Nearly 409,000 illegal immigrants were nabbed at the border in fiscal year 2016 — up from about 331,000 a year earlier — and Homeland Security officials say the increased arrests also mean an increase in the number that are sneaking by them.

Worse yet, the number of illegal immigrants traveling as families, fleeing rough conditions in Central America and enticed by the promise of lax enforcement in the United States, reached a record high of 77,674. Unaccompanied minors — those children traveling without their parents — also rose to nearly 60,000, though that was still shy of the record set in 2014.

“Unaccompanied children and families have presented new challenges in our immigration system,” Homeland Security Secretary Jeh Johnson said in a statement announcing the numbers.

The Obama administration made significant progress in securing the border in 2015, as the number of unaccompanied minors, families and overall illegal immigration dropped significantly. Total apprehensions fell to their lowest point since the 1970s.

But things turned around for the worse over the past year.

Some analysts cite relaxed enforcement in the United States as a cause, saying cartels and would-be migrants have learned to game the more relaxed system under President Obama. Claims of asylum have spiked, earning illegal immigrants a chance to remain in the United States while they fight their cases, and oftentimes disappear into the shadows.

Meanwhile, deportations have plummeted during Mr. Obama’s second term. Final 2016 numbers haven’t been released, but analysts were expecting the fourth straight year of declining removals.

Mr. Johnson said he’s trying to balance competing factors of deporting new arrivals, while giving those with legitimate claims of humanitarian crises a chance to make their cases.

The secretary said the government does need more technology and equipment on the border, but said that’s not going to be enough — and he took a swipe at Republican presidential nominee Donald Trump, who has proposed a border wall to stop the new flow of illegal immigrants.

“Walls alone cannot prevent illegal migration,” Mr. Johnson said. “Ultimately, the solution is long-term investment in Central America to address the underlying push factors in the region.”

The demographics of illegal immigration across the border have changed dramatically over the last decade. Mexicans used to make up most of those caught, but in 2014 Central Americans outnumbered Mexicans for the first time. That remained true in 2016.

Elyse Golob, executive director of the National Center for Border Security and Immigration at the University of Arizona, said the 2008 economic recession here, combined with steadier economic growth and a falling birth rate in Mexico, have changed the incentives for Mexican migration.

At the same time, high murder, violence and unemployment rates in El Salvador, Guatemala and Honduras have fed the surge of migrants from those countries headed north.

That’s also affected which parts of the border are seeing the most activity.

The Yuma sector, in western Arizona, had been a success story in the previous decade, but saw the number of family members trying to sneak in grow tenfold, from just 675 in 2014 to 6,169 in 2016. Meanwhile, the Tucson sector, which 10 years ago was ground zero for illegal immigration, has seen its apprehensions fall precipitously.

Most of the action is now in the Rio Grande sector, which accounts for about half of the illegal immigrant traffic.

Homeland Security officials last year had predicted a surge, particularly among families attempting to make the journey. In court documents, they said judicial rulings prohibiting detention of some illegal immigrants would entice even more to make the trip.

Ms. Golob said it’s impossible to separate the push and pull factors, but said it’s clear there’s been a shift in the thinking of those pondering the journey in the key Central American countries. In the past, the dangers of the trip and the threat of deportation were enough to keep more of them home, but escalating violence and lack of opportunities at home, combined with word-of-mouth stories from relatives and friends who have gained a foothold in the United States, have changed things.

“There’s no doubt that news moves through the grapevine,” Ms. Golob said. “When people hear about unaccompanied children and family units being placed in detention courts and about the overload in the immigration courts that results in people staying here, often for years, that filters back to the Central American countries, and may lead to a perception, rightful or not, that the chances of remaining in the country now are better than ever.”

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