Journal of Coastal Conservation

, Volume 23, Issue 1, pp 71–91 | Cite as

Improved allometric proxies for eelgrass conservation

  • A. Montesinos-López
  • E. Villa-Diharce
  • H. Echavarría-HerasEmail author
  • C. Leal-Ramírez


Current anthropogenic influences threaten the permanence of eelgrass, a relevant macrophyte that brings about important ecological benefits including nursery for waterfowl and fish species, shoreline stabilization, nutrient recycling and carbon sequestration. Eelgrass restoration normally involves transplanted plots and monitoring success requires noninvasive assessments of standing stock and productivity. Allometric scaling of eelgrass leaf biomass and length can provide proxies for these assessments, but accuracy of allometric projections is mainly resultant of uncertainty propagation of parameters, so for the sake of suitability it is very important ensuring the most accurate estimates. The traditional approach for producing estimates of allometric parameters considers a linear regression model involving logarithms of the original response and explanatory variables along with a normally distributed additive error. The suitability of this method has been questioned on the ground of biased results raising nonlinear regression as a necessary amendment. Here we demonstrate that this controversy can be surpassed allowing for a logistic error structure and heteroscedasticity in the traditional method. The present arrangement delivered parameter estimates from raw data surpassing inconveniences of the traditional fitting procedure. Moreover, associated allometric proxies for average leaf biomass in shoots entailed similar reproducibilities than produced by using nonlinear regression and quality controlled data. In achieving suitable accuracy levels, the present approach required a sample of raw data of about 9% of involved in prior estimations based on quality controlled data. The improvements associated to the present approach grant highly consistent non-destructive assessments for the sake of eelgrass conservation.


Eelgrass conservation Allometric scaling Eelgrass leaf biomass Traditional analysis method of allometry Logistically distributed error term Heteroscedasticity 



Completion of this work was achieved while Enrique Villa (CVU:208964) was on a sabbatical leave at Centro de Investigación Científica y de Educación Superior de Ensenada, partially funded by a grant from México’s Consejo Nacional de Ciencia y Tecnología.


