Her family had previously called on the Australian government to provide extra resources to find her, but now say they accept the 34-year-old may never be found. 

Canadian police had called in sniffer dogs and rescue teams from four districts over the weekend to search for Ms Dowsley, who went missing in Canada on July 8, when she went on a hiking trip with her partner, Greg Tiffin, 44. His body was found by a dive team at Statlu Lake on July 18, but Ms Dowsley's family had hoped she would be found alive.

The couple were staying at the Harrison Hot Springs, about 150km east of where they live in Vancouver, when they were reported missing.

Police then traced their movements to a hiking trail at Statlu Lake.

The lake's waterfall is reportedly difficult to see from the hiking path, which has led to previous tourists falling to their deaths while trying to get a better view.

Searchers feared Ms Dowsley may have tried to find a way to access the water after Mr Tiffin fell in. Helicopters and search and research teams were deployed during the weekend, with volunteers coming from the nearby communities of Coquitlam, Maple Ridge, Central Fraser Valley, and Chilliwack.

On Sunday, Sophie’s brother, Jamie Dowsley, said the Royal Canadian Mounted Police had now made the decision to cease the search.

"This decision has been made on the basis that there are no plausible or conceivable areas left to search," Mr Dowsley said.

"After visiting this area and gaining an understanding of the terrain and conditions, our family fully accept this."

Mr Dowsley said the family wanted to thank everyone involved in the dangerous search.

"We acknowledge that this is one of the most dangerous search and recovery operations that you have ever conducted. Every day you put your lives at risk to find Sophie and we thank you for that," he said.

"Thank you to all of Sophie's many friends from all around the world who have offered your support during this time – testament to the incredible person that Sophie is."

Mr Dowsley said they also wanted to thank Primer Minister Malcolm Turnbull and Federal MP Dan Tehan whose "personal support and influence" helped extend the search.

"One of Sophie's personal items has been discovered below the waterfall and the water search will resume when nature allows but we understand that Sophie may never be found," he said.