# Of fish and calculus: URSA Showcase features ‘Fish Math’

*Josh Hartman/Sun Star*

In response to many biology students wondering when calculus was ever going to be useful to them, Milo Adkison, a UAF Fisheries professor, gave a presentation titled: “Fish Math, or Why We Make You Take Calculus.” The lecture took place for this month’s Undergraduate Research and Scholarly Activity (URSA) Research Showcase on Jan. 20 in Schaible Auditorium.

Adkison opened the presentation by explaining how an understanding of mathematics benefits scientists in the biological field. Biologists, like Adkison, who use statistics and applied math to solve problems are called biometricians.

When looking at biology and ecology through a lens of math and statistics you can see things that you wouldn’t have noticed otherwise, Adkison said.

Adkison spoke about a case in Juneau where scientists were puzzled by a 65 percent decline in harbor seals between the years 1992 and 2002. The original hypothesis was that sea lions, whose population has increased, were attacking the harbor seals.

However, it was also possible that the sightings of sea lion attacks were just coincidence.

To test this hypothesis, Adkison and his colleagues looked at data showing the number of sea lions attacking harbor seals observed over the years. If the sea lions were attacking the seals, then the number of attacks should increase as the sea lion population increases.

A technique called bootstrapping was used to analyze the results.

Bootstrapping allows someone to see if a set of data, like the sea lion attacks, is random or statistically significant. Using this technique, it was determined that as the sea lion population increased it was unlikely the attacks were increasing.

The next hypothesis was that there were “A few oddball sea lions eating harbor seals,” according to Adkison.

At one location the data would have been fairly accurate due to constant surveillance by biologists, according to Adkison. The results from this station showed that there was an average of one seal killed every sixty hours.

This average, however, could be skewed due to the fact that it’s more difficult to see attacks at night and that there are less biologists available in the winter. In order to account for this, Adkison and his colleagues came up with a low and a high estimate.

Using their estimate they found out about how many attacks occurred in a year. They determined that sea lion attacks could only cause a 12.4 percent decline.

The conclusion the sea lions were probably contributing to the problem, but were not the main problem themselves.

“Something that looks like common sense… it just doesn’t stand up when you put actual numbers to it and do some calculations,” Adkison said.

The second example began with a look at salmon escapements and nutrients. Escapements are the amount of salmon that are allowed to escape from fishers.

The salmon that escape fishers travel upstream and die, leaving their carcasses. These carcasses are full of nutrients the salmon collected in the ocean. The more nutrients in the ecosystem the healthier it will be, leading to more healthy salmon.

“When you have a healthy salmon population the trees grow much bigger and much faster,” Adkison said. “It’s amazing how big of an impact salmon have.”

Adkison explained Euler’s Identity, which contains mathematical constants like “*e*” and “π”. These constants have an infinitely long tail of numbers after the decimal and they can be estimated by adding together an “infinite series” of other numbers.

“I thought, wow that’s really neat, but I’ll never use it,” Adkison said. “I actually got to use it on a biological problem.”

Adkison and his colleagues created a formula that added up the amount of nutrients from the salmon that accumulated each year. This formula was an infinite series.

“People are thinking about and adjusting escapement to ensure that adequate nutrients are getting back into the system,” Adkison said. “I think that Fish and Game does a pretty good job of setting escapement goals in Alaska.”

However, if it takes very large escapements to increase ecosystem health or if the nutrients are flushed from the ecosystem too quickly it may not make economic sense to increase escapements, according to Adkison.

URSA will sponsor these showcase events for the rest of the semester with one occurring every month on the second to last Wednesday.