Author(s): Raquel Figueira; Ramoni Z. S Azevedo; Jose Carlos R. Silva; Anna Regina C. Costa; Dayse H. Pastore; Claudia M. Dias; Charles H. X Barbosa; Isaac P. Santos; Humberto Fortunato

Linked Author(s): Raquel Figueira, Humberto Fortunato

Keywords: Populational dynamics; Mathematical modeling; Invasive species; Navier-Stokes equations; Species distribution modelling

Abstract: In Brazil, the presence of the invasive species Limnoperna fortunei, known as golden mussel, in rivers and reservoirs can result in several impacts on the environment and economic activities. It is particularly common in hydroelectric plant reservoirs and by 2018 it was found in 38% of Brazilian HPPs, representing 55% of the total installed potential in the national energy matrix. It is estimated that, in the electricity sector alone, annual losses add up to more than USD$ 150 million/year in production interruptions and maintenance costs. The population dynamics of wild species is often driven by ecological processes that are difficult to elucidate. Mathematical modeling proves to be a very useful tool for studying the relationship between species and their environment, having the ability to efficiently integrate and evaluate several complex processes simultaneously and, therefore, it is useful in understanding biological phenomena. Aquatic species, in particular, are affected by hydrodynamic patterns which are often poorly studied. The factors that most influence species distribution are water flow, climatic variables, and phytoplankton availability in the environment. The mathematical models in the literature usually only consider mussels related to the dynamics of algae populations, without taking into account the hydrodynamic factors. In this paper, we propose a three-dimensional model of partial differential equations to illustrate the population dynamics of mussels, where we consider the densities of the adult mussels, mussel larvae, and algae which is the main source of mussel food. This model considers water flow as limiting factor for the development of the populations. The study area is the Pereira Barreto channel, in the state of Sao Paulo, southeastern Brazil. This is an artificially constructed channel which connects the reservoirs of two main hydroelectric power plants of the region to maximize energy production: the Ilha Solteira and the Tres Irmaos HPPs. Both power plants greatly suffer with the golden mussel infestation and the channel itself is entirely occupied by these animals. The generation of a model associated with a local verification of environmental information and biological variables of organisms can be used to provide a more complete and clear view of the ecological and hydrological dynamics of the studied environment, as well as provide crucial information for the infestation management by HPP operators of the region.

DOI: https://doi.org/10.3850/IAHR-39WC252171192022524

Year: 2022