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Model-free information-theoretic approach to infer leadership in pairs of zebrafish

Sachit Butail1,*, Violet Mwaffo2, and Maurizio Porfiri2

  • 1Whiting School of Engineering, Johns Hopkins University, Baltimore, USA
  • 2Department of Mechanical and Aerospace Engineering, New York University Tandon School of Engineering, Brooklyn, New York, USA

  • *sbutail1@jhu.edu
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Phys. Rev. E 93, 042411 – Published 18 April, 2016

DOI: https://doi.org/10.1103/PhysRevE.93.042411

Abstract

Collective behavior affords several advantages to fish in avoiding predators, foraging, mating, and swimming. Although fish schools have been traditionally considered egalitarian superorganisms, a number of empirical observations suggest the emergence of leadership in gregarious groups. Detecting and classifying leader-follower relationships is central to elucidate the behavioral and physiological causes of leadership and understand its consequences. Here, we demonstrate an information-theoretic approach to infer leadership from positional data of fish swimming. In this framework, we measure social interactions between fish pairs through the mathematical construct of transfer entropy, which quantifies the predictive power of a time series to anticipate another, possibly coupled, time series. We focus on the zebrafish model organism, which is rapidly emerging as a species of choice in preclinical research for its genetic similarity to humans and reduced neurobiological complexity with respect to mammals. To overcome experimental confounds and generate test data sets on which we can thoroughly assess our approach, we adapt and calibrate a data-driven stochastic model of zebrafish motion for the simulation of a coupled dynamical system of zebrafish pairs. In this synthetic data set, the extent and direction of the coupling between the fish are systematically varied across a wide parameter range to demonstrate the accuracy and reliability of transfer entropy in inferring leadership. Our approach is expected to aid in the analysis of collective behavior, providing a data-driven perspective to understand social interactions.

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References (80)

