Mapping fish length histograms
Steps of the procedure used for mapping
The geostatistical computations were perform with the R package RGeostats freely available at http://rgeostats.free.fr
The different steps of the procedure were the following
1. Read the data file containing the sardine length distribution at each trawl haul station
1.1 Define a polygon encompassing the data outside which there will be no mapping
2. Work on the positive hauls (no. fish >40)
2.1 Fit the experimental distributions at each point with a linear combination of Legendre polynomials.
The choice of the number of polynomials used a goodness of fit criteria. The results are values of coefficients for each polynomial at each point. These are the data to be mapped by co-kriging.
2.2 Map the coefficients
2.2.1 Adjust a co-variogram for the coefficients with the R function model.auto()
2.2.2 Define a grid for mapping by co-kriging.
2.2.3 Define a moving neighbourhood for mapping.
2.2.4 Map the coefficients by co-kriging with the R function kriging()
2.2.5 Deduce the length distribution at each grid node from the estimated coefficients and the Legendre polynomials
2.3 Map the absence/presence data on the same grid and with the same neighbourhood
2.3.1 Define the indicator of presence: 1 when no. fish>40 and 0 otherwise
2.3.2. Adjust a variogram with the R function model.auto()
2.3.3 perform kriging with the R function kriging()
2.4 Save the results of 2.2.5 and 2.3.3 at each grid node
The covariograms between coefficients are fitted with a nugget effect and three spherical structures
The variograms for presence/absence are fitted with a nugget effect and two spherical structures
The grid has a mesh size of 0.25 x 0.25 decimal degrees square
The moving neighbourhood is a disk with a maximum radius of 80 nautical miles (except for sardine in Juvena where it is 30 the fish being coastal), containing 2 sample points at minimum and 12 at maximum with 3 sample points at maximum per quadrant.