-title":"Predator vigilance and group size in mammals and birds: A critical review of the empirical evidence","volume":"64","author":"Elgar","year":"1989","journal-title":"Biol. Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Techn. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1002\/j.1538-7305.1948.tb00917.x","article-title":"A Mathematical Theory of Communication, Part III: Mathematical Rreliminaries","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Techn. J."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley. [2nd ed.].","DOI":"10.1002\/047174882X"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1086\/392768","article-title":"The concept of information in biology","volume":"67","author":"Smith","year":"2000","journal-title":"Philo. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s10827-010-0271-2","article-title":"Multivariate information-theoretic measures reveal directed information structure and task relevant changes in fMRI connectivity","volume":"30","author":"Lizier","year":"2011","journal-title":"J. Comput. Neurosci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s10827-010-0262-3","article-title":"Transfer entropy\u2014a model-free measure of effective connectivity for the neurosciences","volume":"30","author":"Vicente","year":"2011","journal-title":"J. Comput. Neurosci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.plrev.2004.01.002","article-title":"Information theory in molecular biology","volume":"1","author":"Adami","year":"2004","journal-title":"Phys. Life Rev."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information Theory and Statistical Mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1103\/PhysRevLett.85.461","article-title":"Measuring Information Transfer","volume":"85","author":"Schreiber","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.3390\/e16031315","article-title":"Information Flow in Animal-Robot Interactions","volume":"16","author":"Butail","year":"2014","journal-title":"Entropy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.bbr.2015.04.020","article-title":"Acute caffeine administration affects zebrafish response to a robotic stimulus","volume":"289","author":"Ladu","year":"2015","journal-title":"Behav. Brain Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"042917","DOI":"10.1103\/PhysRevE.87.042917","article-title":"Spurious causalities with transfer entropy","volume":"87","author":"Simirnov","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4077","DOI":"10.1242\/jeb.02487","article-title":"The role of the lateral line and vision on body kinematics and hydrodynamic preference of rainbow trout in turbulent flow","volume":"209","author":"Liao","year":"2006","journal-title":"J. Exp. Biol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1007\/s00360-012-0644-0","article-title":"The effects of dissolved oxygen levels on the metabolic interaction between digestion and locomotion in Cyprinid fishes with different locomotive and digestive performances","volume":"182","author":"Zhang","year":"2012","journal-title":"J. Comp. Physiol. B"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Fu, S.-J. (2015). Flow and stress acclimation both enhance predator avoidance in a common cyprinid fish. Aquat. Biol., 24.","DOI":"10.3354\/ab00633"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/BF00606308","article-title":"Reaction time and stimulus frequency in prey localization in the surface-feeding fish Aplocheilus lineatus","volume":"140","author":"Bleckmann","year":"1980","journal-title":"J. Comp. Physiol. A"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1111\/j.1095-8649.2012.12015.x","article-title":"Effects of age and size on critical swimming speed of juvenile Chinese sturgeon Acipenser sinensis at seasonal temperatures","volume":"82","author":"He","year":"2013","journal-title":"J. Fish Biol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1139\/f03-170","article-title":"Temperature and hunger mediate sablefish (Anoplopoma fimbria) feeding motivation: Implications for stock assessment","volume":"61","author":"Stoner","year":"2004","journal-title":"Can. J. Fish. Aquat. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"026110","DOI":"10.1103\/PhysRevE.77.026110","article-title":"Local information transfer as a spatiotemporal filter for complex systems","volume":"77","author":"Lizier","year":"2008","journal-title":"Phys. Rev. E"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2463","DOI":"10.1242\/jeb.029652","article-title":"Animal escapology I: Theoretical issues and emerging trends in escape trajectories","volume":"214","author":"Domenici","year":"2011","journal-title":"J. Exp. Biol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"158101","DOI":"10.1103\/PhysRevLett.100.158101","article-title":"Symbolic transfer entropy","volume":"100","author":"Staniek","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation entropy: A natural complexity measure for time series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Krause, J., and Ruxton, G.D. (2002). Living in Groups, Oxford University Press.","DOI":"10.1093\/oso\/9780198508175.001.0001"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1006\/anbe.1999.1182","article-title":"Back to the basics of antipredatory vigilance: Can nonvigilant animals detect attack?","volume":"58","author":"Lima","year":"1999","journal-title":"Anim. Behav."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/10\/7230\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:50:51Z","timestamp":1760215851000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/10\/7230"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,23]]},"references-count":33,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2015,10]]}},"alternative-id":["e17107230"],"URL":"https:\/\/doi.org\/10.3390\/e17107230","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,10,23]]}}}