The government suspended the hunt in 2006 over fears of dwindling numbers and declared grizzlies a threatened species in 2010.
The association, which represents about 24,000 hunters and anglers, has passed two resolutions calling for a new, limited hunt.
"It is only where there is a harvestable excess of grizzly bears — where they are causing problems, where they are spreading out beyond their territory because of no hunting anymore," association president Gord Poirier said Wednesday.
"There still has to be protection for the grizzly bears where the population is low."
Poirier said Alberta could allow a limited hunt without removing grizzlies from the threatened species list.
He said such a hunt could be restricted to areas such as southwest Alberta and be open only to residents of the province.
Alberta's current five-year grizzly recovery plan is to expire April 1.
The association is to present its resolutions to Environment Minister Diana McQueen in the next few weeks.
Part of the push for a renewed hunt is coming from ranchers who live in southwest Alberta. They say they are seeing more bears and are worried about their livestock and the safety of their families.
"There appears to be enough grizzly bears causing quite a few problems," Poirier said. "Last year one guy had nine grizzly bears in his yard at one time."
Alberta Environment spokeswoman Nikki Booth said the government will review the association's resolutions and has heard from ranchers who want a grizzly hunt, but there are no plans to change its policy.
"Right now we aren't considering any sort of grizzly hunt," she said. "We are aware there have been requests from different groups indicating that they would like one, but right now what we are trying to do is work on a number of other measures."
Those measures include working with ranchers to reduce conflicts with bears by promoting improved grain storage, trash handling and cattle carcass disposal practises.
A University of Alberta bear expert said there is no scientific reason why the government could not allow a limited grizzly bear hunt in certain areas of the province.
Professor Mark Boyce said there are enough bears in parts of southwestern and northwestern Alberta to sustain a limited hunt.
But he said the issue is probably too politically hot for the government to go that route.
"Biologically, a limited harvest would not jeopardize the viability of Alberta's grizzly bear population, but it would be a very difficult decision for the minister of environment and sustainable resource development to make because of the political repercussions," Boyce said.
The Alberta Wilderness Association is lobbying McQueen against allowing a new grizzly bear hunt.
In a letter to the minister, the association acknowledges there may be more grizzlies in southwest Alberta, but makes the point that no one is really sure, and if there are more bears, why?
Sean Nichols, a conservation specialist, wrote that it would be premature to consider a resumption of the hunt.
"Has the population actually increased, or is it just that bears are moving away from degraded habitat on public lands, and on to more appealing, but visible, habitat on private lands?" he wrote.
The last official estimate in 2008 said Alberta had fewer than 700 grizzly bears.
The association also reminded McQueen that the government made a commitment last fall not to allow a grizzly bear hunt until it had good scientific information about how many bears there are and where the bears live and roam.
In an interview, Nichols noted that grizzlies can move back and forth to different areas, including other jurisdictions such as Montana and British Columbia.
He said allowing grizzlies to be hunted in specific areas wouldn't necessarily reduce the number of encounters between people and the bears.
"If you just starting killing bears you will have more bears coming in," he said. "You are not solving the problem of them being on the ranch or doing any favours to the population in general."
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