Modeling diel vertical migration with membrane computing | Journal of Membrane Computing Skip to main content
Springer Nature Link
Log in

Modeling diel vertical migration with membrane computing

  • Regular Paper
  • Published:
Journal of Membrane Computing Aims and scope Submit manuscript

Abstract

Diel vertical migration (DVM) is an important ecological phenomenon in which zooplankton migrate vertically to deal with trade-offs associated with greater food availability in shallow waters and lower predator risk in deep waters due to lower light availability. Because of these trade-offs, DVM dynamics are particularly sensitive to changes in light intensity at the water surface. Therefore, changes in the proportion of cloudy and sunny days have the potential to disrupt DVM dynamics. We propose a new membrane computing model that captures the effect of cloud cover on DVM in Daphnia, and we use it to explore the impacts of an increased proportion of cloudy days that are predicted to occur with climate change. Our 2-dimensional, spatially explicit model integrates multiple trophic levels from abiotic nutrients to Daphnia predators. We analyzed the effect that different proportions of cloudy and sunny days throughout the summer have on our model. The model simulations suggest that an increase in sunny days promotes a high phytoplankton concentration near the surface but does not necessarily promote an increased abundance of Daphnia. Our model also suggests that a higher proportion of cloudy days would increase Daphnia abundance due to a shift in the vertical distribution of Daphnia populations towards superficial waters. Our results highlight that climate changes in multiple regions will affect animal migrations leading to altered food web dynamics in freshwater ecosystems, and emphasize the potential of membrane computing as a modeling framework for spatially and temporally explicit ecological processes.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Abbaspour, K. C., Yang, J., Maximov, I., Siber, R., Bogner, K., Mieleitner, J., et al. (2007). Modelling hydrology and water quality in the pre-alpine/alpine Thur watershed using SWAT. Journal of Hydrology, 333(2–4), 413–430. https://doi.org/10.1016/j.jhydrol.2006.09.014.

    Article  Google Scholar 

  2. Allan, M. G., Hamilton, D. P., Trolle, D., Muraoka, K., & McBride, C. (2016). Spatial heterogeneity in geothermally-influenced lakes derived from atmospherically corrected Landsat thermal imagery and three-dimensional hydrodynamic modelling. International Journal of Applied Earth Observation and Geoinformation, 50, 106–116. https://doi.org/10.1016/J.JAG.2016.03.006.

    Article  Google Scholar 

  3. Barbuti, R., Bove, P., Milazzo, P., & Pardini, G. (2015). Minimal probabilistic P systems for modelling ecological systems. Theoretical Computer Science, 608(Part 1), 36–56. https://doi.org/10.1016/j.tcs.2015.07.035.

    Article  MathSciNet  MATH  Google Scholar 

  4. Beletsky, D., Schwab, D., Mason, D., Rutherford, E., McCormick, M., Vanderploeg, H., & Janssen, J. (2003). Modeling the transport of larval Yellow Perch in Lake Michigan. In: Estuarine and coastal modeling (pp. 439–454). Reston, VA: American Society of Civil Engineers (2004). https://doi.org/10.1061/40734(145)28

  5. Berec, L. (2002). Techniques of spatially explicit individual-based models: Construction, simulation, and mean-field analysis. Ecological Modelling, 150(1–2), 55–81. https://doi.org/10.1016/S0304-3800(01)00463-X.

    Article  Google Scholar 

  6. Berger, J., Young, J. K., & Berger, K. M. (2008). Protecting migration corridors: Challenges and optimism for Mongolian Saiga. PLoS Biology, 6(7), e165. https://doi.org/10.1371/journal.pbio.0060165.

    Article  Google Scholar 

  7. Besozzi, D., Cazzaniga, P., Pescini, D., & Mauri, G. (2008). Modelling metapopulations with stochastic membrane systems. Biosystems, 91(3), 499–514. https://doi.org/10.1016/j.biosystems.2006.12.011.

    Article  Google Scholar 

  8. Bollens, S. M., Frost, B. W., & Cordell, J. R. (1994). Chemical, mechanical and visual cues in the vertical migration behavior of the marine planktonic copepod Acartia hudsonica. Journal of Plankton Research, 16(5), 555–564. https://doi.org/10.1093/plankt/16.5.555.

