Abstract
Trawl survey data with high spatial and seasonal coverage were analysed using a variant of the Log Gaussian Cox Process (LGCP) statistical model to estimate unbiased relative fish densities. The model estimates correlations between observations according to time, space, and fish size and includes zero observations and over-dispersion. The model utilises the fact the correlation between numbers of fish caught increases when the distance in space and time between the fish decreases, and the correlation between size groups in a haul increases when the difference in size decreases. Here the model is extended in two ways. Instead of assuming a natural scale size correlation, the model is further developed to allow for a transformed length scale. Furthermore, in the present application, the spatial- and size-dependent correlation between species was included. For cod (Gadus morhua) and whiting (Merlangius merlangus), a common structured size correlation was fitted, and a separable structure between the time and space-size correlation was found for each species, whereas more complex structures were required to describe the correlation between species (and space-size). The within-species time correlation is strong, whereas the correlations between the species are weaker over time but strong within the year.
Highlights
A survey design was developed to extend the coverage of the standard ICES (International Council for Exploration of the Sea) Baltic International Trawl Survey (BITS; www.ices.dk) during 2009–2012 in the Western Baltic Sea (WBS)
The resulting survey data with high spatial and seasonal coverage for a range of commercially important fish species are analysed with an extended variant of the Log Gaussian Cox Process (LGCP) statistical model [1,2,3]
The spatial correlation parameter was first tested for independence of size and time for each species and both years, and it was found that it was possible to distinguish between the space and size-time correlation
Summary
A survey design was developed to extend the coverage of the standard ICES (International Council for Exploration of the Sea) Baltic International Trawl Survey (BITS; www.ices.dk) during 2009–2012 in the Western Baltic Sea (WBS). The resulting survey data with high spatial and seasonal coverage for a range of commercially important fish species are analysed with an extended variant of the Log Gaussian Cox Process (LGCP) statistical model [1,2,3]. Other studies have presented extensions of the multinomial distribution to account for data dispersion or correlation [7] or have used the geostatistical kriging approach to account for spatial correlations in the observations [8,9]. Kristensen [1] and Lewy and Kristensen [2] estimated North Sea cod distribution patterns with the LGCP model using a statistical approach to determine spatial correlations between observations from surveys according to age. An extension of the model was applied to mackerel (Scombrus scombrus) larvae survey data [11] based on additional temporal co-variance in spatial distributions
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