Last year, Ms. Jones’s demands for fewer police officers and more investment in communities like hers became the demands of a movement — after the police killing of George Floyd in Minneapolis shook the country, inspired the largest mass demonstrations for civil rights in generations and pushed police reform to the forefront of the national agenda. Now, a year after Mr. Floyd’s death, Los Angeles and other American cities face a surge in violent crime amid pandemic despair and a flood of new guns onto the streets. The surge is prompting cities whose leaders embraced the values of the movement last year to reassess how far they are willing to go to reimagine public safety and divert money away from the police and toward social services... Criminologists and law enforcement leaders largely blame the rise in violence on two things: a historic increase in gun-buying by Americans, with a flood of illegal, so-called ghost guns, often assembled with parts bought online and are untraceable, and the despair and economic devastation of the pandemic. Still, while the number of murders in Los Angeles last year — 350 — was the highest in more than a decade, it was nowhere near the number of killings in the early 1990s, when more than 1,000 people were killed in a year. And other crimes, such as rape and burglary, are down so far this year compared with numbers from last year. And even as the politics shifts a year after the unrest, activists and the ordinary citizens who joined them on the streets can claim a number of wins: Los Angeles officials diverted $150 million from the police budget last year to study alternatives to traditional policing. Voters also elected a new district attorney who promised to prosecute officers and send fewer people to prison, and approved a measure to spend millions of dollars a year on alternatives to incarceration and more social services.