    Article  Google Scholar 

  9. Boriss, H., & Gabriel, W. (1998). Vertical migration in Daphnia: The role of phenotypic plasticity in the migration pattern for competing clones or species. Oikos, 83(1), 129. https://doi.org/10.2307/3546553.

    Article  Google Scholar 

  10. Brewer, M. C., Dawidowicz, P., & Dodson, S. I. (1999). Interactive effects of fish kairomone and light on Daphnia escape behavior. Journal of Plankton Research, 21(7), 1317–1335. https://doi.org/10.1093/plankt/21.7.1317.

    Article  Google Scholar 

  11. Burns, C. W. (1969). Relation between filtering rate, temperature, and body size in four species of Daphnia. Limnology and Oceanography, 14(5), 693–700. https://doi.org/10.4319/lo.1969.14.5.0693.

    Article  Google Scholar 

  12. Cao, J., Guan, W., Truesdell, S., Chen, Y., & Tian, S. (2016). An individual-based probabilistic model for simulating fisheries population dynamics. Aquaculture and Fisheries, 1, 34–40. https://doi.org/10.1016/j.aaf.2016.10.001.

    Article  Google Scholar 

  13. Cardona, M., Colomer, M. A., Margalida, A., Palau, A., Pérez-Hurtado, I., Pérez-Jiménez, M. J., & Sanuy, D. (2011). A computational modeling for real ecosystems based on P systems. In: Natural computing (Vol. 1, pp. 39–53). Springer. https://doi.org/10.1007/s11047-010-9191-3.

  14. Cerco, C. F. (1995). Simulation of long-term trends in Chesapeake Bay eutrophication. Journal of Environmental Engineering, 121(4), 298–310. https://doi.org/10.1061/(ASCE)0733-9372(1995)121:4(298).

    Article  Google Scholar 

  15. Cerco, C. F., & Meyers, M. (2000). Tributary refinements to Chesapeake Bay Model. Journal of Environmental Engineering, 126(2), 164–174. https://doi.org/10.1061/(ASCE)0733-9372(2000)126:2(164).

    Article  Google Scholar 

  16. Chau, K. W., & Jin, H. (1998). Eutrophication model for a Coastal Bay in Hong Kong. Journal of Environmental Engineering, 124(7), 628–638. https://doi.org/10.1061/(ASCE)0733-9372(1998)124:7(628).

    Article  Google Scholar 

  17. Ciencialová, L., Csuhaj-Varjú, E., Cienciala, L., & Sosík, P. (2019). P colonies. Journal of Membrane Computing, 1(3), 178–197. https://doi.org/10.1007/s41965-019-00019-w.

    Article  MathSciNet  MATH  Google Scholar 

  18. Colomer, M., Lavín, S., Marco, I., Margalida, A., Pérez-Hurtado, I., Pérez-Jiménez, M., Sanuy, D., Serrano, E., & Valencia-Cabrera, L. (2011). Modeling population growth of Pyrenean chamois (Rupicapra p. pyrenaica) by using p-systems. In: M. Gheorghe, T. Hinze, G. Păun, G. Rozenberg, A. Salomaa (Eds.) Membrane Computing, Lecture Notes in Computer Science (Vol. 6501, pp. 144–159). Berlin: Springer. https://doi.org/10.1007/978-3-642-18123-8_13.

  19. Colomer, M. A., Margalida, A., & Pérez-Jiménez, M. J. (2013). Population dynamics P aystem (PDP) models: A standardized protocol for describing and applying novel bio-inspired computing tools. PLoS ONE, 8(4), e60698. https://doi.org/10.1371/journal.pone.0060698.

    Article  Google Scholar 

  20. Colomer, M. A., Margalida, A., Sanuy, D., & Pérez-Jiménez, M. J. (2011). A bio-inspired computing model as a new tool for modeling ecosystems: The avian scavengers as a case study. Ecological Modelling, 222(1), 33–47. https://doi.org/10.1016/j.ecolmodel.2010.09.012.

