Bivariate Normal Swimbladder Size Allometry Models and Allometric Exponents for 38 Mesopelagic Swimbladdered Fish Species Commonly Found in the North Sargasso Sea

Abstract

With x and y log-transformed fish standard length/and equivalent swimbladder radius R, respectively, probability density distributions p(x,y) for mesopelagic swimbladdered fish species are assumed to be bivariate normal. From archival measurements, models are developed for 36 nonregressive species, 2 regressive species, and selected species groups found off Bermuda. Statistical tests suggest the hypothesis is valid for many of these species, and that failures are due largely to small sample variability and bias in the available data. Marked differences between regression, major axis, and reduced major axis allometric exponents, which sometimes occur when x,y correlation is low, are explained. A dimensionless allometric law R′* = k* (l′*)m involving structural variables l′* and R′* scaled to lmax is used to compare specific swimbladder growth trends. Major axis estimates of m* and k* for the nonregressive species group are each lognormally distributed with respective means [Formula: see text] and [Formula: see text]. A structural relation model for this group based on the hypothesis that swimbladder wall area grows approximately as the first power of fish volume or mass is verified. Last, detailed buoyancy properties are calculated for 6 nonregressive species with bivariate normal (x,w*)-distributions, where w* is the logarithm of percentage swimbladder volume.