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Construction of Optimal Feedback for Zooplankton Diel Vertical Migration

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Advances in Optimization and Applications (OPTIMA 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1739))

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Abstract

We consider the optimization problem of forming the fittest strategy for zooplankton diel vertical migration. This strategy should maximize the fitness function reflecting the average specific rate of population reproduction. We solve this problem using feedback between the current environmental state and the organism’s local movement. Such feedback reflects the ability of living organisms to adapt to changing habitat conditions. We construct the feedback on the base of the neural network. Its input is the values of environmental factors at a given point and a given time; its output is the corresponding local displacement of zooplankton. The initial optimization problem is reduced to the optimization of the feedback settings or to the optimal choice of the neural network weights. To train the neural network, we apply the new evolution method of stochastic global optimization: Survival of the Fittest by Differential Evolution (SoFDE), based on the Survival of the Fittest algorithm and Differential Evolution. It was shown that this approach permits to form the optimal behavioral strategy for different environmental conditions.

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References

  1. Archibald, K.M., Siegel, D.A., Doney, S.C.: Modeling the impact of zooplankton diel vertical migration on the carbon export flux of the biological pump. Global Biogeochem. Cycles 33(2), 181–199 (2019)

    Article  Google Scholar 

  2. Arcifa, M.S., Perticarrari, A., Bunioto, T.C., Domingos, A.R., Minto, W.J.: Microcrustaceans and predators: diel migration in a tropical lake and comparison with shallow warm lakes. Limnetica 35(2), 281–296 (2016)

    Google Scholar 

  3. Baioletti, M., Di Bari, G., Milani, A., Poggioni, V.: Differential evolution for neural networks optimization. Mathematics 8(1) (2020)

    Google Scholar 

  4. Birch, J.: Natural selection and the maximization of fitness. Biol. Rev. Camb. Philos. Soc. 91(3), 712–727 (2015)

    Article  Google Scholar 

  5. Brest, J., Maucec, M.S., Bošković, B.: The 100-digit challenge: algorithm jDE100. In: 2019 IEEE Congress on Evolutionary Computation (CEC), pp. 19–26 (2019)

    Google Scholar 

  6. Buesseler, K.O., et al.: Revisiting carbon flux through the ocean’s twilight zone. Science 316(5824), 567–570 (2007)

    Article  Google Scholar 

  7. Clark, C., Mangel, M.: Dynamic State Variable Models in Ecology. Oxford University Press (2000)

    Google Scholar 

  8. Danovaro, R., et al.: Implementing and innovating marine monitoring approaches for assessing marine environmental status. Front. Mar. Sci. 3 (2016)

    Google Scholar 

  9. Ducklow, H.W., Steinberg, D.K., Buesseler, K.O.: Upper ocean carbon export and the biological pump. Oceanography 14(4), 50–58 (2001)

    Article  Google Scholar 

  10. Fiksen, O., Giske, J.: Vertical distribution and population dynamics of copepods by dynamic optimization. ICES J. Mar. Sci. 52, 483–503 (1995)

    Article  Google Scholar 

  11. Gabriel, W., Thomas, B.: Vertical migration of zooplankton as an evolutionarily stable strategy. Am. Nat. 132(2), 199–216 (1988)

    Article  Google Scholar 

  12. Gavrilets, S.: Fitness Landscapes and the Origin of Species (MPB-41). Princeton University Press, Princeton (2004)

    Book  Google Scholar 

  13. Godø, O.R., et al.: Marine ecosystem acoustics (MEA): quantifying processes in the sea at the spatio-temporal scales on which they occur. ICES J. Mar. Sci. 71(8), 2357–2369 (2014)

    Article  Google Scholar 

  14. Gorban, A.N.: Selection theorem for systems with inheritance. Math. Model. Nat. Phenom. 2(4), 1–45 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Guerra, D., et al.: Zooplankton diel vertical migration in the Corsica channel (North-Western Mediterranean sea) detected by a moored acoustic doppler current profiler. Ocean Sci. 15(3), 631–649 (2019)

    Article  Google Scholar 

  16. Häfker, N.S., Meyer, B., Last, K.S., Pond, D.W., Hüppe, L., Teschke, M.: Circadian clock involvement in zooplankton diel vertical migration. Curr. Biol. 27(14), 2194–2201 (2017)

    Article  Google Scholar 

  17. Hays, G.C.: A review of the adaptive significance and ecosystem consequences of zooplankton diel vertical migrations. Hydrobiologia 503(1), 163–170 (2003)

    Article  Google Scholar 

  18. Isla, A., Scharek, R., Latasa, M.: Zooplankton diel vertical migration and contribution to deep active carbon flux in the NW Mediterranean. J. Mar. Syst. 143, 86–97 (2015)