    Article  Google Scholar 

  21. Colomer, M. A., Margalida, A., Valencia, L., & Palau, A. (2014). Application of a computational model for complex fluvial ecosystems: The population dynamics of zebra mussel Dreissena polymorpha as a case study. Ecological Complexity, 20, 116–126. https://doi.org/10.1016/j.ecocom.2014.09.006.

    Article  Google Scholar 

  22. Colomer-Cugat, M. A., García-Quismondo, M., Macías-Ramos, L. F., Martínez-del Amor, M. A., Pérez-Hurtado, I., Pérez-Jiménez, M. J., Riscos-Núñez, A., & Valencia-Cabrera, L. (2014). Membrane system-based models for specifying dynamical population systems (pp. 97–132). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-03191-0_4.

  23. Cooke, S. L., Williamson, C. E., Leech, D. M., Boeing, W. J., & Torres, L. (2008). Effects of temperature and ultraviolet radiation on diel vertical migration of freshwater crustacean zooplankton. Canadian Journal of Fisheries and Aquatic Sciences, 65(6), 1144–1152. https://doi.org/10.1139/F08-039.

    Article  Google Scholar 

  24. Coumou, D., & Rahmstorf, S. (2012). A decade of weather extremes. Nature Climate Change, 2(7), 491. https://doi.org/10.1038/nclimate1452.

    Article  Google Scholar 

  25. Dodson, S. (1990). Predicting diel vertical migration of zooplankton. Limnology and Oceanography, 35(5), 1195–1200. https://doi.org/10.4319/lo.1990.35.5.1195.

    Article  Google Scholar 

  26. Dodson, S. I., Tollrian, R., & Lampert, W. (1997). Daphnia swimming behavior during vertical migration. Tech. Rep. 8. https://academic.oup.com/plankt/article-abstract/19/8/969/1471878.

  27. Eiane, K., & Parisi, D. (2001). Towards a robust concept for modelling zooplankton migration. Sarsia, 86(6), 465–475. https://doi.org/10.1080/00364827.2001.10420486.

    Article  Google Scholar 

  28. Elert, E. V., & Pohnert, G. (2000). Predator specificity of kairomones in diel vertical migration of Daphnia: a chemical approach. Oikos, 88(1), 119–128. https://doi.org/10.1034/j.1600-0706.2000.880114.x.

    Article  Google Scholar 

  29. Fiksen, Ø. (1997). Allocation patterns and diel vertical migration: Modeling the optimal Daphnia. Ecology, 78(5), 1446–1456. https://doi.org/10.1890/0012-9658(1997)078[1446:APADVM]2.0.CO;2.

    Article  Google Scholar 

  30. Fischer, J. M., Nicolai, J. L., Williamson, C. E., Persaud, A. D., & Lockwood, R. S. (2006). Effects of ultraviolet radiation on diel vertical migration of crustacean zooplankton: An in situ mesocosm experiment. Hydrobiologia, 563(1), 217–224. https://doi.org/10.1007/s10750-005-0007-x.

    Article  Google Scholar 

  31. García-Quismondo, M. (2014). Modelling and simulation of real-life phenomena in membrane computing. Ph.D. thesis, Department of Computer Science and Artificial Intelligence. University of Sevilla.

  32. García-Quismondo, M., Martínez-del-Amor, M. A., & Pérez-Jiménez, M. J. (2015). Probabilistic guarded P systems, a new formal modelling framework. Lecture Notes in Computer Science, 8961(1), 194–214.

    MathSciNet  MATH  Google Scholar 

  33. García-Quismondo, M., Levin, M., & Lobo, D. (2017). Modeling regenerative processes with membrane computing. Information Sciences, 381, 229–249. https://doi.org/10.1016/j.ins.2016.11.017.

    Article  Google Scholar 

  34. García-Quismondo, M., Reed, J. M., Chew, F. S., del Amor, M. A. M., & Pérez-Jiménez, M. J. (2017). Evolutionary response of a native butterfly to concurrent plant invasions: Simulation of population dynamics. Ecological Modelling, 360, 410–424. https://doi.org/10.1016/j.ecolmodel.2017.06.030.

    Article  Google Scholar 

  35. Gin, K. Y. H., Zhang, Q. Y., Chan, E. S., & Chou, L. M. (2001). Three-dimensional ecological-eutrophication model for Singapore. Journal of Environmental Engineering, 127(10), 928–937. https://doi.org/10.1061/(ASCE)0733-9372(2001)127:10(928).

