Anatomical Distribution of Diarrhetic Shellfish Toxins (DSTs) in the Japanese Scallop Patinopecten yessoensis and Individual Variability in Scallops and Mytilus edulis Mussels: Statistical Considerations.

Diarrhetic shellfish toxins (DSTs) are a group of phycotoxins that include okadaic acid (OA)/dinophysistoxin (DTX) analogues. At present, detailed data on the distribution of DST is insufficient, and studies of the appropriate sample sizes are lacking. This study investigated the DST frequency distribution in scallops and mussels by liquid chromatography-tandem mass spectrometry (LC/MS/MS) and a resampling analysis of existing data was carried out. The DST population-interval and the necessary sample size were also estimated. DSTs are localized in the scallop digestive-gland, and the DST concentrations in scallops were water-depth-dependent. DST concentrations in scallops and mussels showed normal distributions, but mussels tended to contain more DSTs than scallops. In the statistical resampling analysis of the acquired data on scallops and mussels, especially that using the bootstrap method, sample size was difficult to estimate when the DST variation was large. Although the DST population-interval could be statistically estimated from the sample standard deviation of three samples, the sample size corresponded to the risk management level, and the use of 13 or more samples was preferable. The statistical methods used here to analyze individual contents and estimate population content-intervals could be applied in various situations and for shellfish toxins other than DSTs.

A novel growth function incorporating the effects of reproductive energy allocation.

Ontogenetic growth functions provide basic information in biological and ecological studies. Various growth functions classified into the Pütter model have been used historically, regardless of controversies over their appropriateness. Here, we present a novel growth function for fish and aquatic organisms (generalised q-VBGF) by considering an allocation schedule of allometrically produced surplus energy between somatic growth and reproduction. The generalised q-VBGF can track growth trajectories in different life history strategies from determinate to indeterminate growth by adjusting the value of the 'growth indeterminacy exponent' q. The timing of maturation and attainable body size can be adjusted by the 'maturation timing parameter' τ while maintaining a common growth trajectory before maturation. The generalised q-VBGF is a comprehensive growth function in which exponentials in the traditional monomolecular, von Bertalanffy, Gompertz, logistic, and Richards functions are replaced with q-exponentials defined in the non-extensive Tsallis statistics, and it fits to actual data more adequately than these conventional functions. The relationship between the estimated parameter values τ and rq forms a unique hyperbola, which provides a new insight into the continuum of life history strategies of organisms.

On the analytical solution for the Pütter-Bertalanffy growth equation.

This study develops the basic idea of Pütter and Bertalanffy addressing the allometric scaling of anabolism and catabolism on somatic growth dynamics. We proposed a standardized form of the Pütter-Bertalanffy equation (PBE), which is given as the extended model of Richards function, and subsequently solved it. The analytical solution of the PBE was defined by an incomplete beta function and can take a wide range of shapes in its growth curve. The mathematical behavior of PBE due to the change in parameter values was briefly discussed. Most forms of solution consistently hold the implicit functional type with respect to the variable of body size.