Mathieu Doray

A geostatistical method for assessing biomass of tuna aggregations around moored fish aggregating devices with star acoustic surveys

Universal kriging was used to model the spatio-temporal variability in the acoustic density of tuna aggregations recorded during star echosounding surveys around moored fish aggregating devices (FADs) in Martinique (Lesser Antilles). The large-scale deterministic drift in the tuna spatial distribution was modeled using an advection–diffusion equation applied to animal grouping. Residuals from the drift were modeled as a random component with small-scale spatial correlation. An estimation variance formula was derived from this deterministic–statistical mixed model to assess the mean precision of density estimates of daytime tuna aggregation. The mean relative error obtained with our star design for daytime surveys was 24%. The methodology was applied to estimate daily maxima of tuna biomass around moored FADs during four monthly sea cruises. The daily peak of tuna biomass aggregated around moored FADs was 9 t on average (standard deviation = 4). Estimation variances for different survey designs were compared for optimizing sampling strategy. Resume:

A Geostatistical Definition of Hotspots for Fish Spatial Distributions

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.

Indicator-Based Geostatistical Models For Mapping Fish Survey Data

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.