Dual-level toxicity assessment of biodegradable pesticides to aquatic species
Introduction
The global increase in agricultural activities to ensure food security has resulted to the upsurge in pesticide usage which has undoubtedly reduced crop loss and improved crop yield (Ntow et al., 2006). However, contamination of aquatic ecosystems arises from the off-site movement of pesticides either through spray drift, runoff and leaching (Van Den Brink, 2013, Wijngarden, Brock, Van Den Brink, 2005). The effects of pesticides and other toxicants on aquatic ecosystems have been the subject of an enormous number of studies in the past several decades (Ozekeke, Tongo, Lawrence, 2015, Schafer, de Brink, Liess, 2011). Many ecotoxicological studies have shown that biological populations in both terrestrial and aquatic habitants are stressed by pesticides released into the environment (Hassard, Kazarinoff, Wan, 1981, Kumar, Agrawal, Hasan, Misra, 2016, Patin, 1982). There is vast evidence that pesticides pose a major threat to aquatic life and humans (Tongo, Lawrence, Kingsley, 2016, Tu, Niu, Liu, Xu, 2013, Uddin, Saha, Chowdhury, Rahman, 2013). Pesticide residues contaminate soil, sediments and water and enter the food chain, where these pesticides may eventually get to humans through consumption of aquatic organisms and food products (Ntow et al., 2006). When some pesticides enter into the aquatic environment they undergo degradation (photo, biological, microbiological or chemical) to simpler compounds which may be more toxic or more persistent than the parent compounds (Kavita, Greeta, 2014, Satish, Ashokrao, Arun, 2017, Yichen, Lijuan, Feiyu, Mengshi, Derong, Xraomei, Zhijun, 2018). Varying levels of pesticides have been detected in surface water, sediments and aquatic biota and along with their attendant degradation products (Oerke, Dehne, 2004, Rahman, 2013, Tongo, Lawrence, Kingsley, 2016).
With the increasing global awareness of environmental protection, it is imperative to evaluate the effects of pesticides in aquatic environment. Ecotoxicological risk assessment of pesticides in the aquatic environment is one of the most significant areas for the evaluation of pesticide effects for the protection of biodiversity (Cochard, Maneepifak, Kumar, 2014, Halstead, McMahon, Johnson, Raffel, Romansic, Crumrine, Rohr, 2014). The ultimate goal of ecotoxicological risk assessment for contaminants is to provide knowledge that can be used to protect the components of ecosystems from chemical stressors (Boithias et al., 2014). To this end, ecological models have been used as tools for assessing the ecological implications of observed or predicted effects of toxic chemicals especially pesticides on biological species (Anita, Kokila, Vatsala, 2017, Anuj, Khan, Agrawal, 2016, Bagchi, Azad, Alomgir, Chowdhury, Uddin, Al-Reza, Rahman, 2009, Brock, Lahre, Van Den Brick, 2000, Dubey, Hussain, Raw, Ranjit, 2015, Shukla, Agrawal, 1999). These mathematical models are used to describe the relationship as well as assumptions and uncertainties in the extrapolation between endpoints (Van Den Brink, 2013, Wijngarden, Brock, Van Den Brink, 2005).
Mathematical models have been used extensively to study the effect of toxicants on biological species. The study (Anuj et al., 2016) reported on the effect of an external toxicant on population density and deformity of a biological species. The results of the model showed that when emission of the external toxicant increased, total population density decreased and the density of the deformed subclass increased. A study reported in Shukla and Agrawal (1999) showed that as the cumulative rates of emission and formation of toxicant into environment increased, the densities of population and its resources decreased. Sandeep and Nitu (2017) proposed a mathematical model to investigate the role of rain in the removal of air pollutants and its subsequent impacts on human population and concluded that rain is a cleaning agent of air pollution. Kumar et al. (2016) proposed and analyzed a model to study the effect of pollution on biological population. Results of the study showed that the population density settled down to its equilibrium level and the magnitude was dependent on the equilibrium levels of emission, washout rates of pollutant as well as on the rate of precursor formation and its depletion. The rate of precursor formation was reported to be critical in affecting the population. It has also noted that the survival of the population would be threatened if the concentration of pollutant increases unabatedly. Recently, a mathematical model to study the effect of pollutants in aquatic environment was carried out by Anita et al. (2017) who reported that the discharge of high concentration of toxicant beyond the permissible level lead to extinction of the biological species.
Although quite a number of studies have been carried out on the effect of toxicants on aquatic biological species, to the best of our knowledge, none of the existing models have considered the effect of dual-level pesticides toxicity (presence of pesticides in water and sediments) and take into account the effect of biodegradable pesticides on aquatic species. In this study therefore, we proposed and analyzed a novel nonlinear mathematical model that assesses the effect of two pesticides on the population of aquatic species where both pesticides are available in water and sediments with one of the pesticides capable of biodegrading into the other but not vice versa (Satish, Ashokrao, Arun, 2017, Schafer, de Brink, Liess, 2011, Tu, Niu, Liu, Xu, 2013).
This paper is organized as follows. In Section 2, we formulate the nonlinear model to study the impact of the dual-level toxicity (water and sediments) on aquatic species. In Section 3, we carryout some rigorous mathematical analysis of the formulated model, while in Section 4, we present the numerical simulation of the model equations to validate our analytical results. We discuss our results in Section 5 and conclude in Section 6.
Section snippets
Mathematical model
We assumed that the aquatic environment is polluted by two major pesticides (Pesticide 1 and 2) in water and sediments. We also assumed that pesticide 1 is capable of degrading into pesticide 2 but not vice versa. We compartmentalized our model into seven(7) state variables: is the population of the aquatic species (e.g., fish) at time t; is the concentration of pesticide 1 in water at time t; is the concentration of pesticide 2 in water at time t; is the concentration
Existence of equilibria and their stability
It is paramount that we investigate the dynamics of the non-linear model (2.1). We shall consider two cases as follows:
Case 1:
In this case, there is no discharge of pesticides into the aquatic environment. Hence, the model system (2.1) has two non-negative equilibria, and and
The equilibrium, is a trivial equilibrium, hence its qualitative behaviour will not be investigated. The
Numerical simulation
In this section, we use the inbuilt MATLAB function ode45 for the numerical simulations of the model (2.1). Note that the numerical simulations herein were carried out to illustrate some of the analytical results presented in the previous section; here, we assume a hypothetical aquatic environment with aquatic species that are affected by two pesticides. We consider the following particular form of the implicit functions in model (2.1):
Discussion
In this paper, a mathematical model that investigate the effects of two pesticides on aquatic species where two pesticides are present in water and sediments and one of the pesticides is capable of biodegrading into the other pesticide but not vice versa is formulated and rigorously analyzed.
The model had four equilibria namely, two pesticides free equilibria (PFE): and two pesticides present equilibria (PPE): . We paid attention to the realistic equilibria: and . An
Conclusion
In this paper, we have presented model investigating the impact of dual-level toxicity on aquatic bio-species. The model system has four critical points: one trivial and three non-trivial. In the first two non-trivial critical points the population thrive and died completely respectively. In the third non-trivial critical point, the aquatic species population thrive in the presence of the four pesticides. The stability of the first non-trivial critical point was ignored since there is no
Declaration of Competing Interest
None.
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