It is usually not possible to test the impacts of different types of pollutants on the biological populations in river systems because these substances can damage the entire ecosystem. Instead, the effects of insecticides, plastic debris, pathogens, chemicals, and other toxic substances are tested on individual species under controlled laboratory conditions.
Although this approach helps identify which species are more or less susceptible to which pollutants, it does consider population effects or take into account the physical and hydrological features of river systems, in which water moves continuously in one direction and transports materials with it.
In a recent study, however, Peng Zhou (Shanghai Normal University) and Qihua Huang (Southwest University, Chongqing) developed a model that describes the interactions between a population and a toxicant in a system characterized by fluid moving in one direction. This model replicates the conditions found in a flowing river and will be of assistance to scientists who wish to predict how the movement of a pollutant through a river will affect the health and distribution of the river’s inhabitants.
When formulating environmental policies to limit the effects of river pollution, it is important that scientists understand a toxicant’s impact on the health of the entire natural community that is exposed to the substance over the long term. This cannot be assessed fully using controlled laboratory tests but mathematical modelling can help simulate river conditions. “Mathematical models play a crucial role in translating individual responses to population-level impacts,” Huang said.
Unfortunately, many existing models that simulate the potential effects of toxicants on population dynamics often ignore the critical properties of water bodies.
“In reality, numerous hydrological and physical characteristics of water bodies can have a substantial impact on the concentration and distribution of a toxicant,” Huang said. “For example, once a toxicant is released into a river, several dispersal mechanisms – such as diffusion and transport – are present that may aid in the spread of the toxicant.”
Some models do take into account the movement of pollutants through a river by making use of reaction-advection-diffusion equations. Such models can show how pollutants become distributed under different hydrological influences, such as changes in the water flow rate, and enable researchers to predict toxicant concentrations and the impacts of these on the environment. However, these mathematical models do not consider the influence of toxicants on the dynamics of affected populations.
Zhou and Huang thus expanded upon this type of model, adding new elements that allowed them to explore the interaction between a toxicant and a biological population in a polluted river. Details of their model were published today in the SIAM Journal on Applied Mathematics.
The researchers’ model consists of two reaction-diffusion-advection equations – one that governs the population’s growth and dispersal under the toxicant’s influence, and another that describes the processes that the toxicant experiences. “As far as we know, our model represents the first effort to model the population-toxicant interactions in an advective environment by using reaction-diffusion-advection equations,” Zhou said. “This new model could potentially open a [novel] line of research.”
This arrangement allows the researchers to test different scenarios and tweak parameters to see what potential impacts this has on the environment or the population of organisms. For example, they tried altering the river’s flow speed and the advection rate – the rate at which the toxicant or organisms are carried downstream – and observing the effects of these changes on the survival and distribution of the toxicant and the biological population.
One scenario involved a toxicant that had a much slower advection rate than the population and thus was not washed away as easily. The model showed that, intuitively, the population density decreases with increasing water flow because more individuals are carried downstream and out of the river area in question. However, the concentration of the toxicant increases with the increasing flow speed because it can resist the downstream current and the organisms are often swept away before they are affected by it.
In the opposite case, the toxicant has a faster advection rate and is therefore much more sensitive to water flow speed than the population. Increasing the water flow then reduces the toxicant concentration by sweeping the pollutants away. For a medium flow speed, the highest population density occurs downstream because the water flow plays a trade-off role; it transports more toxicants away but also carries more individuals downstream.
“In the absence of toxicants, it is generally known that the higher the flow speed, the more individuals will be washed out of the river,” Zhou said. “However, our findings suggest that, for a given toxicant level, population abundance may increase as flow rate increases.”
By using different parameters for certain species and various pollutants, the model can help identify criteria that are important for protecting and maintaining aquatic life in the face of pollution. This could ultimately aid in the development of policy guidelines surrounding the target species and toxicants. “The findings here offer the basis for effective decision-making tools for water and environment managers,” Huang said.
Further modifications to Zhou and Huang’s new model could make it even more applicable to real river ecosystems, for example, by allowing the flow velocity and release of toxicants to vary over time, or accounting for the different ways in which separate species may respond to the same pollutant. This mathematical model may thus help scientists to assess more accurately the risk of a specific pollutant to the populations present in biological communities inhabiting a river.