Skip to main content
Log in

Collective Pulsing in Xeniid Corals: Part I—Using Computer Vision and Information Theory to Search for Coordination

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Xeniid corals (Cnidaria: Alcyonacea), a family of soft corals, include species displaying a characteristic pulsing behavior. This behavior has been shown to increase oxygen diffusion away from the coral tissue, resulting in higher photosynthetic rates from mutualistic symbionts. Maintaining such a pulsing behavior comes at a high energetic cost, and it has been proposed that coordinating the pulse of individual polyps within a colony might enhance the efficiency of fluid transport. In this paper, we test whether patterns of collective pulsing emerge in coral colonies and investigate possible interactions between polyps within a colony. We video recorded different colonies of Heteroxenia sp. in a laboratory environment. Our methodology is based on the systematic integration of a computer vision algorithm (ISOMAP) and an information-theoretic approach (transfer entropy), offering a vantage point to assess coordination in collective pulsing. Perhaps surprisingly, we did not detect any form of collective pulsing behavior in the colonies. Using artificial data sets, however, we do demonstrate that our methodology is capable of detecting even weak information transfer. The lack of a coordination is consistent with previous work on many cnidarians where coordination between actively pulsing polyps and medusa has not been observed. In our companion paper, we show that there is no fluid dynamic benefit of coordinated pulsing, supporting this result. The lack of coordination coupled with no obvious fluid dynamic benefit to grouping suggests that there may be non-fluid mechanical advantages to forming colonies, such as predator avoidance and defense.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Abaid N, Bollt E, Porfiri M (2012) Topological analysis of complexity in multiagent systems. Phys Rev E 85:041907-1–9

    Article  Google Scholar 

  • Bartolini T, Mwaffo V, Showler A, Macrí S, Butail S, Porfiri M (2016) Zebrafish response to 3D printed shoals of conspecifics: the effect of body size. Bioinspir Biomimet 11:026003

    Article  Google Scholar 

  • Battista NA, Samson JE, Khatri S, Miller LA (2018) Under the sea: pulsing corals in ambient flow. In: Anguelov R, Lachowicz M (eds) Mathematical methods and models in biosciences. Biomath Forum, Irvine, pp 22–34

    Google Scholar 

  • Butail S, Ladu F, Spinello D, Porfiri M (2014) Information flow in animal–robot interactions. Entropy 16:1315

    Article  Google Scholar 

  • Butail S, Mwaffo V, Porfiri M (2016) Model-free information-theoretic approach to infer leadership in pairs of zebrafish. Phys Rev E 93(4):1–12

    Article  Google Scholar 

  • Couzin ID (2009) Collective cognition in animal groups. Trends Cognit Sci 13:36–43

    Article  Google Scholar 

  • DeLellis P, Porfiri M, Bollt EM (2013) Topological analysis of group fragmentation in multiagent systems. Phys Rev E 87:022818-1–9

    Article  Google Scholar 

  • DeLellis P, Polverino G, Ustuner G, Abaid N, Macrí S, Bollt EM et al (2014) Collective behaviour across animal species. Sci Rep 4:3723

    Article  Google Scholar 

  • Durieux DM, Clos KTD, Gemmell BJ (2019) Aggregation and Benthic Locomotion in Upside-down Jellyfish: Impacts on Feeding and Defense. In: 2019 Annual meeting of the society for integrative biology. Available from: http://69.36.180.54/meetings/2019

  • Filella A, Nadal F, Sire C, Kanso E, Eloy C (2018) Hydrodynamic interactions influence fish collective behavior. Phys Rev Lett 120:198101

    Article  Google Scholar 

  • Gajamannage K, Butail S, Porfiri M, Bollt EM (2015) Dimensionality reduction of collective motion by principal manifolds. Physica D 291:62–73

    Article  MathSciNet  Google Scholar 

  • Gohar HAF (1940) Studies on the Xeniidae of the Red Sea: their ecology, physiology, taxonomy and phylogeny. Publ Mar Biol Stat Al-Ghardaqa (Red Sea) 2:24–118

    Google Scholar 

  • Gohar HAF, Roushdy HM (1959a) The neuromuscular system of the Xeniidae (Alcyonaria). I. Histological. Pub Mar Biol Stat Al-Ghardaqa (Red Sea). 10:63–81

    Google Scholar 

  • Gohar HAF, Roushdy HM (1959b) On the physiology and neuromuscular system of Heteroxenia (Alcyonaria). Publ Mar Biol Stat Al-Ghardaqa (Red Sea) 10:91–143

    Google Scholar 

  • Gonzalez RC, Woods RE (2018) Digital image processing, 4th edn. Pearson, London

    Google Scholar 

  • Hedrick TL (2008) Software techniques for two- and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspir Biomimet 3:034001

    Article  Google Scholar 

  • Jackson BE, Evangelista DJ, Ray DD, Hedrick TL (2016) 3D for the people: multi-camera motion capture in the field with consumer-grade cameras and open source software. Biol Open 5(9):1334–1342

    Article  Google Scholar 

  • James R, Barnett N, Crutchfield J (2015) Information flows? a critique of transfer entropies. Phys Rev Lett 12:116

    Google Scholar 

  • Kong Z, Fuller N et al (2016) Perceptual modalities guiding bat flight in a native habitat. Sci Rep 6:27252

    Article  Google Scholar 

  • Kremien M, Shavit U, Mass T, Genin A (2013) Benefit of pulsation in soft corals. Proc Natl Acad Sci 110(22):8978–8983

