(CNN)An American scientist whose body was discovered several days after she went missing on the island of Crete was asphyxiated, police said Wednesday.
Police in Greece say they have opened a homicide investigation in the death of Suzanne Eaton, 59, according to Eaton's employer, the Max Planck Institute at Dresden University in Germany. Eaton's body was found on Monday, the institute said.
Eaton, who worked as a biologist, had been attending a conference at the Orthodox Academy in northwest Crete when she is believed to have disappeared during a run on July 2.
"There is an ongoing homicide investigation being led by the police in Crete, which has taken comprehensive measures to ensure that the responsible party(ies) will be brought to justice," the institute said in a statement.
The institute offered its condolences to Eaton's family.
"We will remember forever the extraordinary scientist so caring and devoted to her family and friends and so beloved by us all," the statement said. "We remain in disbelief of this shocking and awful tragedy."
Hans Müller-Steinhagen, university rector, said in a statement, "We have lost an immensely renowned scientist and a truly outstanding human being."
Local authorities "have not yet completed their investigation regarding the events that may have transpired" on the afternoon Eaton went missing, the institute said in an earlier statement.
"We are deeply shocked and disturbed by this tragic event," it added. "Suzanne was an outstanding and inspiring scientist, a loving spouse and mother, an athlete as well as a truly wonderful person beloved to us all."
Eaton was the wife of British scientist Tony Hyman and mother of two sons, Max and Luke, according to the institute.
On Tuesday morning, a post on the Facebook page set up by her family -- called "Searching for Suzanne" -- said: "We cannot comment on anything at this time, but I will post a message here when the time is appropriate."
Eaton usually ran for 30 minutes every day and was a regular face at the conference, according to the Facebook page. Her family believe she went missing during a run within 5 kilometers (3.1 miles) of the academy complex.
"Due to the rough terrain and extreme heat, we believe the most likely possibility is that Suzanne may have either become overheated and looked for shade or that she may have fallen," said a Facebook post.
While Eaton's employer acknowledged in an earlier statement that the "most likely" scenario was that she had gone for a run, it added: "There are many observations that challenge such a theory, including the heat of the day suggesting that a swim would have been more attractive."
"As well as being a leading scientist in her field, Suzanne is a strong athlete, runner and senior black belt in Tae Kwon Do," the statement added. "If anyone can find her way out of a difficult situation it is Suzanne."