Indicator-Based Geostatistical Models For Mapping Fish Survey Data

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.

Spatial variations, origins, and risk assessments of polycyclic aromatic hydrocarbons in French soils

“…Current sources of PAHs, such as road traffic, local industries, and residential emissions (household heating; Cachada et al, 2012a;Gateuille et al, 2014a;Lohmann et al, 2000), as well as legacy contamination due to former industries (Bertrand et al, 2015;Pies et al, 2007), could contribute to soil PAH content. However, precise source identification and apportionment cannot be done based only on PAH molecular diagnostic ratios, which only provide information about pyrogenic, petrogenic, or mixed PAHs in soils (Brändli et al, 2008;Tobiszewski and Namieśnik, 2012;Yunker et al, 2014).…”

“…These factors are the spatial counterpart of the standard principal component analysis (PCA), and their mapping could help regionalise the origin of PAHs and estimate the risk using alternate nonlinear methods such as discrete disjunctive kriging. Finally, other fingerprinting methods involving new analyses, such as carbon isotopes (Kim et al, 2008;Petrišič et al, 2013; or alkyl PAHs (Morales-Caselles et al, 2017;Yuan et al, 2015), could be used to complete source identification and apportionment.…”

Analysing Temporal Variability in Spatial Distributions Using Min–Max Autocorrelation Factors: Sardine Eggs in the Bay of Biscay

“…In fisheries ecology, MAFs have been applied on multiple time series in one-dimension (Fujiwara and Mohr 2009;Woillez et al 2009) to extract the most continuous common patterns in time, and in geographical space in two-dimensions (Petitgas et al 2018) to perform kriging with a discrete approach. This study extends the application of MAFs to the analysis of space-time data.…”

“…Higher order MAFs (i> q) showing variograms with high nugget effects, were not considered for mapping the data series. Considering that they carried noise and not locally significant information, mapping without these components was then more robust (Petitgas et al 2018). Kriging in a particular year relied on the spatially structured MAFs (the spatial patterns common to all years) and their time-varying amplitudes.…”

Geostatistical tools to assess shifts in recreational fishing

“…Fishing and its impacts are known to change spatially and temporally (Petitgas et al 2003;Kleisner et al 2010); however, this has been documented mainly for commercial fisheries. Spatial modelling approaches using recreational fishing data were initially investigated in 2010 (Parnell et al 2010); however, spatio-temporal modelling has been limited, with few studies exploring survey data (Tao et al 2012;Aidoo et al 2015Aidoo et al , 2016Winfield 2016;Petitgas et al 2018;Polansky et al 2018;Navarro et al 2020). Understanding these spatial and temporal shifts is important because sharing of the stock and fishing grounds in a multi-sector fishery could potentially cause a particular species or area to be overexploited.…”