Hybrid Model of the Collapse of the Commercial Crab Paralithodes camtschaticus (Decapoda, Lithodidae) Population of the Kodiak Archipelago

Degradation of commercial populations remains a frequent phenomenon even with the use of methods of stocktaking and control of production volume. In fish farming, the concept of “overfishing” is used with and the signs of this condition are well known. However, the processes leading to the degradation of reserves develope in various ways. According to the theory of nonlinear dynamical systems, several types of crisis development can be classified. Of particular interest are the phenomena of collapse, that is, variants of a rapid decline in numbers, which are unexpected for the organizations controlling the fishery. Immediately before the collapse, the state of the stock can be assessed as relatively stable and it may experience fluctuations. Contrary to expectations, there was no rapid recovery after a rapid reduction in cod, whitefish Coregonus clupeaformis of the Great Lakes, halibut and other valuable species. This paper considers a hybrid model for the collapse of red king crab Paralithodes camtschaticus stocks of the Kodiak archipelago of Alaska with unusual distinctive oscillating dynamics. The computational scenario in a hybrid system with survival and growth equations considers the logic of decision-making in operation management. The scenario differs in that after the fall of catches, the crab population goes into the sporadic fluctuations that do not have a regular character and are not characteristic of the population. The collapse itself occurs after a long interval of fishing while the population is in an unstable mode. The analysis shows that a long species life cycle is not a decisive factor for eliminating the risk of a collapse scenario. The presence of reserve generations does not change the situation qualitatively, the efficiency of their reproduction in crab and cod off the coast of Labrador turned out to be unexpectedly low. The status of stocks of large predators that require seasonal moratoriums on fishing must be regularly checked.