    Article  Google Scholar 

  19. Ismailov, V.E.: On the approximation by neural networks with bounded number of neurons in hidden layers. J. Math. Anal. Appl. 417(2), 963–969 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kaelo, P., Ali, M.M.: Some variants of the controlled random search algorithm for global optimization. J. Optim. Theory Appl. 130(2), 253–264 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Kaiser, M., et al.: Marine Ecology: Processes, Systems and Impacts. Oxford University Press, Oxford (2011)

    Google Scholar 

  22. Kuzenkov, O., Morozov, A.: Towards the construction of a mathematically rigorous framework for the modelling of evolutionary fitness. Bull. Math. Biol. 81(11), 4675–4700 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  23. Kuzenkov, O.A., Grishagin, V.A.: Global optimization in Hilbert space. In: AIP Conference Proceedings, vol. 1738, no. 1, p. 400007 (2016)

    Google Scholar 

  24. Lampert, W.: The adaptive significance of diel vertical migration of zooplankton. Funct. Ecol. 3(1), 21–27 (1989)

    Article  Google Scholar 

  25. Lee, E.B., Lawrence, M.: Foundations of Optimal Control Theory (1967)

    Google Scholar 

  26. Lippmann, R.: An introduction to computing with neural nets. IEEE ASSP Mag. 4(2), 4–22 (1987)

    Article  Google Scholar 

  27. Morozov, A., Kuzenkov, O.A., Arashkevich, E.G.: Modelling optimal behavioural strategies in structured populations using a novel theoretical framework. Sci. Rep. 9(1), 15020 (2019)

    Article  Google Scholar 

  28. Morozov, A.Y., Kuzenkov, O.A.: Towards developing a general framework for modelling vertical migration in zooplankton. J. Theor. Biol. 405, 17–28 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  29. Morozov, A.Y., Kuzenkov, O.A., Sandhu, S.K.: Global optimisation in Hilbert spaces using the survival of the fittest algorithm. Commun. Nonlinear Sci. Numer. Simul. 103, 106007 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  30. Parvinen, K., Dieckmann, U., Heino, M.: Function-valued adaptive dynamics and the calculus of variations. J. Math. Biol. 52(1), 1–26 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  31. Price, K., Storn, R., Lampinen, J.: Differential Evolution: A Practical Approach to Global Optimization (2005)

    Google Scholar 

  32. Price, W.L.: A controlled random search procedure for global optimisation. Comput. J. 20, 367–370 (1977)

    Article  MATH  Google Scholar 

  33. Price, W.L.: Global optimization by controlled random search. J. Optim. Theory Appl. 40, 333–348 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  34. Ringelberg, J.: Diel Vertical Migration of Zooplankton in Lakes and Oceans, pp. 1–9. Springer, Dordrecht (2010)

    Google Scholar 

  35. Santos, C., Gonçalves, M., Hernández Figueroa, H.E.: Designing novel photonic devices by bio-inspired computing. IEEE Photonics Technol. Lett. 22, 1177–1179 (2010)

    Article  Google Scholar 

  36. Sergeyev, Y.D., Grishagin, V.A.: Parallel asynchronous global search and the nested optimization scheme. J. Comput. Anal. Appl. 3(2), 123–145 (2001)

    MathSciNet  MATH  Google Scholar 

  37. Sergeyev, Y.D., Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-Filling Curves. Springer, New York (2013)

    Book  MATH  Google Scholar 

  38. Storn, R., Price, K.: Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341–359 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  39. Strongin, R.G., Sergeyev, Y.D.: Global Optimization with Non-convex Constraints: Sequential and Parallel Algorithms (2000)

    Google Scholar 

  40. He, X., Xu, S.: Feedback process neural networks. In: He, X., Xu, S. (eds.) Process Neural Networks, pp. 128–142. Springer, Cham (2010). https://doi.org/10.1007/978-3-540-73762-9_6

    Chapter  Google Scholar 

  41. Zhigljavsky, A., Žilinskas, A.: Stochastic Global Optimization. Springer, Cham (2008)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Lobachevsky State University, Gagarin Avenue 23, 603950, Nizhny Novgorod, Russia

    O. Kuzenkov & D. Perov

Authors
  1. O. Kuzenkov
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  2. D. Perov
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Corresponding author

Correspondence to O. Kuzenkov .

Editor information

Editors and Affiliations

  1. FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  4. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  5. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

  6. FRC CSC RAS, Moscow, Russia

    Igor Pospelov

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Kuzenkov, O., Perov, D. (2022). Construction of Optimal Feedback for Zooplankton Diel Vertical Migration. In: Olenev, N., Evtushenko, Y., Jaćimović, M., Khachay, M., Malkova, V., Pospelov, I. (eds) Advances in Optimization and Applications. OPTIMA 2022. Communications in Computer and Information Science, vol 1739. Springer, Cham. https://doi.org/10.1007/978-3-031-22990-9_10

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  • DOI: https://doi.org/10.1007/978-3-031-22990-9_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22989-3

  • Online ISBN: 978-3-031-22990-9

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