    Article  Google Scholar 

  36. van Gool, E., & Ringelberg, J. (1997). The effect of accelerations in light increase on the phototactic downward swimming of Daphnia and the relevance to diel vertical migration. Journal of Plankton Research, 19(12), 2041–2050. https://doi.org/10.1093/plankt/19.12.2041.

    Article  Google Scholar 

  37. Grimm, V. (1999). Ten years of individual-based modelling in ecology: What have we learned and what could we learn in the future? Ecological Modelling, 115(2), 129–148. https://doi.org/10.1016/S0304-3800(98)00188-4.

    Article  Google Scholar 

  38. Grimm, V., Wyszomirski, T., Aikman, D., & Uchmański, J. (1999). Individual-based modelling and ecological theory: Synthesis of a workshop. Ecological Modelling, 115(2), 275–282. https://doi.org/10.1016/S0304-3800(98)00186-0.

    Article  Google Scholar 

  39. Han, B. P., & Straškraba, M. (2001). Control mechanisms of diel vertical migration: Theoretical assumptions. Journal of Theoretical Biology, 210(3), 305–318. https://doi.org/10.1006/JTBI.2001.2307.

    Article  Google Scholar 

  40. Hansson, L. A., & Hylander, S. (2009). Size-structured risk assessments govern Daphnia migration. Proceedings of the Royal Society B: Biological Sciences, 276(276), 331–336. https://doi.org/10.1098/rspb.2008.1088.

    Article  Google Scholar 

  41. Hays, G. C. (2003). A review of the adaptive significance and ecosystem consequences of zooplankton diel vertical migrations. Hydrobiologia, 503(1–3), 163–170. https://doi.org/10.1023/B:HYDR.0000008476.23617.b0.

    Article  Google Scholar 

  42. Hoellein, T. J., Bruesewitz, D. A., & Hamilton, D. P. (2012). Are geothermal streams important sites of nutrient uptake in an agricultural and urbanising landscape (Rotorua, New Zealand)? Freshwater Biology, 57(1), 116–128. https://doi.org/10.1111/j.1365-2427.2011.02702.x.

    Article  Google Scholar 

  43. Huntley, B., Collingham, Y. C., Green, R. E., Hilton, G. M., Rahbek, C., & Willis, S. G. (2006). Potential impacts of climatic change upon geographical distributions of birds. Ibis, 148, 8–28. https://doi.org/10.1111/j.1474-919X.2006.00523.x.

    Article  Google Scholar 

  44. Hylander, S., Larsson, N., & Hansson, L. A. (2009). Zooplankton vertical migration and plasticity of pigmentation arising from simultaneous UV and predation threats. Limnology and Oceanography, 54(2), 483–491. https://doi.org/10.4319/lo.2009.54.2.0483.

    Article  Google Scholar 

  45. Juayong, R. A. B., & Adorna, H. N. (2020). A survey of results on evolution-communication P systems with energy. Journal of Membrane Computing, 2(1), 59–69. https://doi.org/10.1007/s41965-020-00034-2.

    Article  MathSciNet  Google Scholar 

  46. Kessler, K., & Lampert, W. (2004). Depth distribution of Daphnia in response to a deep-water algal maximum: The effect of body size and temperature gradient. Freshwater Biology, 49(4), 392–401. https://doi.org/10.1111/j.1365-2427.2004.01190.x.

    Article  Google Scholar 

  47. Laaksonen, T., Ahola, M., Eeva, T., Väisänen, R., & Lehikoinen, E. (2006). Climate change, migratory connectivity and changes in laying date and clutch size of the pied flycatcher. Oikos, 114(2), 277–290. https://doi.org/10.1111/j.2006.0030-1299.14652.x.

    Article  Google Scholar 

  48. Lampert, W. (1989). The adaptive significance of diel vertical migration of zooplankton. Functional Ecology, 3(1), 21. https://doi.org/10.2307/2389671.