  1. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control AC-19:716–723Google Scholar
  2. Blackburn T, Nedwell D, Wiebe W (1994) Active mineral cycling in a Jamaican seagrass sediment. Mar Ecol Prog Ser 110(2-3):233–239Google Scholar
  3. Campbell ML, Paling EI (2003) Evaluating vegetative transplant success in posidonia australis: a field trial with habitat enhancement. Mar Pollut Bull 46(7):828–834Google Scholar
  4. Costanza R, d’Arge R, De Groot R, Farber S, Grasso M, Hannon B, Limburg K, Naeem S, O’neill RV, Paruelo J et al (1997) The value of the world’s ecosystem services and natural capital. Nature 387:253–260Google Scholar
  5. Duan N (1983) Smearing estimate: a nonparametric retransformation method. J Am Stat Assoc 78:605–610Google Scholar
  6. Dubey SD (1969) A new derivation of the logistic distribution. Naval Research Logistics Quarterly 16(1):37–40Google Scholar
  7. Echavarría-Heras H, Leal-Ramírez C, Villa-Diharce E, Cazarez-Castro NR (2015) 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(1):1–21Google Scholar
  8. Echavarría-Heras H, Lee KS, Solana-Arellano E, Franco-Vizcano E (2011) Formal analysis and evaluation of allometric methods for estimating above-ground biomass of eelgrass. Ann Apl Biol 159(2011):503–515Google Scholar
  9. Echavarría-Heras H, Solana-Arellano E, Leal-Ramírez C, Vizcaino EF (2013) An allometric method for measuring leaf growth in eelgrass, Zostera marina, using leaf length data. Bot Mar 56(3):275–286Google Scholar
  10. Filgueira R, Labarta U, Fernndez-Reiriz MJ (2008) Effect of condition index on allometric relationships of clearance rate in Mytilus galloprovincialis Lamarck, 1819. Revista de Biologa Marina y Oceanografa 43(2):391–398Google Scholar
  11. Fishman JR, Orth RJ, Marion S, Bieri J (2004) A comparative test of mechanized and manual transplanting of eelgrass, Zostera marina, in Chesapeake bay. Restor Ecol 12(2):214–219Google Scholar
  12. Genoud RDMM, Hemelrijk CK (2005) Problems of allometric scaling analysis: examples from mammalian reproductive biology. J Exp Biol 2008(1):1731–1747Google Scholar
  13. Grech A, Chartrand-Miller K, Erftemeijer P, Fonseca M, McKenzie L, Rasheed M, Taylor H, Coles R (2012) A comparison of threats, vulnerabilities and management approaches in global seagrass bioregions. Environ Res Lett 7(2):024006(8pp)Google Scholar
  14. Gumbel EJ (1944) Ranges and midranges. Ann Math Stat 15(4):414–422Google Scholar
  15. Harris LA, Duarte CM, Nixon SW (2006) Allometric laws and prediction in estuarine and coastal ecology. Estuar Coasts 29(2):340–344Google Scholar
  16. Henry M, Picard N, Trotta C, Manlay R, Valentini R, Bernoux M, Saint-Andr L (2011) Estimating tree biomass of Sub-Saharan African forests: a review of available allometric equations. Silva Fennica 45 (3B):477–569Google Scholar
  17. Holmquist J, Powell G, Sogard S (1989) Decapod and stomatopod assemblages on a system of seagrass-covered mud banks in Florida bay. Mar Biol 100(4):473–483Google Scholar
  18. Hui D, Jackson RB (2007) Uncertainty in allometric exponent estimation: a case study in scaling metabolic rate with body mass. J Theor Biol 249(1):168–177Google Scholar
  19. Jacobs R (1979) Distribution and aspects of the production and biomass of eelgrass, Zostera marina l., at Roscoff, France. Aquat Bot 7:151–172Google Scholar
  20. Kaitaniemi P (2008) How to derive biological information from the value of the normalization constant in allometric equations. PLoS ONE 3(4):e1932Google Scholar
  21. Kalbfleisch JG (1985) Probability and statistical inference, volume 2: statistical inference, 2nd edn. Springer, BerlinGoogle Scholar
  22. Kennedy H, Beggins J, Duarte CM, Fourqurean JW, Holmer M, Marbá N, Middelburg JJ (2010) Seagrass sediments as a global carbon sink: isotopic constraints. Glob Biogeochem Cycles 24(4):GB4026Google Scholar
  23. Kerkhoff AJ, Enquist BJ (2009) Multiplicative by nature: logarithmic transformation in allometry. J Theor Biol 257(3):519–521Google Scholar
  24. Lin LI-K (1989) A concordance correlation coefficient to evaluate reproducibility. Biometrics 45(1):255–268Google Scholar
  25. Lin LI-K (1992) Assay validation using the concordance correlation coefficient. Biometrics 48(2):599–604Google Scholar
  26. Liu X, Zhou Y, Yang H, Ru S (2013) Eelgrass detritus as a food source for the sea cucumber apostichopus Japonicus Selenka (echinidermata: Holothuroidea) in coastal waters of north china: an experimental study in flow-through systems. PLoS ONE 8(3):e58293Google Scholar
  27. Marquet PA, Quiñones RA, Abades S, Labra F, Tognelli M, Arim M, Rivadeneira M (2005) Scaling and power-laws in ecological systems. J Exp Bio 208:1749–1769Google Scholar
  28. Mascaro J, Litton CM, Hughes RF, Uowolo A, Schnitzer SA (2011) Minimizing bias in biomass allometry: model selection and log-transformation of data. Biotropica 43(6):649–653Google Scholar