  1. E. Shaw, Schooling fishes, Am. Sci. 66, 166 (1978).
  2. P. F. Major, Predator-prey interactions in two schooling fishes, Caranx ignobilis and Stolephorus purpureus, Anim. Behav. 26, 760 (1978).
  3. J. Herskin and J. F. Steffensen, Energy savings in sea bass swimming in a school: Measurements of tail beat frequency and oxygen consumption at different swimming speeds, J. Fish Biol. 53, 366 (1998).
  4. D. S. Wilson and E. Sober, Reviving the superorganism, J. Theor. Biol. 136, 337 (1989).
  5. A. Huth and C. Wissel, The simulation of the movement in fish schools, J. Theor. Biol. 156, 365 (1992).
  6. S. Marras, R. S. Batty, and P. Domenici, Information transfer and antipredator maneuvers in schooling herring, Adaptive Behavior 20, 44 (2012).
  7. S. Marras and P. Domenici, Schooling fish under attack are not all equal: Some lead, others follow, PLoS One 8, e65784 (2013).
  8. I. D. Couzin, J. Krause, N. R. Franks, and S. A. Levin, Effective leadership and decision-making in animal groups on the move, Nature (London) 433, 513 (2005).
  9. A. J. W. Ward, D. J. T. Sumpter, I. D. Couzin, P. J. B. Hart, and J. Krause, Quorum decision-making facilitates information transfer in fish shoals, Proc. Natl. Acad. Sci. USA 105, 6948 (2008).
  10. C. M. Lindeyer and S. M. Reader, Social learning of escape routes in zebrafish and the stability of behavioural traditions, Anim. Behav. 79, 827 (2010).
  11. J. Krause, D. Hoare, S. Krause, C. K. Hemelrijk, and D. I. Rubenstein, Leadership in fish shoals, Fish Fish. 1, 82 (2000).
  12. C. Leblond and S. G. Reebs, Individual leadership and boldness in shoals of golden shiners (Notemigonus crysoleucas), Behavior 143, 1263 (2006).
  13. J. L. Harcourt, T. Z. Ang, and G. Sweetman, Social feedback and the emergence of leaders and followers, Curr. Biol. 19, 248 (2009).
  14. S. Nakayama, J. L. Harcourt, R. A. Johnstone, and A. Manica, Initiative, personality and leadership in pairs of foraging fish, PLoS One 7, e36606 (2012).
  15. F. Ladu, S. Butail, S. Macrì, and M. Porfiri, Sociality modulates the effects of ethanol in zebrafish, Alcohol. Clin. Exp. Res. 38, 2096 (2014).
  16. N. W. F. Bode, D. W. Franks, and A. J. Wood, Leading from the front? Social networks in navigating groups, Behav. Ecol. Sociobiol. 66, 835 (2012).
  17. N. Marwan and J. Kurths, Nonlinear analysis of bivariate data with cross recurrence plots, Phys. Lett. A 302, 299 (2002).
  18. Y. Katz, K. Tunstrøm, C. C. Ioannou, C. Huepe, and I. D. Couzin, Inferring the structure and dynamics of interactions in schooling fish, Proc. Natl. Acad. Sci. USA 108, 18720 (2011).
  19. C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27, 379 (1948).
  20. K. Hlavácková-Schindler, M. Paluš, M. Vejmelka, and J. Bhattacharya, Causality detection based on information-theoretic approaches in time series analysis, Phys. Rep. 441, 1 (2007).
  21. M. Zanin, E. Menasalvas, S. Boccaletti, and P. Sousa, Feature selection in the reconstruction of complex network representations of spectral data, PLoS One 8, e72045 (2013).
  22. M. Timme and J. Casadiego, Revealing networks from dynamics: An introduction, J. Phys. A 47, 343001 (2014).
  23. O. Stetter, D. Battaglia, J. Soriano, and T. Geisel, Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals, PLoS Comput. Biol. 8, e1002653 (2012).
  24. R. Vicente, M. Wibral, M. Lindner, and G. Pipa, Transfer entropy—A model-free measure of effective connectivity for the neurosciences, J. Comput. Neurosci. 30, 45 (2011).
  25. R. Kleeman, Information theory and dynamical system predictability, Entropy 13, 612 (2011).
  26. O. Kwon and J.-S. Yang, Information flow between stock indices, Europhys. Lett. 82, 68003 (2008).
  27. G. Ver Steeg and A. Galstyan, Information transfer in social media, in Proceedings of the International Conference on World Wide Web (ACM, New York, 2012), pp. 509–518.
  28. S. Butail, F. Ladu, D. Spinello, and M. Porfiri, Information flow in animal-robot interactions, Entropy 16, 1315 (2014).
  29. F. Ladu, V. Mwaffo, J. Li, S. Macrì, and M. Porfiri, Acute caffeine administration affects zebrafish response to a robotic stimulus, Behav. Brain Res. 289, 48 (2015).
  30. F. Hu, L.-J. Nie, and S.-J. Fu, Information dynamics in the interaction between a prey and a predator fish, Entropy 17, 7230 (2015).