    Article  Google Scholar 

  49. Leporati, A., Manzoni, L., Mauri, G., Porreca, A. E., & Zandron, C. (2020). Shallow laconic P systems can count. Journal of Membrane Computing, 2(1), 49–58. https://doi.org/10.1007/s41965-020-00032-4.

    Article  MathSciNet  Google Scholar 

  50. Loose, C. J., & Dawidowicz, P. (1994). Trade-offs in diel vertical migration by zooplankton: The costs of predator avoidance. Ecology, 75(8), 2255. https://doi.org/10.2307/1940881.

    Article  Google Scholar 

  51. Morozov, A. Y., Petrovskii, S. V., & Nezlin, N. P. (2007). Towards resolving the paradox of enrichment: The impact of zooplankton vertical migrations on plankton systems stability. Journal of Theoretical Biology, 248(3), 501–511. https://doi.org/10.1016/J.JTBI.2007.05.028.

    Article  MathSciNet  MATH  Google Scholar 

  52. Orellana-Martín, D., Valencia-Cabrera, L., Riscos-Núñez, A., & Pérez-Jiménez, M. J. (2019). Minimal cooperation as a way to achieve the efficiency in cell-like membrane systems. Journal of Membrane Computing, 1(2), 85–92. https://doi.org/10.1007/s41965-018-00004-9.

    Article  MathSciNet  MATH  Google Scholar 

  53. Park, R. A., Clough, J. S., & Wellman, M. C. (2008). AQUATOX: Modeling environmental fate and ecological effects in aquatic ecosystems. Ecological Modelling, 213(1), 1–15. https://doi.org/10.1016/j.ecolmodel.2008.01.015.

    Article  Google Scholar 

  54. Pinheiro, J., Bates, D., DebRoy, S., & Sarkar, D. (2017). R Core Team: nlme: Linear and nonlinear mixed effects models. https://cran.r-project.org/package=nlme.

  55. Păun, G. (2000). Computing with membranes. Journal of Computer and System Sciences, 61(1), 108–143. https://doi.org/10.1006/jcss.1999.1693.

    Article  MathSciNet  MATH  Google Scholar 

  56. R Core Team. (2017). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing. https://www.r-project.org/.

  57. Ramos-Jiliberto, R., & González-Olivares, E. (2000). Relating behavior to population dynamics: A predator-prey metaphysiological model emphasizing zooplankton diel vertical migration as an inducible response. Ecological Modelling, 127(2–3), 221–233. https://doi.org/10.1016/S0304-3800(99)00214-8.

    Article  Google Scholar 

  58. Richards, S. A., Possingham, H. P., & Noye, J. (1996). Diel vertical migration: modelling light-mediated mechanisms. Journal of Plankton Research, 18(12), 2199–2222. https://doi.org/10.1093/plankt/18.12.2199.

    Article  Google Scholar 

  59. Rinke, K., & Petzoldt, T. (2003). Modelling the effects of temperature and food on individual growth and reproduction of Daphnia and their consequences on the population level. Limnologica - Ecology and Management of Inland Waters, 33(4), 293–304. https://doi.org/10.1016/S0075-9511(03)80024-5.

    Article  Google Scholar 

  60. Rinke, K., Petzoldt, T. (2008). Individual-based simulation of diel vertical migration of Daphnia: A synthesis of proximate and ultimate factors. Limnologica - Ecology and Management of Inland Waters 38(3-4), 269–285. https://doi.org/10.1016/j.limno.2008.05.006. http://linkinghub.elsevier.com/retrieve/pii/S0075951108000297.

  61. Rose, K. C., Williamson, C. E., Fischer, J. M., Connelly, S. J., Olson, M., Tucker, A. J., et al. (2012). The role of ultraviolet radiation and fish in regulating the vertical distribution of Daphnia. Limnology and Oceanography, 57(6), 1867–1876. https://doi.org/10.4319/lo.2012.57.6.1867.

    Article  Google Scholar 

  62. Ryabov, A. B. (2012). Phytoplankton competition in deep biomass maximum. Theoretical Ecology, 5(3), 373–385. https://doi.org/10.1007/s12080-012-0158-0.

    Article  Google Scholar 

  63. Samanta, S., Alquran, M., & Chattopadhyay, J. (2015). Existence and global stability of positive periodic solution of tri-trophic food chain with middle predator migratory in nature. Applied Mathematical Modelling, 39(15), 4285–4299. https://doi.org/10.1016/j.apm.2014.12.044.