  29. Mascaro J, Litton CM, Hughes RF, Uowolo A, Schnitzer SA (2014) Is logarithmic transformation necessary in allometry? ten, one-hundred, one-thousand-times yes. Biol J Linn Soc 111(1):230–233Google Scholar
  30. McBride GB (2005) A proposal for strength-of-agreement criteria for lins concordance correlation coefficient. NIWA Client Report HAM2005-062, National Institute of Water and Atmospheric Research, Hamilton, New ZeelandGoogle Scholar
  31. McLachlan GJ, Krishnan T (2008) The EM algorithm and etensions, 2nd edn. Wiley, New YorkGoogle Scholar
  32. McRoy CP (1970) Standing stocks and other features of eelgrass (Zostera marina) populations on the coast of Alaska. Fish Res Board Can 27(10):1811–1821Google Scholar
  33. Meeker WQ, Escobar LA (1998) Statistical methods for reliability data. New York, WileyGoogle Scholar
  34. Montague CL, Ley JA (1993) A possible effect of salinity fluctuation on abundance of benthic vegetation and associated Fauna in northeastern Florida bay. Estuaries 16(4):703–717Google Scholar
  35. Nadarajah S (2004) Information matrix for logistic distributions. Math Comput Model 40:953–958Google Scholar
  36. Newman M (1993) Regression analysis of log-transformed data: statistical bias and its correction. Environ Toxicol 12:1129–1113Google Scholar
  37. Newman M (2005) Power laws, pareto distributions and Zipf’s law. Contemp Phys 46(5):323–351Google Scholar
  38. Orth RJ, Harwell MC, Fishman JR (1999) A rapid and simple method for transplanting eelgrass using single, unanchored shoots. Aquat Bot 64(1):77–85Google Scholar
  39. Packard GC (2009) On the use of logarithmic transformations in allometric analyses. J Theor Biol 257 (3):515–518Google Scholar
  40. Packard G. C (2013, 06) Is logarithmic transformation necessary in allometry? Biol J Linn Soc 109(2):476–486Google Scholar
  41. Packard GC, Birchard GF (2008) Traditional allometric analysis fails to provide a valid predictive model for mammalian metabolic rates. J Exp Biol 211(22):3581–3587Google Scholar
  42. Packard GC, Boardman TJ (2008) Model selection and logarithmic transformation in allometric analysis. Physiol Biochem Zool 81(4):496–507Google Scholar
  43. Park S-R, Li W-T, Kim S-H, Kim J-W, Lee K-S (2010) A comparison of methods for estimating the productivity of Zostera marina. J Ecol Environ 33(1):59–65Google Scholar
  44. Phillips R (1974) Temperate grass flats, vol 2. Conservation Foundation, Washington, pp 244–299Google Scholar
  45. Plummer ML, Harvey CJ, Anderson LE, Guerry AD, Ruckelshaus MH (2013) The role of eelgrass in marine community interactions and ecosystem services: results from ecosystem-scale food web models. Ecosystems 16(2):237–251Google Scholar
  46. Polson NG, Scott JG, Windle J (2013) Bayesian inference for logistic models using Pólya -gamma latent variables. J Am Stat Assoc 108(504):1339–1349Google Scholar
  47. Savage VM, Gillooly JF, Woodruff WH, West GB, Allen AP, Enquist BJ, Brown JH (2004) The predominance of quarter-power scaling in biology. Funct Ecol 18(2):257–282Google Scholar
  48. Short FT, Coles RG, Pergent-Martini C (2001) Global seagrass distribution. In: Short FT, Short CA, Coles RG (eds) Global seagrass research methods, chap 1. Elsevier Science, Amsterdam, pp 5–30Google Scholar
  49. Short FT, Neckles HA (1999) The effects of global climate change on seagrasses. Aquat Bot 63(3):169–196Google Scholar
  50. Solana-Arellano E, Echavarria-Heras H, Gallegos-Martinez M (2003) Improved leaf area index based biomass estimation for Zostera marina l. Mathematical Medicine and Biology 20(4):367–375Google Scholar
  51. Stefanski LA (1990) A normal scale mixture representation of the logistic distribution. Stat Probab Lett 11:69–70Google Scholar
  52. Team RC (2015) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, AustriaGoogle Scholar
  53. Unsworth RK, van Keulen M, Coles RG (2014) Seagrass meadows in a globally changing environment. Mar Pollut Bull 83(2):383– 386Google Scholar
  54. Villa ER, Escobar LA (2006) Using moment generating functions to derive mixture distributions. The American Statistician 60 (1):75–80Google Scholar
  55. West GB, Brown JH (2005) The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization. J Exp Biol 208:1575–1592Google Scholar
  56. Williams R (1973) Nutrient level and phytoplankton productive in the estuary. In: Chabreck R (ed) Proceedings of the coastal Marsh and estuary management symposium, vol 59. Louisiana State University, Baton RougeGoogle Scholar

Copyright information

© The Author(s) 2018
corrected publication August/2018

Authors and Affiliations

  • A. Montesinos-López
    • 1
  • E. Villa-Diharce
    • 2
  • H. Echavarría-Heras
    • 3
    Email author
  • C. Leal-Ramírez
    • 3
  1. 1.Departamento de MatemáticasCentro Universitario de Ciencias Exactas e Ingenierías (CUCEI)GuadalajaraMéxico
  2. 2.Centro de Investigación en MatemáticasValencianaMexico
  3. 3.Centro de Investigación Cientifica y de Estudios Superiores de EnsenadaFraccionamiento Zona PlayitasMexico

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