Mathematical Geosciences

, Volume 48, Issue 1, pp 65–77 | Cite as

A Geostatistical Definition of Hotspots for Fish Spatial Distributions

  • Pierre Petitgas
  • Mathieu Woillez
  • Mathieu Doray
  • Jacques Rivoirard
Special Issue


Research surveys at sea are undertaken yearly to monitor the distribution and abundance of fish stocks. In the survey data, a small number of high fish concentration values are often encountered, which denote hotspots of interest. But statistically, they are responsible for important uncertainty in the estimation. Thus understanding their spatial predictability given their surroundings is expected to reduce such uncertainty. Indicator variograms and cross-variograms allow to understand the spatial relationship between values above a cutoff and the rest of the distribution under that cutoff. Using these tools, a “top” cutoff can be evidenced above which values are spatially uncorrelated with their lower surroundings. Spatially, the geometric set corresponding to the top cutoff corresponds to biological hotspots, inside which high concentrations are contained. The hotspot areas were mapped using a multivariate kriging model, considering indicators in different years as covariates. The case study considered here is the series of acoustic surveys Pelgas performed in the Bay of Biscay to estimate anchovy and other pelagic fish species. The data represent tonnes of fish by square nautical mile along transects regularly spaced. Top cutoffs were estimated in each year. The areas of such anchovy hotspots are then mapped by co-kriging using all information across the time series. The geostatistical tools were adapted for estimating hotspot habitat maps and their variability, which are key information for the spatial management of fish stocks. Tools used here are generic and will apply in many engineering fields where predicting high concentration values spatially is of interest.


Hotspots Indicators Non-linear geostatistics  Multivariate geostatistics Anchovy Biscay 



We are thankful to the crew of R/V Thalassa for operating the vessel during the annual surveys and to P. Duhamel, P. Grellier and M. Rabiller technicians at Ifremer for their work with the biological and acoustic data. We would like to thank the reviewers and the editor for their comments which improved the manuscript.


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Copyright information

© International Association for Mathematical Geosciences 2015

Authors and Affiliations

  • Pierre Petitgas
    • 1
  • Mathieu Woillez
    • 2
  • Mathieu Doray
    • 1
  • Jacques Rivoirard
    • 3
  1. 1.IFREMERResearch Unit EMHNantesFrance
  2. 2.IFREMERResearch Unit STHPlouzanéFrance
  3. 3.MINES ParisTech, Centre for Geosciences and GeoengineeringPSL Research UniversityFontainebleauFrance

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