Article Preview
TopIntroduction
Determining the fish growth parameters plays a fundamental role not only in the correct detection of the fish stock age and size structure, but also in the process of stock assessment procedure, studies of the population dynamics and sustainable stock management in terms of fish stock exploitation restrictions or specific recommendations for minimum limits on the size (length) of species to be caught legally, selectivity of the fishing gears and equipment, etc. Historic data on growth parameters estimates has been successfully used as a basis for analysis of the stock biological development over time in addition to the analysis of the impact of environmental factors – food availability, variability in specific environmental conditions, such as water temperature, the concentration of dissolved oxygen, the types of species interactions and others. Several functions have been developed to model the growth of fish (Gompertz growth model, Schnute-Richards, logistic, etc.), however the von Bertalanffy model is the most popular and is in the scope of the present material.
The von Bertalanffy mathematical model of individual-based approach to predicting fish growth expresses the length as a function of the age of the fish
(1) where:
is the age of the respective fish,
- is the asymptotic length (or mean length of the cohort at age equal to infinity when the study refers to population dynamics),
is a curvature parameter which shows how fast a given individual approaches its asymptotic (finite) length,
– is the initial condition parameter (determining the point in which the length of the fish is =0) (Cadima, 2003, Sparre & Venema, 1998).
Equation (1) has three unknown coefficients , and , to be determined analytically on the basis of given experimental data (i.e. the length and age measurements of the species under analysis). A great number of methods for estimating von Bertalanffy growth parameters have been successfully implemented in practice, with their main disadvantage being the requirement for regularity of the corresponding measurements. Failure to collect and process the data on a regular basis distorts the results of the methods discussed so far except for the Gulland-and-Holt plot, and what is more, they usually provide estimates for only 2 of the 3 unknown parameters (Sparre & Venema, 1998), with the exception of (Melnikova, 2009).
Norbert Winner and Ludwig von Brtalanffy conclusively proved in their works the existence of close similarities in the operation and control of the machines and the living organisms. It follows, therefore, that the common principles, methods and approaches developed for the analysis and control of large technical systems can be successfully modified or adapted in the research and modeling of biological objects and systems. The System theory and more specifically the development of the System identification scientific area appear to be very suitable theoretical basis for further improvement and elaboration of the object/system modeling methods and principles (Eykhoff, 1974; Genov, 2004; Hoffman & Frankel, 2001; Soderstrom & Stoica, 1989).