Grand Teton National Park’s elk hunt is under fire after a grizzly bear shooting, but hunters aren’t killing park wapiti fast enough to suit game managers.

Through Wednesday, 162 elk had been killed in Grand Teton’s “elk reduction program,” which ends Sunday. Seven hundred and twenty-five permits were authorized, all for cow elk. Wyoming Game and Fish Department and the park set a soft goal to thin Grand Teton’s summering herd of 1,600 elk by 300, Game and Fish wildlife biologist Doug Brimeyer said.

“I can’t stress enough that we need to continue to see some reduction in the population that come from the southern portion of the valley,” Brimeyer said. “Ultimately our goal is to bring elk numbers down to within the stated objective that both the state and federal government are trying to achieve.”

About 7,700 elk stayed on the National Elk Refuge during the 2011-12 winter, 54 percent above the population objective of 5,000 wintering animals.

A 2007 U.S. Fish and Wildlife Service management plan requires Grand Teton and the National Elk Refuge to reach that objective by 2022.

The post-hunt Jackson Hole elk population is expected to be about 11,900 — close to the 2007 objective of 11,000. But southern segments of the herd are reproducing at twice the rate of elk that migrate from Yellowstone National Park and northern reaches of the valley, Brimeyer said.

The harvest goal for the entire Jackson Hole herd is 1,000, but it’s early to say if that will be reached, Brimeyer said. Seven of 65 collared elk from the herd have been killed this year, which exceeds the 2011 hunt total.

Two other hunt units — one on private land south of the park and another east of the elk refuge — could “pick up the slack” for a low Grand Teton harvest, Brimeyer said.

“We’ll probably make up for it,” he said. “We look collectively at all the hunt areas on the southern part of the valley. The park is only one part of that.”

The Grand Teton goal represents 30 percent of the total Jackson Hole planned harvest.

Looking at historical data, it’s clear the park hunt has been scaled down significantly.

In 2011, 750 permits were authorized in the park, and hunters bagged 278 animals. But that number included bulls, making a comparison with this year’s cow-only hunt undependable: Cows have much more to do with herd growth than bulls.

Those numbers are low compared to the 1990s, when an average of 1,000 elk were taken annually. Harvests of more than 700 were normal.

“We’re fine-tuning this hunt as we move forward,” Brimeyer said. “We’ve been focusing more on the antlerless harvest and have changed the way hunting is allowed in the park. Based on migratory patterns, we’ve adjusted [the hunt] on the Antelope Flats.”

Grand Teton spokeswoman Jackie Skaggs attributed low harvest numbers this year to mild weather.

“A lot of it depends on weather, and we are due for some,” she said. “Snow and cold temps will trigger the elk to start moving from higher elevation areas where they may be lingering.”

On Thanksgiving day, 48-year-old David Trembly, of Dubois, and Trembly’s 20- and 17-year-old sons killed an adult male grizzly bear while elk hunting near Schwabachers Landing. It was the first grizzly killed in the history of the Grand Teton hunt, and it spurred renewed calls to scale back or shut down the program.

Brimeyer suggested the grizzly death was “emotional.” But he said the killing shouldn’t mar the public’s perception of the park hunt, which he said includes many ethical and careful hunters.

“The bottom line is when [the elk] come to the refuge and they’re way over the objective number that the agencies have agreed to, we’ve got to work to achieving a harvest that lets us achieve the goal,” he said.