Optimization of Harvesting Fish Return From Norongoza Pond in Mwanjari Ward Southern Division Kabale Municipality. - Nuwaha, Louis (Kabale University, 2024)
The integration of resource biology and ecology with socioeconomic and institutional factors have been used by harvesters and ecologists. Extinction of species in aquatic systems have been studied globally and the study focused on optimization of fish harvest returns. Biological and economic conditions were applied in optimizing the returns in fish pond and the two species fish population was described as x' = F(x,y)and y' = G(x, y). Justification of optimization was done using the equation J(u) = f: g[t, y(t), u(t)]dt. x and y represented the population of tilapia and Nile perch respectively.A prey-predator model was developed and F(x, y), G(x, y) were given by F(x, y) = x(11. - ax - by and G(x,y) = y(µ - cx- dy) respectively . A parameter a was incorporated into the functions in the study. At the equilibrium point, F(x, y) and G(x,y)=0 and it gave one of the equilibrium points as (0,0) that resulted in trivial and unacceptable results to any farmer.t (Q- ax - by) = 0 and (u- cx - dy) = 0 were solved and the equilibrium points were (0,0). (0,%),a/a 0, and (9-" 3-) The equilibrium points were solved and d ad-be a -bc analyzed. More food for the predators was supplied and more breeding grounds for prey population. The most stable equilibrium was denoted by ("bi 3Eh» as a desirable ad-be ad-be equilibrium to any farmer. F(x, y) and G(x, y) were redefined to reflect a prey-predator model relationship that is x' = x(Q- ax + by) +h,(t,x) and y' = y(bx- cy + ) + ht,y). The two functions h1 (t, x) and h2 (t, y) were denoted for the extent of harvesting of tilapia and Nile perch, respectively, by the farmer. The study revealed that the most realistic model is one where h,(t,x) depends on the fishing effort size of the tilapia population while h,(t, y) was assumed to depend on the effort and the size of Nile perch alone that is h,(t,x) = o,h,(x) and h,(t,y) = o, ha(). The interacting species can co-exist in the same environment for example tilapia and mukene in water pond. Competition of two co-existing species can be controlled by providing plenty food supply for one species and in this, the prey was considered and finally the study recommended that optimization of fish harvest returns should be looked at in all fisheries.