Table 1 Notation used in this paper

i

Grid cell. Each grid cell is divided into nine nested grids. See Fig. 1 for the location of grid cell i.

s

Fish stock

a _i

The swept (trawled) area in grid cell i

T _i

The area of grid cell i. See Appendix Table 4 for the area of grid cell i.

y _si

Number (or weight) of fish stock s, caught by a standard trawl in one of the nine nested grids in grid cell i. This quantity is defined as the sampling unit.

N

The total number of possible tows in the population area.

Y _s

The survey index (in number) of a fish stock s.

B _s

The survey index (in weight) of a fish stock s.

d _si

Differences between successive sampling units, i.e., d_si = y_{s, i + 1} − y_si.

n

The number of the entire tows, which is the sample size.

^

In this paper, the hat notation is the expected value of a random variable, e.g., \( \widehat{Y_s}\equiv \)E{Y_s}