ARMONK, N.Y. — As the sun went down one night in September, 16-year-old Violet Clinton marched into a meadow of goldenrod with her butterfly net.

Every few minutes she flicked it toward a speck in the air. She knelt to examine a bug that looked like a toasted pecan with antennae.

“This is a three-lined leafroller moth,” she said. “There’s one kind of woodgrain leafroller moth that looks similar, but those came earlier in the year.”

She snapped a picture with her smartphone, then set the moth free. Onward she went toward a cluster of pines where an even greater variety of insects awaited.

“That’s a pug moth. That’s an elegant grass-veneer moth. And that’s a wasp.”

Violet is a high school junior by day and a moth researcher by night.…