Pete Buttigieg had been mayor just 13 weeks when he faced a leadership crisis.

It was March 2012, and 300 residents of South Bend, Ind. solemnly marched to the Martin Luther King Center to protest the killing in Florida of a black teenager, Trayvon Martin.

A prominent figure at the demonstration was Darryl Boykins, South Bend’s first black police chief. Admired for teaching tennis and boxing to young people, he had been promoted to chief five years earlier after winning the respect of both black and white officers in a department that sometimes divided along racial lines.