It is critical to understand the distinct dangers that different contaminants represent to different species when developing environmental policy to reduce the damage caused by river pollution. It is simply not possible to assess the effects of toxicants such as pesticides, plastic waste, viruses, and chemicals on entire groups of creatures without severely harming their entire ecosystems.
Without damaging the ecosystem, mathematical modeling can give a flexible technique to examine toxicants’ influence on river populations. In a paper that published today in the SIAM Journal on Applied Mathematics, Peng Zhou (Shanghai Normal University) and Qihua Huang (Southwest University, Chongqing) develop a model that describes the interactions between a population and a toxicant in an advective environment a setting in which a fluid tends to transport material in one direction, like a river.
Scientists can use such a model to investigate how the movement of a pollution through a river impacts the health and distribution of the river’s inhabitants. Much of the prior experimental research on the ecological dangers of toxicants was done on single organisms in controlled laboratory settings over a very short period of time.
Environmental management measures, on the other hand, necessitate a grasp of toxicants’ long-term effects on the health of entire natural populations exposed to them. There is, thankfully, a middleman.
“Mathematical models play a crucial role in translating individual responses to population-level impacts,” Huang said.
Many of the features of water bodies are ignored in existing models that describe how toxicants affect population dynamics. However, they are missing a crucial piece of the puzzle in the process.
In reality, numerous hydrological and physical characteristics of water bodies can have a substantial impact on the concentration and distribution of a toxicant. 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.
Qihua Huang
“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.”
Similarly, the models that mathematicians frequently employ to depict the passage of contaminants through a river do not incorporate all of the components required for this research. These are reaction-advection-diffusion equation models, and their solutions can indicate how pollutants spread and change in response to various factors such as changes in water flow rate.
While such models allow researchers to forecast the evolution of toxicant concentrations and estimate their environmental impact, they ignore the impact of toxicants on the dynamics of impacted populations. As a result, Zhou and Huang added new aspects to this type of model, allowing them to investigate the interaction between a toxicant and a population in a polluted river.
The authors’ model is made up of two reaction-diffusion-advection equations: one that drives population dispersal and growth under the impact of the toxicant, and another that represents the toxicant’s operations.
“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.”
The model allows Zhou and Huang to experiment with different variables and see how the ecosystem evolves as a result. They experimented with changing the river’s flow speed and advection rate, or the rate at which toxicants or organisms are conveyed downstream, and observing the effects of these parameters on population persistence and toxicant distribution. When combined with other data, these theoretical results can yield insights that can assist inform ecological policies.
The researchers looked at one situation in which a toxicant had a considerably slower advection rate than the population and hence was not washed away as quickly. The model demonstrated that, intuitively, as water flow increases, population density declines as more individuals are moved downstream and out of the river area in issue.
However, because the toxicant may resist the downstream current, its concentration rises as the flow speed rises, and organisms are frequently swept away before they can absorb it.
The toxicant, on the other hand, has a faster advection rate than the population and is thus considerably more susceptible to water flow speed. By sweeping the pollutants away, increasing the water flow lowers the toxicant concentration.
Because the water flow plays a trade-off, it moves more toxicants away while simultaneously carrying more individuals downstream, the largest population density occurs downstream for a medium flow speed. This illustrates that a pollutant’s sensitivity to water flow is often beneficial to population persistence.
“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 feeding this model parameters for certain species and pollutants, one may be able to derive water quality criteria that are required to keep aquatic life alive. This finding could eventually be used to help formulate policy guidelines for the target species and toxicants.
“The findings here offer the basis for effective decision-making tools for water and environment managers,” Huang said. Managers could connect the results from the model with other factors, such as what may happen to the pollutant after it washes downstream.
By enabling the flow velocity and release of toxicants to fluctuate over time, or accounting for the diverse ways in which different species may respond to the same pollutant, Zhou and Huang’s proposed model might be made even more appropriate to real river ecosystems. The capacity of this mathematical model to determine the population-level impacts of toxicants could be crucial in determining the risk of pollutants to rivers and their populations.
