Allegations of sexual assault on cruise ships that left or returned to the United States jumped 67% year-over-year between July and September, according to statistics released last month by the Department of Transportation.

During that period, the third quarter of the year, there were 35 reported sexual assault incidents on a total of six cruise lines. Of those, the vast majority - 27 - were allegedly committed by passengers, five by crew and three by people who were neither passengers nor crew. That compares with 21 reported cases in the same time span in 2018.

So far for 2019, allegations of sexual assault have increased from 60 incidents in the first nine months of last year to 79 during the same time period this year - a nearly 32% increase. There was no increase between 2017 and 2018. There was no clear explanation for the increase, although a lawyer who tracks the cruise industry said pure numbers could be one reason; more people are expected to have gone on a cruise this year than last.

Most cruise lines whose ships embark and disembark in the United States have to report allegations of certain criminal acts as well as missing people to the Federal Bureau of Investigation under the Cruise Vessel Security and Safety Act. Crimes include homicide, suspicious death, kidnapping, assault with serious bodily injury, tampering with a vessel, theft of more than $10,000 and sexual assault. They must also report missing US nationals, which includes cases of people going overboard. Sexual assault is the category with the most number of reports by far.

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Carnival Cruise Line, which sails most of its ships from the United States, had the highest number of reported incidents during the third quarter, at 20, up from 14 during the third quarter of 2018. The tally for the first nine months of the year is 35 on Carnival, compared with 30 during the same time last year.

In a statement, the Miami-based cruise company said that nearly 6 million people cruise on the line every year, and nearly 90% of its capacity and operations are from US ports, which means incident reporting is required.

"Many of our US competitors sail from Europe and other non-US ports, so they are not mandated to submit CVSSA data as part of the reporting process," the statement said. "In essence, we report a higher number of cruise operations than others because we have a much higher percentage of US operations than others. Not because we have more incidents."

Royal Caribbean International, which reported eight sexual assault incidents this summer, compared with three a year earlier, said in a statement that the line takes every allegation seriously.

"When an incident is reported, our policy triggers immediate notification to appropriate law-enforcement authorities in compliance with mandatory reporting standards, as well as ... industry reporting guidelines," spokeswoman Melissa Charbonneau said in an email.

Both Carnival and Royal Caribbean said their security teams include many former members of law enforcement, and both cited certification by the Rape, Abuse & Incest National Network.

Despite this year's increase, the industry group Cruise Lines International Association pointed to the numbers in a larger context. About 30 million people are expected to cruise around the world this year, compared with 28.5 million last year. North America is the largest single-source market for cruise passengers.

"The latest Department of Transportation report shows that allegations of serious crime onboard cruise ships remain extremely rare, especially compared to crimes that occur on land," spokeswoman Bari Golin-Blaugrund said in an email. She pointed to a report commissioned by the group that shows crime rates on a ship are significantly lower than in a typical US city.

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The report by James Alan Fox, a professor of criminology at Northeastern University, says cruising is "exceptionally safe in terms of the risks associated with violent criminal activity," especially given potential risk factors such as the number of people packed in a tight space, the number of closed areas and consumption of alcohol, according to the report.

"And, of course, the confined perimeter of a cruise ship, particularly when at sea, would make it difficult for an individual who is contemplating an aggressive act to make an escape," he wrote. "While no vacation destination is completely free of risk, cruising is clearly a relatively safe option."

Still, those who watch the cruise industry and advocate for victims of crime are pushing for higher standards. International Cruise Victims, an organization of victims and family members of those who were injured on cruises, supports new legislation filed last month that would make sure cruise lines notified the FBI within four hours of an alleged incident; report to authorities before a ship leaves a US port if an incident happened in port; report allegations to the US Consulate in the next port of call; have video surveillance equipment in all passenger common areas; and indicate whether crimes were committed against children, among other requirements.

Jim Walker, a maritime lawyer who runs the Cruise Law News blog, said in an email that the increase in crimes can be partially attributed to the rise in the number of passengers who sail. But, he said, cruise lines can still do more.

"The cruise industry has focused primarily on its PR gobbledygook ('the safety of our passengers is our number-one priority') instead of making real improvements to its shipboard security, hiring and vetting practices, and crime-prevention procedures," he said.