Numerical modeling of pre-spawning and spawning migrations of the representative of the family hexagrammidae: the case of the arabesque greenling

This paper presents a spatio-temporal model of greenling dynamics during pre-spawning and spawning mass migrations. The developed model is based on original verified long-term observations and data on industrial fishing in the Peter the Great Bay (Sea of Japan), and the equations of the dynamics of the density of males/females and the mass daily movements of fish are written in terms of the transfer equations. These equations are written in the form of the modified Patlak-Keller-Segel equations, according to which the flow of objects/substances is directed along the gradients of stimulus introduced. It is believed that in the pre-spawning season, adaptation in morpho-physiological (biochemical thermoregulation and a number of other endogenous processes) and behavioral responses of fish to sufficiently long and energy-consuming spawning can occur, where the stimulus for mass movements of fish is optimal environmental conditions for spawning events. During the spawning period, selected sites will be found in convenient and well-aerated embayments located at the bottom of reservoir in the coastal area. Modeling of stimuli-related movements is performed based on information about the preferred water depths of the fish's pre-spawning area and relevant features relating to a selection of suitable bedding sites. It is assumed that the intensity of daily motion is proportional to their linear size (the larger the fish becomes, the faster it is). The equations for the spawning stage take into account the spatial competition of males, but in natural conditions it is observed only in the vicinity of spawning areas. Being away from these areas, males continued to look for new sites good for the spawn. For females, their movement is provoked by males that assembled in schools, the signal of which can be certain chemical elements released by males (for example, mucus secretion from males) or visual contact. The diffusion of fish distribution and the viscosity of the habitat (velocity diffusion) are taken into account. The initial distribution of fish is given according to the average distribution of fish in July over a long-term observation period in the Peter the Great Bay.

fish migration, spawning, Patlak-Keller-Segel equations, adaptation zone