Invasive grass covered UC Santa Barbara's Lagoon Island before restoration (behind) brought back the functional diversity of the region's coastal sage scrub. Credit: Jeremiah Bender

There's a conundrum that has perplexed biologists since Charles Darwin himself. Why do some exotic species take off as invasive pests while others don't?

Scientists have documented dozens of factors influencing the spread of exotic plants and animals across scores of ecosystems. But they've struggled to identify overarching patterns and the primary mechanisms that generate them.

Now, however, scientists have access to electronic records that report the locations and day of year when specimens of thousands of species were collected across vast geographic regions over more than two centuries.…