The measurement error in marine survey catches: the bottom trawl case

We have formulated a model for analyzing the measurement error in marine survey abundance estimates by using data from parallel surveys (trawl haul or acoustic measurement). The measurement error is defined as the component of the variability that cannot be explained by covariates such as temperature, depth, bottom type, etc. The method presented is general, but we concentrate on bottom trawl catches of cod (Gadus morhua). Catches of cod from 10 parallel trawling experiments in the Barents Sea with a total of 130 paired hauls were used to estimate the measurement error in trawl hauls. Based on the experimental data, the measurement error is fairly constant in size on the logarithmic scale and is independent of location, time, and fish density. Compared with the total variability of the winter and autumn surveys in the Barents Sea, the measurement error is small (approximately 2–5%, on the log scale, in terms of variance of catch per towed distance). Thus, the cod catch rate is a fairly precise measure of fish density at a given site at a given time.

Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices

Let A and B be nonsingular M-matrices. A lower bound on the minimum eigenvalue q(B circle A(-1)) for the Hadamard product of A(-1) and B, and a lower bound on the minimum eigenvalue q(A star B) for the Fan product of A and B are given. In addition, an upper bound on the spectral radius rho(A circle B) of nonnegative matrices A and B is also obtained. These bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices A and B. (C) 2009 Elsevier Inc. All rights reserved.