A Takagi–Sugeno-Kang Fuzzy Model Formalization of Eelgrass Leaf Biomass Allometry with Application to the Estimation of Average Biomass of Leaves in Shoots: Comparing the Reproducibility Strength of the Present Fuzzy and Related Crisp Proxies

  • Hector Echavarria-HerasEmail author
  • Cecilia Leal-Ramirez
  • Juan Ramón Castro-Rodríguez
  • Enrique Villa Diharce
  • Oscar Castillo
Part of the Studies in Computational Intelligence book series (SCI, volume 749)


The identification of the functional relationship that regulates the variation of individual leaf biomass in terms of related area in eelgrass, allows the derivation of convenient proxies for a nondestructive estimation of the average biomass of the leaves in shoots. The concourse of these assessment methods is fundamental for assessing the performance of restoration efforts for this species that are based on transplanting techniques. Prior developments proposed proxies for a nondestructive estimation of aforementioned average biomass of leaves in shoots derived from allometric models for the dependence of leaf biomass in terms of linked area. The reproducibility power of these methods is highly dependent on analysis method and data quality. Indeed, previous results show that allometric proxies for average biomass of leaves in shoots produced by parameter estimates fitted from quality controlled data via nonlinear regression yield the highest reproducibility strength. Nevertheless, the use of data processing entails subtleties mainly related to the subjectivity of the criteria for the rejection of inconsistent replicates in raw data. Here we introduce efficient- data quality control- free surrogates derived from a first order Takagi-Sugeno-Kang fuzzy model aimed to approximate the mean response of eelgrass leaf biomass depending on associated area. A comparison of the performances of the allometric and the fuzzy model constructs identified using available raw data shows that the Takagi-Sugeno-Kang paradigm for individual leaf biomass in terms of related area produced the most precise proxies for observed average biomass of leaves in shoots. The present results show how gains derived from the outstanding approximation capabilities of the first order Takagi-Sugeno-Kang fuzzy model for the nonlinear dynamics can be extended to the realm of eelgrass allometry.


Eelgrass conservation Nondestructive assessments Allometric models Takagi-Sugeno-Kang fuzzy model 