  31. T. Bartolini, V. Mwaffo, A. Showler, S. Macrì, S. Butail, and M. Porfiri, Zebrafish response to 3D printed shoals of conspecifics: the effect of body size, Bioinspiration & Biomimetics 11, 026003 (2016).
  32. N. Orange and N. Abaid, A transfer entropy analysis of leader-follower interactions in flying bats, Eur. Phys. J. 224, 3279 (2015).
  33. V. Mwaffo, R. P. Anderson, S. Butail, and M. Porfiri, A jump persistent turning walker to model zebrafish locomotion, J. R. Soc. Interface 12, 20140884 (2015).
  34. J. Gautrais, F. Ginelli, R. Fournier, S. Blanco, M. Soria, H. Chaté, and G. Theraulaz, Deciphering interactions in moving animal groups, PLoS Comput. Biol. 8, e1002678 (2012).
  35. G. J. Lieschke and P. D. Currie, Animal models of human disease: Zebrafish swim into view, Nat. Rev. Genet. 8, 353 (2007).
  36. R. Gerlai, Using zebrafish to unravel the genetics of complex brain disorders, in Current Topics in Behavioral Neurosciences, Behavioral Neurogenetics Vol. 12 (Springer, Berlin, 2012), pp. 3–24.
  37. Zebrafish Protocols for Neurobehavioral Research, edited by A. V. Kalueff and A. M. Stewart Neuromethods, Vol. 66 (Humana Press, New York, 2012).
  38. M. Pham, J. Raymond, J. Hester, E. Kyzar, S. Gaikwad, I. Bruce, C. Fryar, S. Chanin, J. Enriquez, S. Bagawandoss, I. Zapolsky, J. Green, A. M. Stewart, B. D. Robison, and A. V. Kalueff, Assessing social behavior phenotypes in adult zebrafish: Shoaling, social preference, and mirror biting tests, in Zebrafish Protocols for Neurobehavioral Research, edited by A. V. Kalueff and A. M. Stewart, Neuromethods, Vol. s66 (Humana Press, New York, 2012), pp. 231–246.
  39. J. J. Videler, Fish Swimming (Springer, 1993).
  40. A. V. Kalueff et al., Towards a comprehensive catalog of zebrafish behavior 1.0 and beyond, Zebrafish 10, 70 (2013).
  41. T. Bartolini, V. Mwaffo, S. Butail, and M. Porfiri, Effect of acute ethanol administration on zebrafish tail beat motion, Alcohol 49, 721 (2015).
  42. V. Mwaffo and M. Porfiri, Turning rate dynamics of zebrafish exposed to ethanol, Int. J. Bifurcation Chaos 25, 1540006 (2015).
  43. V. Mwaffo, S. Butail, M. diBernardo, and M. Porfiri, Measuring zebrafish turning rate, Zebrafish 12, 250 (2015).
  44. N. Miller and R. Gerlai, Quantification of shoaling behavior in zebrafish (Danio rerio), Behav. Brain Res. 184, 157 (2007).
  45. N. Miller and R. Gerlai, From schooling to shoaling: Patterns of collective motion in zebrafish (Danio rerio), PLoS One 7, e48865 (2012).
  46. R. Q. Quiroga, T. Kreuz, and P. Grassberger, Event synchronization: A simple and fast method to measure synchronicity and time delay patterns, Phys. Rev. E 66, 041904 (2002).
  47. C. W. J. Granger, Testing for causality: A personal viewpoint, J. Econ. Dyn. Control 2, 329 (1980).
  48. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 2006).
  49. M. Vejmelka and M. Paluš, Inferring the directionality of coupling with conditional mutual information, Phys. Rev. E 77, 026214 (2008).
  50. J. Hlinka, D. Hartman, M. Vejmelka, J. Runge, N. Marwan, J. Kurths, and M. Paluš, Reliability of inference of directed climate networks using conditional mutual information, Entropy 15, 2023 (2013).
  51. T. Schreiber, Measuring Information Transfer, Phys. Rev. Lett. 85, 461 (2000).
  52. B. W. Silverman, Density Estimation for Statistics and Data Analysis (CRC Press, Boca Raton, FL, 1986).
  53. N. Malik, B. Bookhagen, N. Marwan, and J. Kurths, Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks, Clim. Dyn. 39, 971 (2012).
  54. V. Mwaffo, R. P. Anderson, and M. Porfiri, Collective dynamics in the Vicsek and vectorial network models beyond uniform additive noise, J. Nonlinear Sci. 25, 1053 (2015).
  55. J. Gautrais, C. Jost, M. Soria, A. Campo, S. Motsch, R. Fournier, S. Blanco, and G. Theraulaz, Analyzing fish movement as a persistent turning walker, J. Math. Biol. 58, 429 (2009).
  56. D. S. Calovi, U. Lopez, S. Ngo, C. Sire, H. Chaté, and G. Theraulaz, Swarming, schooling, milling: Phase diagram of a data-driven fish school model, New J. Phys. 16, 015026 (2014).
  57. A. Zienkiewicz, D. A. Barton, M. Porfiri, and M. di Bernardo, Leadership emergence in a data-driven model of zebrafish shoals with speed modulation, Eur. Phys. J. 224, 3343 (2015).
