Aquatic Sciences

, 81:58 | Cite as

A simple model for the numerical characterization of spatiotemporal variability in aquatic ecosystems

  • Rodrigo Gonzalez-Valencia
  • Felipe Magaña-Rodriguez
  • Armando Sepulveda-Jauregui
  • Teresa Aguirrezabala-Campano
  • Oscar Gerardo-Nieto
  • Frederic ThalassoEmail author
Research Article


Aquatic ecosystems are subject to spatiotemporal variations that are important to quantify and understand for a proper assessment of their diversity and complexity. The objective of the present study was to develop a simple model that gives a numerical value to homogeneity and other spatiotemporal attributes for an easier analysis of aquatic ecosystem structure. The model allows for the comparison among different ecosystems, or different periods of time or zones of a given aquatic ecosystem. The model developed sets a numerical value to homogeneity, establishes the fraction of the ecosystem that contains a given percentage of the total amount of a compound, quantifies the fraction of the aquatic ecosystem in which no detectable levels of the measured compound are found, identifies the fraction of the ecosystem that represents an adequate habitat for a given process, and defines a simplified bidimensional vector of heterogeneity. This model is applicable to the two main maps used in the field of limnology: maps showing a particular parameter over two spatial dimensions, and maps showing a particular parameter over one spatial and one temporal dimension. The model was tested with different parameters obtained from three contrasting aquatic ecosystems, a highly polluted Mexican highland reservoir, a naturally acidic German bog lake, and a mesotrophic Patagonian lake.


Depth-space Depth-time Distribution Homogeneity Maps Methane 

List of symbols


Dead area/section of parameter P

λP, X

Unidimensional (X) dead section of parameter P

ΩP, X, Y

Magnitude of the bidimensional (X, Y) vector of anisotropy for parameter P

ωP, X, Y

Direction of the bidimensional (X, Y) vector of anisotropy for parameter P


Grid cell area


Cumulative normalized grid cell area

\(A_{P}^{\% }\)

Fraction of the map that contains a given percentage (superscript %) of parameter P

\(A_{P,X}^{\% }\)

Unidimensional (X) fraction of a profile, that contains a given percentage (superscript %) of parameter P


Concentration of disolved methane


Concentration of dissolved oxygen



Eh, P

Relative absolute error of homogeneity factor for parameter P


Flux of parameter P


Homogeneity factor of parameter P

hP, X

Unidimensional (X) homogeneity factor of parameter P


Apparent affinity constant for methane


Apparent affinity constant for dissolved oxygen




Cumulative normalized length


Methanotrophic potential


Magnitude of parameter P present in grid cell area


Cumulative normalized magnitude of parameter P


Unidimensional (X) magnitude of parameter P


Unidimensional (X) cumulative normalized magnitude of parameter P





Coefficient of variation


Dissolved oxygen


Inorganic carbon


Lake Grosse Fuchskuhle


Lake Guadalupe


Sampling sites in LG (1–8)


Lake Hambre


Median absolute deviation


Numerical homogeneity model


Relative water column stability


Total carbon


Total nitrogen


Total organic carbon



We gratefully acknowledge Consejo Nacional de Ciencia y Tecnología (Conacyt), Mexico for financial support to Rodrigo Gonzalez-Valencia, Felipe Magana-Rodriguez, and Teresa Aguirrezabala-Campano (Grant nos. 266244, 419562, and 531383, respectively). We also thank Secretaría del Medio Ambiente y Recursos Naturales (Semarnat) for financial support received through project 23661, and Victoria T. Velázquez-Martínez, Juan Corona-Hernández, Francisco Silva-Olmedo, and David Flores-Rojas for technical assistance.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.

Supplementary material

27_2019_652_MOESM1_ESM.docx (660 kb)
Supplementary material 1 (DOCX 659 kb)


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departamento de Biotecnología Y BioingenieríaCinvestavMexico CityMexico
  2. 2.Department of Experimental LimnologyLeibniz Institute of Freshwater Ecology and Inland FisheriesStechlinGermany
  3. 3.University of Magallanes, Faculty of SciencesPunta ArenasChile

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