Um estudo hipotético baseado em modelos de crescimento e competição para a dinâmica populacional do mexilhão dourado

Abstract

The presence of the invasive golden mussel in Brazilian waters represents a series of impacts, whether ecological or economic. Given this scenario, an alternative for population control is promising: the immersion of a genetically modified species to produce, in contact with the

wild mollusc, future infertile generations. Thus, a proposal for a mathematical model that con- templates such competition becomes of great value, since it can provide information to guide

laboratory experiments. However, the competition model needs a well-established growth dy- namic. Therefore, this work presents two models for the dynamic of wild mussels, which will

be studied analytically and numerically. The analytical study exposes the equilibrium solutions,

their local stability at stationary points and a sensitivity analysis of the basal reproduction num- bers (R0’s). Through the sensitivity of the parameters that compose the R0’s, one of the growth

models is chosen to receive the competition parcels. Once a more adequate model is defined, a

system of ordinary differential equations is proposed to model the competition with the modi- fied mussel. Numerical simulations are performed for the system of equations in order to assess

possible outcomes of the competition, using the fourth order Runge-Kutta method. The study presents two important conclusive points: eradication can be achieved and there is a need for

competitive advantages for the strategy to work. The sensitivity of the parameters and the nu- merical approximation of the competition model attest that greater reproductive efficiency and

a modified mussel less susceptible to predation are the most promising advantages. Finally, in

view of such an important topic, this work is necessary so that this population control strat- egy can be studied and tested to help the development of the modified species and respect the ecology.