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Mathematical Geosciences

, Volume 50, Issue 2, pp 187–208 | Cite as

Indicator-Based Geostatistical Models For Mapping Fish Survey Data

  • Pierre PetitgasEmail author
  • Mathieu Woillez
  • Mathieu Doray
  • Jacques Rivoirard
Special Issue

Abstract

Marine research survey data on fish stocks often show a small proportion of very high-density values, as for many environmental data. This makes the estimation of second-order statistics, such as the variance and the variogram, non-robust. The high fish density values are generated by fish aggregative behaviour, which may vary greatly at small scale in time and space. The high values are thus imprecisely known, both in their spatial occurrence and order of magnitude. To map such data, three indicator-based geostatistical methods were considered, the top-cut model, min–max autocorrelation factors (MAF) of indicators, and multiple indicator kriging. In the top-cut and MAF approaches, the variable is decomposed into components and the most continuous ones (those corresponding to the low and medium values) are used to guide the mapping. The methods are proposed as alternatives to ordinary kriging when the variogram is difficult to estimate. The methods are detailed and applied on a spatial data set of anchovy densities derived from a typical fish stock acoustic survey performed in the Bay of Biscay, which show a few high-density values distributed in small spatial patches and also as solitary events. The model performances are analyzed by cross-validating the data and comparing the kriged maps. Results are compared to ordinary kriging as a base case. The top-cut model had the best cross-validation performance. The indicator-based models allowed mapping high-value areas with small spatial extent, in contrast to ordinary kriging. Practical guidelines for implementing the indicator-based methods are provided.

Keywords

Top-cut MAF Indicators Co-kriging Skewed distribution Anchovy Bay of Biscay Fisheries survey data Aggregation 

Notes

Acknowledgements

We are grateful to the crew of the research vessel Thalassa and to E. Duhamel, F. Sanchez and P. Grellier from Ifremer for preparing the biological and acoustic data. We would also like to thank the referees, whose comments allowed us to improve the manuscript. D. Renard (Mines Paris Tech) helped to improve the English. The work was partly funded by the European Union H2020 project CERES. The data were collected by Ifremer within the French national observation plan, a part of the EU fisheries data collection framework.

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Copyright information

© International Association for Mathematical Geosciences 2018

Authors and Affiliations

  1. 1.IFREMERNantesFrance
  2. 2.IFREMERPlouzanéFrance
  3. 3.Centre de GeosciencesMINES ParisTech, PSL Research UniversityFontainebleauFrance

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