  1. 1.
    R.M. McCloskey, R.K.F. Unworthy, Decreasing seagrass density negatively influences associated fauna, vol. 3 (PeerJ, 2015), p. e1053Google Scholar
  2. 2.
    M.L. Plummer, C.J. Harvey, L.E. Anderson, A.D. Guerry, M.H. Ruckelshaus, The role of eelgrass in marine community interactions and ecosystem services: results from ecosystem-scale food web models. Ecosystems 16(2), 237–251 (2013)CrossRefGoogle Scholar
  3. 3.
    E.I. Paling, M. Fonseca, M.M. van Katwijk, M. van Keulen, Seagrass restoration, ed. by M.E. Gerardo, E.W. Perillo, R.C. Donald, M.B. Mark. Coastal Wetlands: An Integrated Ecosystem Approach, 1st edn. (Elsevier Science, 2009) pp. 1–62Google Scholar
  4. 4.
    W.T. Li, Y.K. Kim, J.I. Park, X.M. Zhang, G.Y. Du, K.S. Lee, Comparison of seasonal growth responses of Zostera marina transplants to determine the optimal transplant season for habitat restoration. Ecol. Eng. 71, 56–65 (2014)CrossRefGoogle Scholar
  5. 5.
    M.S. Fonseca, Addy revisited: what has changed with seagrass restoration in 64 years? Ecol. Restor. 29(1–2), 73–81 (2011)CrossRefGoogle Scholar
  6. 6.
    H. Echavarría-Heras, C. Leal-Ramírez, E. Villa-Diharce, E. Montiel-Arzate, On the appropriateness of an allometric proxy for nondestructive estimation of average biomass of leaves in shoots of eelgrass (Zostera marina). Submitted, (2017)Google Scholar
  7. 7.
    H.A. Echavarría-Heras, C. Leal-Ramírez, E. Villa-Diharce, N.R. Cazarez-Castro, The effect of parameter variability in the allometric projection of leaf growth rates for eelgrass (Zostera marina L.) II: the importance of data quality control procedures in bias reduction. Theor. Biol. Med. Model. 12(30), 2015Google Scholar
  8. 8.
    S.L. Chiu, Fuzzy model identification based on cluster estimation. J. Intell. Fuzzy Syst. 2(3), 267–278 (1994)Google Scholar
  9. 9.
    J.R. Castro, O. Castillo, M.A. Sanchez, O. Mendoza, A. Rodríguez-Díaz, P. Melin, Method for higher order polynomial sugeno fuzzy inference systems. Inf. Sci. 351, 76–89 (2016)CrossRefGoogle Scholar
  10. 10.
    L.X. Wang, J.M. Mendel, Fuzzy basis functions, universal approximation, and orthogonal least-squares learning. IEEE Trans. Neural Netw. 3(5), 807–814 (1992)CrossRefGoogle Scholar
  11. 11.
    J.S.R. Jang, C.T. Sun, E.S. Mizutani, Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence (Prentice Hall, USA, 1997)Google Scholar
  12. 12.
    L.I.K. Lin, A concordance correlation coefficient to evaluate reproducibility. Biometrics 45, 255–268 (1989)CrossRefzbMATHGoogle Scholar
  13. 13.
    C. Leal-Ramírez, H.A. Echavarría-Heras, O. Castillo, Exploring the suitability of a genetic algorithm as tool for boosting efficiency in monte carlo estimation of leaf area of eelgrass, ed. by P. Melin, O. Castillo, J. Kacprzyk. Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization. Stud. Comput. Intell. vol. 601, (Springer, 2015) pp. 291–303Google Scholar
  14. 14.
    C. Leys, O. Klein, P. Bernard, L. Licata, Detecting outliers: do not use standard deviation around the mean, use absolute deviation around the median. J. Exp. Soc. Psychol. 49(4), 764–766 (2013)CrossRefGoogle Scholar
  15. 15.
    P.J. Huber, Robust statistics (Wiley, New York, 1981)CrossRefzbMATHGoogle Scholar
  16. 16.
    M. Sugeno, G.T. Kang, Structure identification of fuzzy model. Fuzzy Sets Syst. 28, 15–33 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    J.R. Castro, O. Castillo, P. Melin, A. Rodríguez-Díaz, A hybrid learning algorithm for a class of interval type-2 fuzzy neural networks. Inf. Sci. 179(13), 2175–2193 (2009)CrossRefzbMATHGoogle Scholar
  18. 18.
    D.W. Marquardt, An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    M.K. Transtrum, J.P. Sethna, Improvements to the Levenberg-Marquardt algorithm for nonlinear least-squares minimization. Cornell University, USA, (2012). doi:arXiv:1201.5885
  20. 20.
    S. Jang, ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans. Syst Man Cybern. 23, 665–685 (1993)CrossRefGoogle Scholar
  21. 21.
    D. Hui, R.B. Jackson, Uncertainty in allometric exponent estimation: a case study in scaling metabolic rate with body mass. J TheorBiol 249, 168–177 (2007)MathSciNetGoogle Scholar
  22. 22.
    C. Leal-Ramírez, H.A. Echavarría-Heras, O. Castillo, E. Montiel-Arzate, On the use of parallel genetic algorithms for improving the efficiency of a monte carlo-digital image based approximation of eelgrass leaf area I: comparing the performances of simple and master-slaves structures, ed. by P. Melin, O. Castillo, J. Kacprzyk. Nature-Inspired Design of Hybrid Intelligent Systems, Volume 667 of the series Studies in Computational Intelligence, pp. 431–455, Springer (2016)Google Scholar
  23. 23.
    J. Miller, Reaction time analysis with outlier exclusion: Bias varies with sample size. Q. J. Exp. Psychol. 43(4), 907–912 (1991)CrossRefGoogle Scholar
  24. 24.
    L.I.K. Lin, Assay validation using the concordance correlation coefficient. Biometrics 48, 599–604 (1992)CrossRefGoogle Scholar
  25. 25.
    G.B. McBride, A proposal for strength-of-agreement criteria for lin’s concordance correlation coefficient. NIWA Client Report: HAM2005-062; National Institute of Water & Atmospheric Research: Hamilton, New Zealand, May 2005. Available online:

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Hector Echavarria-Heras
    • 1
    Email author
  • Cecilia Leal-Ramirez
    • 1
  • Juan Ramón Castro-Rodríguez
    • 2
  • Enrique Villa Diharce
    • 3
  • Oscar Castillo
    • 4
  1. 1.Centro de Investigación Científica y de Educación Superior de EnsenadaEnsenadaMexico
  2. 2.Facultad de Ciencias Químicas e IngenieríaUABCTijuanaMexico
  3. 3.Centro de Investigación en MatemáticasGuanajuatoMexico
  4. 4.Instituto Tecnológico de TijuanaTijuanaMexico

Personalised recommendations