TUCSON, Ariz. » In the Pima County Medical Examiner’s Office here — repository of the nation’s largest collection of missing-person reports for immigrants who vanished crossing the United States-Mexico border — 774 sets of remains awaited identification in mid-May, stored in musty body bags coated in dust.

For the family of Andres Valenzuela Cota, the remains represent a chance to turn the page on a sad chapter of family history. Cota was 45 when he disappeared on July 15, 2011, after calling a niece in Los Angeles and asking her to send $100 to a Western Union office in Cananea, Mexico, a staging point for smugglers bringing migrants through Arizona.

As Congress debates the most sweeping changes to the country’s immigration system in decades, the remains stored here are also a nagging reminder of the complicated variables of the border-security equation. The number of migrant apprehensions declined precipitously in recent years, one of the strongest indicators that fewer people have tried to cross the border illegally. But the number of migrant deaths has remained high.

"Less people are coming across," said Bruce Anderson, the chief forensic anthropologist at the medical examiner’s office, "but a greater fraction of them are dying."

There were 463 deaths in the past fiscal year, which ended Sept. 30 — the equivalent of about five migrants dying every four days, according to an analysis by the Washington Office on Latin America, a human rights group. In the time federal statistics have been compiled, only 2005 had more deaths, and in that year, there were more than three times as many apprehensions.

As security at the border has tightened, pushing migrants to seek more remote and dangerous routes, the largest number of the deaths last year occurred along the punishing stretch of desert that spans the southernmost tip of the Border Patrol’s Tucson sector, the busiest along the border.

The only riskier stretch is the Rio Grande Valley sector in Texas, where, from Oct. 1 to April 30, law enforcement officers or ranchers found the bodies of 77 immigrants, or nearly half the number of bodies recovered there in all of the past fiscal year: 150.

In that sector, the most deaths have occurred in Brooks County, small and struggling at 944 square miles, where the average household income is $25,000. The number of migrant remains recovered is on pace to double that of last year, a record for the county, at 129, said a county judge, Raul Ramirez. Most of the dead are believed to be from Central America, Ramirez said.

In Tucson, the medical examiner’s office, which handles autopsies for the border counties in the Tucson sector — three of Arizona’s four border counties — received 49 sets of remains from Jan. 1 to May 9, Anderson said. Each was assigned a number, then photographed, cataloged, weighed and measured. Clothes, tattered by the elements and wildlife, were placed in plastic bags.

For years, identification of the remains was elusive because there were so few clues. Few immigrants from impoverished rural communities could be traced with dental records. ID cards, found in pockets and backpacks, were unreliable because many were forgeries, bought by Central Americans to elude the authorities in Mexico, which the migrants had to cross illegally before reaching the United States.

Assembling the remains, like linking a mandible that arrived in the office early this spring to a set of remains that was missing one, is like solving a grisly puzzle. It requires manually searching the color-coded paper case files lining the walls in Anderson’s office: one shelf for cases from the late 1990s, when there were few, and the rest for the more than 2,100 deaths since 2001.

"The cause and manner of death is easy: it’s either there or it’s undetermined," said Dr. Gregory L. Hess, chief medical examiner in Pima County. "It’s what goes on in trying to identify the person that can take a long time."

Early this month, the office unveiled a computerized mapping database bearing the records of 1,826 migrants who died in the desert, listing GPS coordinates for where they were found and, if known, their sex, age and cause of death. It gives the public the first comprehensive glimpse of the complexity of the problem. Combined, the hundreds of red dots that represent people who died of exposure to the intense desert heat and cold, by far the most common among the causes of death, look like an unshapely bruise.

The project began five years ago, through a partnership with Humane Borders, a nonprofit group that had already been plotting the deaths. An anonymous donor provided $175,000 to develop the database.

The lone mandible had been plucked from deep inside the desert near Three Points, west of Tucson. Angela Soler, a forensic anthropologist at the office, searched the database for bodies found in the same area. There were 52 in a six-mile radius.

Soler started by focusing on those that were closest. One was the complete body of a man found and identified in 2008. Another was found in 2012, an unidentified Hispanic man between 20 and 35, the most common demographic among dead migrants. She pulled the file and found that the body was missing a mandible. (DNA tests are underway to determine whether they are a match.)

"It took hours to do what might have taken months," she said.

In March, the Pima County Medical Examiner’s Office asked the family of Cota, the migrant who disappeared in 2011, for his dental records to see if he was among the unidentified dead stored there. There were seven possible matches among the bodies found in Cochise County, for which the office handles autopsies and where Cota is believed to have entered the country, based on what he told his relatives on his last phone call.

A brother-in-law, who asked not to be identified because he feared the drug cartels that control the human-smuggling business, said the family had filed missing-person reports on both sides of the border; visited local hospitals, police stations and prisons in Arizona; and retraced Cota’s route, posting fliers bearing his name and photograph in communities along the way.

"Every door we’re knocking is closed," the brother-in-law said. "Nothing opens."

Cota lived for 20 years in California, most of it illegally, overstaying a visa. When his mother became deathly ill, he left for Los Mochis, in the Mexican state of Sinaloa, to say goodbye.

In September 2010, he tried to cross back through San Diego using a fake passport, but he was caught and imprisoned for 45 days. After his release, he tried twice to sneak across the border, without success. A relative eventually told him to go to a Mexican border city, Nogales, where a smuggler could bring him into Arizona "for a discounted rate," his brother-in-law said.

On his last call, Cota said he was about to start his journey, but had to leave his cellphone behind. He promised to call again in six days.

On May 9, Robin C. Reineke, a cultural anthropologist at the medical examiner’s office, searched the database for a match, going through the cases from Cochise County one by one.

Cota was not among them. The search goes on.

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