Estimating the underwater shape of tuna longlines with micro-bathythermographs

An estimation method for the three-dimensional underwater shape of tuna longlines is developed, using measurements of depth obtained from micro-bathythermographs (BTs) attached to the main line at equally spaced intervals. The shape of the main line is approximated by a model which consists of a chain of unit length lines (folding-rule model), where the junction points are placed at the observed depths. Among the infinite number of possible shapes, the most likely shape is considered to be the smoothest one that can be obtained with a numerical optimization algorithm. To validate the method, a series of experimental longline operations were conducted in the equatorial region of the eastern Pacific Ocean, using 13 or 14 micro-BTs per basket of main line. Concurrent observations of oceanographic conditions (currents and temperature structure) were obtained. The shape of the main line can be calculated at arbitrary times during operations. Shapes were consistent with the current structure. On the equator, the line was elevated significantly by the Equatorial Undercurrent. It is shown that the shape of main line depends primarily upon the vertical shear and direction of the current relative to the gear. Time sequences of calculated shapes reveals that observed periodic (1-2 hours) oscillations in depth of the gear was caused by swinging movements of the main line. The shortening rate of the main line is an important parameter for formulating the shape of the longline, and its precise measurement is desirable.

A note on the von Bertalanffy growth function concerning the allocation of surplus energy to reproduction

We propose an extended form of the von Bertalanffy growth function (VBGF), where the allocation of surplus energy to reproduction is considered. Any function can be used in our model to describe the ratio of energy allocation for reproduction to that for somatic growth. As an example, two models for energy allocation were derived: a step-function and a logistic function. The extended model can jointly describe growth in adult and juvenile stages. The change in growth rate between the two stages can be either gradual or steep; the latter gives a biphasic VBGF. The results of curve fitting indicated that a consideration of reproductive energy is meaningful for model extension. By controlling parameter values, our comprehensive model gives various growth curve shapes ranging from indeterminate to determinate growth. An increase in the number of parameters is unavoidable in practical applications of this new model. Additional information on reproduction will improve the reliability of model estimates.

An evaluation of back-calculation methodology using simulated otolith data

I simulated somatic growth and accompanying otolith growth using an individual-based bioenergetics model in order to examine the performance of several back-calculation methods. Four shapes of otolith radius-total length relations (OR-TL) were simulated. Ten different back-calculation equations, two different regression models of radius length, and two schemes of annulus selection were examined for a total of 20 different methods to estimate size at age from simulated data sets of length and annulus measurements. The accuracy of each of the twenty methods was evaluated by comparing the back-calculated length-at-age and the true length-at-age. The best back-calculation technique was directly related to how well the OR-TL model fitted. When the OR-TL was sigmoid shaped and all annuli were used, employing a least squares linear regression coupled with a log-transformed Lee back-calculation equation (y-intercept corrected) resulted in the least error; when only the last annulus was used, employing a direct proportionality back-calculation equation resulted in the least error. When the OR-TL was linear, employing a functional regression coupled with the Lee back-calculation equation resulted in the least error when all annuli were used, and also when only the last annulus was used. If the OR-TL was exponentially shaped, direct substitution into the fitted quadratic equation resulted in the least error when all annuli were used, and when only the last annulus was used. Finally, an asymptotically shaped OR-TL was best modeled by the individually corrected Weibull cumulative distribution function when all annuli were used, and when only the last annulus was used.