John Chater remembers the day vividly. He was about two years old. His grandfather gave him a dark, purplish pomegranate. Happily, he opened it and starting eating.

He quickly realized his mistake. He was wearing his new light brown suede shoes. The pomegranate juice quickly found the shoes, leaving a permanent scar.

“That was my first experience, that I remember, with pomegranates, and it involved getting in trouble,” Chater said. “Because it was so delicious, I didn't realize it would stain.”

More than 30 years later, Chater is a Ph.D. student at the University of California, Riverside, with a focus on pomegranate...