A model for competition between the golden mussel and its genetically modified version
DOI:
https://doi.org/10.35819/remat2024v10iespecialid7077Keywords:
mathematical modeling, competition model, population dynamics, stability analysis, biomathematicsAbstract
The presence of the invasive golden mussel in Brazilian waters brings ecological or economic consequences. An alternative and promising populational control is the immersion of a genetically modified species with the aim of, upon contact with wild mollusks, producing infertile generations. A proposed mathematical model that encompasses such competition becomes important, as it can provide information to guide future experiments. However, the competition model requires a well-established growth dynamics. This work presents two models for the dynamics of wild mussels, studied analytically. The study exposes equilibrium solutions, their local stability at stationary points, and a sensitivity analysis of the basic reproduction numbers (R_0's). Through these results, the most suitable model for incorporating competition components is defined. Numerical simulations are performed to gauge possible competition outcomes, using the fourth-order Runge-Kutta method. The study is able to present two important conclusive points: that eradication can be achieved through planned competition and that there is a need for competitive advantages for the strategy to work. This study highlights the need for competitive advantages for the modified mussel. Among the possible advantages, the study indicates reproductive efficiency and the mortality rate of the modified mussel as the most promising ones. Given such an important topic, this work is necessary for this population control strategy to be studied and tested to assist in the development of the modified species in a way that respects ecology.
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