Human remains found this week in the Southern California desert are believed to be a San Diego-area family of four who disappeared more than three years ago, and their deaths appear to be homicides, authorities said Friday.

San Bernardino County Sheriff John McMahon confirmed that 40-year-old Joseph McStay and his 43-year-old wife, Summer, were found in shallow graves near Victorville, about 60 miles northeast of Los Angeles.

The couple and their two sons _ ages 3 and 4 _ disappeared in February 2010.

Authorities believe the other remains belong to the two boys, but they have more work to do to confirm it, McMahon said at a news conference.

"Their DNA evidence is on file with the DOJ (Department of Justice), and we will be sending that information to the DOJ for positive identification," he said.

McMahon added the manner of death appears to be homicide, and it doesn't appear the family ever went to Mexico after they disappeared. Investigators earlier said they thought they spotted the McStays crossing the border on grainy surveillance video.

Investigators wrapped up a three-day excavation in barren scrubland near heavily traveled Interstate 15 on Wednesday after an off-road motorcyclist reported finding bones there.

Additional skeletal remains were found near the graves, and the coroner's investigators later confirmed they were human. Authorities said the remains had been in the desert for an extended period.

Autopsies were still being completed, and the cause of death has not been released.

The McStays' disappearance launched what San Diego County sheriff's investigators called their most extensive missing-persons search ever.

Joseph McStay's brother, Michael McStay, said it's been a "hard road" for the family not knowing where the couple and their sons were.

"It's not really the outcome we were looking for, but it gives us courage to know that they're together and they're in a better place," said a tearful Michael McStay.

There were no signs of forced entry at the family's home in Fallbrook, about 55 miles north of San Diego, or in their SUV parked near the border. Authorities found rotten eggs on the kitchen counter of the home and two dogs in the backyard.

Neither Joseph nor Summer had told family or friends they were leaving, and tens of thousands of dollars left in business bank accounts were never claimed.

Investigators pursued hundreds of tips and eventually came to believe the family left voluntarily for Mexico. Investigators were convinced that four people seen on a dimly lit surveillance video walking into Tijuana, Mexico, were the McStays.

But McMahon said there's no indication _ at this point _ the family ever went to Mexico.

Some family members doubted the video showed the couple and their children. The case was later turned over to the FBI.

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Information from: KFMB-TV, http://www.kfmb.com/