Our associated genetics research has been focused primarily on ensuring that the fish released for replenishment do not have a significant negative impact on the natural population.
Wilson, S. K. et al. Climatic forcing and larval dispersal capabilities shape the replenishment of fishes and their habitat-forming biota on a tropical coral reef.
Among the yellowfin tuna that predominate in the area, these are the younger fish that are vital to replenishment.
The practical significance of studying the order-1 periodic solution is that it provides the possibility to determine the replenishment rate of prey fish and the harvesting rate of predator fish, which makes the impulsive control to be not a real-time monitoring of fisheries, but rather a periodic one.
Denote F as the total profit in one period of system (7), which is a function of replenishment rate of prey fish (tau_{h}) and the harvesting rate of predator fish (q_{h}).
The optimization problem is solved to yield the optimal threshold (h^), which results in the optimal replenishment rate of prey fish (tau^=p_{h^), the optimal harvesting rate of predator fish (q^=q_{h^), and the optimal impulse period (T^=T tau^, q^)).
In order to maintain the ecological balance of fisheries, further determine the optimal replenishment rate of prey fish and the optimal harvesting rate of predator fish, and make sure the harvest period is shortest and the profit is highest, we consider the following optimization problem to find the optimal threshold.
From Figure 10, the optimal threshold is (h^=5), then the optimal replenishment rate of prey fish (tau ^=1.2977), the optimal harvesting rate of predator fish (q^=0.5583), and the optimal impulse period is (T^=1.2767).
Almany, G. R., Berumen, M. L., Thorrold, S. R., Planes, S. & Jones, G. P. Local replenishment of coral reef fish populations in a marine reserve.
Saenz Agudelo, P., Jones, G. P., Thorrold, S. R. & Planes, S. Connectivity dominates larval replenishment in a coastal coral reef fish metapopulation.