  58. R. C. Eaton, R. A. Bombardieri, and D. L. Meyer, The Mauthner-initiated startle response in teleost fish, J. Exp. Biol. 66, 65 (1977).
  59. A. Zienkiewicz, D. A. W. Barton, M. Porfiri, and M. di Bernardo, Data-driven stochastic modeling of zebrafish locomotion, J. Math. Biol. 71, 1081 (2014).
  60. J. W. Jolles, A. Fleetwood-Wilson, S. Nakayama, M. C. Stumpe, R. A. Johnstone, and A. Manica, The role of social attraction and its link with boldness in the collective movements of three-spined sticklebacks, Anim. Behav. 99, 147 (2015).
  61. D. J. Higham, An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations, SIAM Rev. 43, 525 (2001).
  62. J. Runge, J. Heitzig, V. Petoukhov, and J. Kurths, Escaping the Curse of Dimensionality in Estimating Multivariate Transfer Entropy, Phys. Rev. Lett. 108, 258701 (2012).
  63. P. Sonego, A. Kocsor, and S. Pongor, ROC analysis: Applications to the classification of biological sequences and 3D structures, Briefings Bioinf. 9, 198 (2008).
  64. D. Wright, L. B. Rimmer, V. L. Pritchard, R. K. Butlin, and J. Krause, Inter and intra-population variation in shoaling and boldness in the zebrafish (Danio rerio), J. Fish Biol. 63, 258 (2003).
  65. S. Boccaletti, V. Latora, and Y. Moreno, Complex networks: Structure and dynamics, Phys. Rep. 424, 175 (2006).
  66. V. Kopman, J. Laut, G. Polverino, and M. Porfiri, Closed-loop control of zebrafish response using a bioinspired robotic-fish in a preference test, J. R. Soc. Interface 10, 20120540 (2013).
  67. M. Lungarella, M. Lungarella, and Y. Kuniyoshi, Information transfer at multiple scales, Phys. Rev. E 76, 056117 (2007).
  68. G. Gómez-Herrero, W. Wu, K. Rutanen, M. C. Soriano, G. Pipa, and R. Vicente, Assessing coupling dynamics from an ensemble of time series, Entropy 17, 1958 (2015).
  69. J. Sun and E. M. Bollt, Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings, Phys. D: (Amsterdam, Neth.) 267, 49 (2014).
  70. Y. Sun, L. F. Rossi, C.-C. Shen, J. Miller, X. R. Wang, J. T. Lizier, M. Prokopenko, and U. Senanayake, Information transfer in swarms with leaders, arXiv:1407.0007.
  71. X. R. Wang, J. M. Miller, J. T. Lizier, M. Prokopenko, and L. F. Rossi, Quantifying and tracing information cascades in swarms, PLoS One 7, e40084 (2012).
  72. J. T. Lizier, M. Prokopenko, and A. Y. Zomaya, Local information transfer as a spatiotemporal filter for complex systems, Phys. Rev. E 77, 026110 (2008).
  73. S. Marras, S. S. Killen, G. Claireaux, P. Domenici, and D. J. McKenzie, Behavioural and kinematic components of the fast-start escape response in fish: Individual variation and temporal repeatability, J. Exp. Biol. 214, 3102 (2011).
  74. A. L. J. Burns, J. E. Herbert-Read, L. J. Morrell, and A. J. W. Ward, Consistency of leadership in shoals of mosquitofish (Gambusia holbrooki) in novel and in familiar environments, PLoS One 7, e36567 (2012).
  75. A. I. Dell, J. A. Bender, K. Branson, I. D. Couzin, G. G. de Polavieja, L. P. J. J. Noldus, A. Pérez-Escudero, P. Perona, A. D. Straw, M. Wikelski, and U. Brose, Automated image-based tracking and its application in ecology, Trends Ecol. Evol. 29, 417 (2014).
  76. A. M. Stewart, M. Nguyen, K. Wong, M. K. Poudel, and A. V. Kalueff, Developing zebrafish models of autism spectrum disorder (ASD), Prog. Neuro-Psychopharmacol. Biol. Psychiatry 50, 27 (2014).
  77. R. Du, Z. Li, K. Youcef-Toumi, and P. V. y Alvarado, Robot Fish: Bio-inspired Fishlike Underwater Robots (Springer, Berlin, 2015).
  78. A. M. Stewart, R. Gerlai, and A. V. Kalueff, Developing higher-throughput zebrafish screens for in-vivo CNS drug discovery, Front. Behav. Neurosci. 9, 1 (2015).
  79. MathWorks, matlab R2014b, Natick, MA, 2014.
  80. H. Akaike, E. Parzen, T. Kunio, and K. Genshiro (Eds.), Information theory and an extension of the maximum likelihood principle, in Selected Papers of Hirotugu Akaike (Springer, New York, 1998), pp. 199–213.

Outline

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Phys. Rev. E 93, 042411– Published 18 April, 2016
  • Received 2 November 2015
  • Revised 15 February 2016
Article part of CHORUS

©2016 American Physical Society

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