The Numerical Model of Fish Growth Dynamics (On the Example of Okhotsk Atka Mackerel Pleurogrammus azonus)

Abstract

A complex model of the system is proposed, the dynamic variables of which are the length, fish’s weight and the weight of its food lump. The model’s mathematical formalization is performed in terms of the ordinary differential equations apparatus. The solution to the parametric identification problem of the model is based on the author's representative sample for long-term observations. Computational experiments show that the representation of the indicators dynamics fish’s weight, length and the weight of the food lump is determined by some functions of the components from this set. The hierarchy of relationships between indicators determines the structure of these functions. It turned out that the dynamics of length is practically independent of the food lump’s weight, which in this case is an external energy source of the body’s vital activity. The energy “mediator” is body weight. The dynamics of body weight is determined by the weight of the food lump and the actual body weight. The negative coefficient calculated when solving the problem of parametric identification with body weight reduces the intensity of its dynamics. It seems that this coefficient reflects the expenditure of the body on the processes of its metabolism. The dynamics of length has a cumulative character (only positive gains). The body weight dynamics is determined by the accumulation and loss of vital activity of organic matter (positive and negative gains). The jump in the dynamics of weight is due to the high energy costs of fish for the intensive formation of reproductive products in the pre-spawning period and the energy costs of subsequent spawning. The dynamics of the food lump depends on the weight of the fish and is regulated by seasonal endogenous and exogenous rhythms of the fish's life cycle. Weight gain largely determines the intensity of nutrition than the diet determines the rate of weight growth. A measure of the adequacy between the model and sample distributions here is the correlation coefficient between them. In the case under consideration, it is close to its maximum (single) value, which indicates their high proximity.