    Article  MathSciNet  MATH  Google Scholar 

  64. Samanta, S., & Chattopadhyay, J. (2013). Effect of kairomone on predator-prey dynamics—A delay model. International Journal of Biomathematics, 06(05), 1350035. https://doi.org/10.1142/S1793524513500356.

    Article  MathSciNet  MATH  Google Scholar 

  65. Song, B., Li, K., Orellana-Martín, D., Valencia-Cabrera, L., & Pérez-Jiménez, M. J. (2020). Cell-like P systems with evolutional symport/antiport rules and membrane creation. Information and Computation,. https://doi.org/10.1016/j.ic.2020.104542.

    Article  MathSciNet  MATH  Google Scholar 

  66. Sydeman, W. J., García-Reyes, M., Schoeman, D. S., Rykaczewski, R. R., Thompson, S. A., Black, B. A., et al. (2014). Climate change and wind intensification in coastal upwelling ecosystems. Science, 345(6192), 77–80. https://doi.org/10.1126/science.1251635.

    Article  Google Scholar 

  67. Visser, M. E., Perdeck, A. C., van Balen, J. H., & Both, C. (2009). Climate change leads to decreasing bird migration distances. Global Change Biology, 15(8), 1859–1865. https://doi.org/10.1111/j.1365-2486.2009.01865.x.

    Article  Google Scholar 

  68. Wetzel, R. G. (2001). Limnology: Lake and river ecosystems. San Diego: Academic Press.

    Google Scholar 

  69. Wilcove, D. S., & Wikelski, M. (2008). Going, going, gone: Is animal migration disappearing. PLoS Biology, 6(7), e188. https://doi.org/10.1371/journal.pbio.0060188.

    Article  Google Scholar 

  70. Williamson, C. E., Fischer, J. M., Bollens, S. M., Overholt, E. P., & Breckenridge, J. K. (2011). Toward a more comprehensive theory of zooplankton diel vertical migration: Integrating ultraviolet radiation and water transparency into the biotic paradigm. Limnology and Oceanography, 56(5), 1603–1623. https://doi.org/10.4319/lo.2011.56.5.1603.

    Article  Google Scholar 

  71. Williamson, C. E., Zepp, R. G., Lucas, R. M., Madronich, S., Austin, A. T., Ballaré, C. L., et al. (2014). Solar ultraviolet radiation in a changing climate. Nature Climate Change, 4(6), 434–441. https://doi.org/10.1038/nclimate2225.

    Article  Google Scholar 

  72. Xu, H., Paerl, H. W., Qin, B., Zhu, G., Hall, N. S., & Wu, Y. (2015). Determining critical nutrient thresholds needed to control harmful cyanobacterial blooms in Eutrophic Lake Taihu, China. Environmental Science & Technology, 49(2), 1051–1059. https://doi.org/10.1021/es503744q.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Jefferson Project at Lake George, which is a collaboration between Rensselaer Polytechnic Institute, IBM, and The FUND for Lake George. The funding sources had no involvement in the model design, implementation and simulation, the writing of this article, or in the decision to submit this article for publication.

Author information

Authors and Affiliations

  1. Research Group on Natural Computing, University of Sevilla, ETS Ingeniería Informática. Av. Reina Mercedes, s/n, 41012, Sevilla, Spain

    Manuel García-Quismondo

  2. Darrin Fresh Water Institute, Rensselaer Polytechnic Institute, 110 8th Street, 307 MRC, Troy, NY, 12180, USA

    Manuel García-Quismondo, William D. Hintz, Matthew S. Schuler & Rick A. Relyea

Authors
  1. Manuel García-Quismondo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William D. Hintz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Matthew S. Schuler
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rick A. Relyea
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manuel García-Quismondo.

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 128 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

García-Quismondo, M., Hintz, W.D., Schuler, M.S. et al. Modeling diel vertical migration with membrane computing. J Membr Comput 3, 35–50 (2021). https://doi.org/10.1007/s41965-020-00038-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41965-020-00038-y

Keywords

Search

Navigation