A criminal complaint has been filed and arrest warrants have been issued for three Canadian men shown walking off-trail illegally at Yellowstone National Park in a video that surfaced on the internet over the weekend.

Federal warrants were issued for Charles Ryker Gamble, Alexey Andriyovych Lyakh and Justis Cooper Price-Brown for walking off-boardwalk and creating a hazardous or physically offensive condition at Grand Prismatic Spring in Yellowstone National Park.

Yellowstone spokeswoman Charissa Reid said that as of Tuesday afternoon the men had not been arrested. She said the investigation is ongoing.  

A fourth member of the group — Parker Heuser — was not issued an arrest warrant. Reid said that was because park law enforcement found that he had been using a different name on the internet than what was on his driver's license. 

The violations were brought to the attention of park officials after videos and photos of the men walking off-boardwalk were posted online on Saturday. A criminal complaint filed in federal court says a witness to the incident provided park law enforcement with 26 photos and a 22-second video of the men illegally off-trail, taking photos of themselves and reaching into the spring.

"The nearest boardwalk is approximately 25 yards from where they are located," the document says.  

The men are members of High on Life, a Canadian clothing company and producer of travel and adventure videos. The group sent a short statement to the Chronicle late Tuesday night.

"We did not respect the protected environment we were exploring and we want to acknowledge our wrongdoing and apologize to the community and to the public," the group said.

In a posting to their website and Facebook page Tuesday morning, the group admitted heading off the boardwalk at the hot springs.

"In an attempt to get the perfect shot, we acted in a way that doesn't reflect our respect for the environment we were trying to capture," they said. "It was the wrong decision to make. We realize that now."

After the video and photos went viral Monday, internet searches turned up other photos and videos from the park posted by the same men to Instagram, Facebook and YouTube.

The group's own video -- posted to YouTube on May 16 and unpublished after news of their antics broke -- shows the men entering the park in a large blue motorhome. At one point in the video, park rangers warn the group after one of the men strips naked and runs out onto the surface of a frozen lake. In another portion of the video, the group is at Grand Prismatic, where some of their video appears to have been taken while off the boardwalk.

Yellowstone park rules explicitly prohibit tourists from traveling off boardwalks or designated trails in hydrothermal areas. Additionally, park policy prohibits filming from the social trails above Grand Prismatic Spring.

The park requires film permits for commercial, nonprofit, documentary, promotional or educational filming, including entertainment broadcasts and some student projects.

Rachel Cudmore, who works in the film office at Yellowstone National Park, told the Chronicle in an email that no permits were on file for High On Life or any of the four men associated with the project. She added that the project "would have required a commercial film permit."

"Typically, anyone that is filming or photographing for reasons other than personal enjoyment should contact the Film Office to inquire about a special use permit for these activities," Cudmore said. 

Filming without a permit was not one of the charges listed in the criminal complaint filed Tuesday, though Reid said it was possible that charge could arise later on. 

Cudmore said filming without a permit was a misdemeanor crime with a maximum prison term of six months and a maximum fine of $5,000.

The group said, as a form of recompense, they would donate $5,000 to the park.

Cudmore said commercial film crews are allowed to film in thermal areas, such as Midway Geyser Basin, with a Park Service monitor and must always stay — and keep all of their equipment — on designated boardwalks and paths. A trail above the spring is closed to film crews for revegetation efforts. 

Late Monday, as public criticism on social media channels piled on, High on Life removed photos and video showing the men flouting Yellowstone rules from Instagram and Facebook.

"We take your comments, messages and every piece of feedback seriously, and we will be accepting the ramifications of our actions," the group said in their Facebook post. 

As of Tuesday afternoon, the Facebook post with their apology had garnered more than 1,700 comments, many from people outraged by the group's actions. Some even claimed that they had done irreparable harm to the spring. 

The criminal complaint filed related to their actions also says they were in contact with a park ranger in Mesa Verde National Park in Colorado. It doesn't describe the nature of that incident. 

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