The mathematical study for mortality coefficients of small pelagic species

Abstract

In the past few years, the parapenaeus longirostris population stock has seen a sharp reduction. In this work, we propose a bioeconomic model that represents the biomass evolution of this marine population in two moroccan maritime patches: protected area and unprotected area. In the model construction, we take in consideration the predation interaction between the parapenaeus longirostris population and the small pelagic species of moroccan coastal zones. We suppose the existence of coastal trawlers that exploit both the predator and prey populations. Our objective is to study the influence of the predator mortality rate variation on the evolution of prey biomass and the profit of coastal trawlers. It should be underlined that, coastal trawlers are constrained by the conservation of marine biodiversity. One of the key consequences of this is that the increase in the mortality rate of small pelagics leads to an evolution in the parapenaeus longirostris stock, and consequently to an increase in the profit of coastal trawlers after exploitation of this species. On the other hand, the level of fishing effort and catches of small pelagics is decreasing, which leads to a reduction in the profit of coastal trawlers after exploiting small pelagics.