    Article  Google Scholar 

  • Ladu F, Mwaffo V, Li J, Macrí S, Porfiri M (2015) Acute caffeine administration affects zebrafish response to a robotic stimulus. Behav Brain Res 289:48

    Article  Google Scholar 

  • Lieske E, Myers RF (2004) Coral reef guide: red sea, 2nd edn. Harper Collins, New York

    Google Scholar 

  • Moore DG, Valentini G, Walker SI, Levin M (2017) Inform: A toolkit for information-theoretic analysis of complex systems. In: 2017 IEEE symposium series on computational intelligence (SSCI). ieeexplore.ieee.org; pp 1–8. Available from: http://dx.doi.org/10.1109/SSCI.2017.8285197. Accessed 23 Jun 2020

  • Mwaffo VF, Butail S, Porfiri M (2017) Analysis of pairwise interactions in a maximum likelihood sense to identify leaders in a group. Front Robot AI 5:35

    Article  Google Scholar 

  • Nagy M, Zsuzsa A, Biro D, Vicsek T (2010) Hierarchical group dynamics in pigeon flocks. Nature 464:890–893

    Article  Google Scholar 

  • Orange N, Abaid N (2015) A transfer entropy analysis of leader-follower interactions in flying bats. Eur Phys J 224:3279

    Google Scholar 

  • Pilkiewicz KR, Lemasson BH, Rowland MA, Hein A, Sun J et al (2020) Decoding collective communications using information theory tools. J R Soc Interface 17:20190563

    Article  Google Scholar 

  • Quick CM, Venugopal AM, Gashev AA, Zawieja DC, Stewart RH (2007) Intrinsic pump-conduit behavior of lymphangions. Am J Physiol Regul Integr Comp Physiol 292:R1510–R1518

    Article  Google Scholar 

  • R Core Team (2018) R: a language and environment for statistical computing. Vienna, Austria; 2018. Available from: https://www.R-project.org/. Accessed 23 Jun 2020

  • Roy S, Abaid N (2017) Interactional dynamics of same-sex marriage legislation in the United States. R Soc Open Sci 4(6):170130

    Article  MathSciNet  Google Scholar 

  • Roy S, Howes K, Müller R, Butail S, Abaid N (2019) Extracting interactions between flying bat pairs using model-free methods. Entropy 21(1):42

    Article  Google Scholar 

  • Samson JE, Miller LA, Ray D, Holzman R, Shavit U, Khatri S (2019) A novel mechanism of mixing by pulsing corals. J Exp Biol 222(15):jeb192518

    Article  Google Scholar 

  • Schneidman E II, Berry MJ, Segev R, Bialek W (2006) Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440:1007–1012

    Article  Google Scholar 

  • Schreiber T (2000) Measuring information transfer. Phys Rev Lett 85:461

    Article  Google Scholar 

  • Sutherland KR, Weihs D (2017) Hydrodynamic advantages of swimming by salp chains. J R Soc Interface 14(133):20170298

    Article  Google Scholar 

  • Tenenbaum JB, de Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319–2323

    Article  Google Scholar 

  • Valentini G (2018) rinform: An R wrapper of the inform c library for information analysis of complex systems;. R package version 1.0.0. Available from: https://elife-asu.github.io/rinform/. Accessed 23 Jun 2020

  • Wang XR, Miller JM, Lizier JT, Prokopenko M, Rossi LF (2012) Quantifying and tracing information cascades in swarms. PLoS ONE 7:e40084

    Article  Google Scholar 

  • Weidenmüller A, Kleindam C, Tautz J (2002) Collective control of nest climate parameters in bumblebee colonies. Anim Behav 63(6):1065–1071

    Article  Google Scholar 

  • Wild C, Naumann MS (2013) Effect of active water movement on energy and nutrient acquisition in coral reef-associated benthic organisms. Proc Natl Acad Sci 110(22):8767–8768

    Article  Google Scholar 

  • Wild C, Hoegh-Guldberg O, Naumann MS, Colombo-Pallotta MF, Ateweberhan M, Fitt WK et al (2011) Climate change impedes scleratinian corals as primary reef ecosystem engineers. Mar Freshw Res 62(2):205–215

    Article  Google Scholar 

  • Zawieja DC (2009) Contractile physiology of lymphatics. Lymphat Res Biol 7:87–96

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Statistical and Applied Mathematical Sciences Institute (SAMSI) for hosting the workshop that got this project started. This material was based upon work partially supported by the National Science Foundation (NSF) under Grant DMS-1638521 to the Statistical and Applied Mathematical Sciences Institute. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.” FundingLAM was supported by NSF PHY Grant #1504777 (to LAM), NSF DMS Grant #1127914 (to the Statistical and Applied Mathematical Sciences Institute), and the DFG Centre of Excellence 2117 “Centre for the Advanced Study of Collective Behaviour” (ID: 422037984). Travel support for JES was obtained from a Travelling Fellowship from the Company of Biologists. During this project, JES was supported by a SAMSI Fellowship and a Howard Hughes Medical Institute International Student Research Fellowship, and by the Women Diver’s Hall of Fame for dive training. MP was supported by NSF through Grant # CMMI-1433670 and CBET-1547864.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Simon Garnier.

Ethics declarations

Conflict of interest

The authors declare that they have no the conflict interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 825 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Samson, J.E., Ray, D.D., Porfiri, M. et al. Collective Pulsing in Xeniid Corals: Part I—Using Computer Vision and Information Theory to Search for Coordination. Bull Math Biol 82, 90 (2020). https://doi.org/10.1007/s11538-020-00759-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11538-020-00759-2

Keywords

Navigation