Bivariate swimbladder size allometry properties of mesopelagic fish and bioacoustic prediction

Abstract

One of the fundamental problems in modeling the low‐frequency contributions to scattering strength of swimbladder fish is to transform a measured or theoretical size‐depth distribution h(l|z) for an individual species to the corresponding distribution q(R|z) of equivalent swimbladder radius R. This is usually done using a y‐on‐x regression line relation for the species, where y = 1n R, x = 1n l, and l = fish standard length. Analysis of archival Ocean Acre swimbladder size allometry data for 38 species indicates that this procedure is physically inadequate. Due to biological variability, a wide range of R values is associated with a fish of length l. Since resonance scattering from gas‐filled swimbladders is depth dependent, important scattering contributions may come from fish with bladder sizes R not lying on the regression line. To avoid systematic prediction errors, the x,y distribution p (x,y) rather than the regression line must be used to calculate q(R|z). This transformation problem and its modeling consequences are examined in light of the fact that p(x,y) for many swimbladder species has been found to be bivariate normal.