Mathematics is about solving complex problems and finding answers. Dr. Rana Parshad, assistant professor of mathematics at Iowa State University, is harnessing the power of mathematics to solve the problem of invasive species and halt the damage that these unwanted invaders inflict on ecosystems.
“In a lab setting, we’re able to document the extinction of these predators,” said Parshad. “Our mathematical models enable us to calculate how quickly a specific control will eliminate an invasive species.”
Non-native organisms that take up residence in new environments often cause untold economic loss and serious environmental damage as they devour, destroy and displace native plants and animals.
“Once an invasive species spreads, establishes and flourishes within local populations, it could be very destructive and difficult to control,” said Parshad.
In Iowa, the emerald ash borer has burrowed its way through trees in 64 counties and has killed millions of ash trees in the Midwest. Zebra mussels and Asian carp have ravaged many Iowa lakes and rivers by depleting the foundational plankton that sustain most freshwater aquatic species.
Kim Bogenschutz, the Iowa Department of Natural Resources’ Aquatic Invasive Species Coordinator, describes Iowa’s invasive-species problem as, “challenging” and “very expensive.”
“Control is very difficult, if not impossible,” she said. “Right now, there is nothing that will kill Iowa’s expanding populations of zebra mussels and Asian carp, that will not kill native species as well.”
Strength in Numbers
The wall-to-wall chalkboard in Dr. Parshad’s office is overcrowded with formulas, derivatives and equations. Although this tangle of numbers may seem random, or even chaotic—these custom calculations are purposeful in how they help wildlife biologists and conservationists chose the best methods for eradicating a particular invasive species.
“We’re able to give researchers a finite timeline that reveals how long it will take the control to eradicate a species,” said Parshad.
Specific timeframes provide vital data and added value to a researcher’s body of work. Knowing when an ecosystem could be free of an unwanted and out-of-control pest, helps researchers illustrate definite plans to field experts who are entrenched in the marshes and wading in the lakes—fighting these invasive species on the front lines.
A Global Problem Causing Local Impacts
From unwanted zebra mussels and Asian carp that have infiltrated Iowa lakes—to poisonous Cane toads that have plagued Australian forests—the crisis of invasive species has worsened during the last few decades.
“We are a global world now,” said Parshad. “Increased international trade, as well as ships coming and going from all over the world, have transported unwanted species into environments where they otherwise do not belong.”
As invasive species have proliferated and destabilized delicate ecosystems throughout the planet, so has the immediate need to assess, calculate and clearly understand the resulting environmental destruction.
“Now researchers want to quantify this damage,” said Parshad. “This is where the mathematicians come in.”
“Mathematical models could help us to determine the number of species that we need to eliminate, during a specific time frame, in order to meet the long-term goal of crashing these populations,” said Bogenschutz.
Researching Biocontrol Solutions
For Dr. Parshad and his research team, invasive-species modeling begins with their group on the Iowa State campus. Team members include Eric Takyi, a Ph.D. candidate studying applied mathematics at Iowa State; David Uselman (’21, mathematics), and graduate student Sureni Wickramsooriya from Clarkson University in Potsdam, NY.
The group focuses on analyzing biologically based—or natural—solutions that are better for the environment and less harmful to the native fauna.
“Poisons are common, but they are toxic and can kill plants and animals,” said Parshad.
The first method, which is currently being researched in collaboration with an evolutionary biologist at Clarkson University, tries to eliminate an invasive species with a predator that is being fed an additional food source. The added nutrition boosts the predator’s strength, efficiency, and ability to wipe out the invasive species.
The second biocontrol—the Trojan-Y Chromosome strategy (TYC)—introduces a genetically-modified group of organisms into an ecosystem that could trigger the extinction of an invasive species. In this case, male fish with YY chromosomes are released into the environment. Mating with YY fish results in only male offspring. This slowly breeds out the females. Eventually, with only male fish remaining and unable to reproduce, the invasive species disappears. This ongoing research is being conducted in collaboration with the United States Geological Survey in Gainesville, FL.
Although Parshad and his team do not design or conduct the lab experiments, they collaborate with these researchers and develop tailored math models that add value to this research.
“We analyze the data from these experiments, then we develop customized mathematical models that help these researchers quantify how efficient their biocontrols will be in the field,” said Parshad.
The final numbers reveal if the biocontrol will be successful at eliminating the invasive pest and also how long it will take to extinguish the targeted trespassers.
Building Community and Igniting Interest
Bogenschutz describes Parshad’s research as “valuable and promising.”
“The numbers from these mathematical models could help us to determine if a particular solution is viable, affordable, or even feasible,” she said. “The spread of invasive species is a huge problem and knowing how long it would take to get an invasive species under control would be extremely helpful.”
Mathematical modeling on the TYC research earned Parshad a $420,000 National Science Foundation grant from the Division of Mathematical Sciences, Mathematical Biology Program.
As Parshad partners with invasive-species researchers, he’s also committed to growing a collaborative community at Iowa State that is dedicated to solving the invasive-species problem.
“I’d like to see more students interested in the science of invasive species,” he said. “I hope to get math students enjoying ecology and biology and excited about watching their equations crystallize in a lab setting.”
Dr. Hal Schenck, professor and chair of the mathematics department at Iowa State University, says that partnerships between the worlds of biology and mathematics are examples of cross-disciplinary collaboration that is valued and encouraged at Iowa State.
“All science comes down to quantifying things,” said Schenck. “We are working hard at Iowa State to build bridges between the mathematics department, private industry and researchers in other fields.”