Insects around the world are in a crisis, according to a small but growing number of long-term studies showing dramatic declines in invertebrate populations. A new report suggests that the problem is more widespread than scientists realized. Huge numbers of bugs have been lost in a pristine national forest in Puerto Rico, the study found, and the forest’s insect-eating animals have gone missing, too.

In 2014, an international team of biologists estimated that, in the past 35 years, the abundance of invertebrates such as beetles and bees decreased by 45 percent. In places where long-term insect data are available, mainly in Europe, insect numbers are plummeting. A study last year showed a 76 percent decrease in flying insects in the past few decades in German nature ­preserves.

The latest report, published Monday in the Proceedings of the National Academy of Sciences, shows that the problem extends to the Americas. The study’s authors implicate climate change in the loss of tropical invertebrates.

“This study in PNAS is a real wake-up call — a clarion call — that the phenomenon could be much, much bigger, and across many more ecosystems,” said David Wagner, an expert in invertebrate conservation at the University of Connecticut who was not involved with this research. He added: “This is one of the most disturbing articles I have ever read.”

Bradford Lister, a biologist at Rensselaer Polytechnic Institute in New York, has been studying rain forest insects in Puerto Rico since the 1970s. If Puerto Rico is the island of enchantment — “la isla del encanto” — then its rain forest is “the enchanted forest on the enchanted isle,” he said. Birds and coqui frogs trill beneath a 50-foot-tall emerald canopy. The forest, named El Yunque, is well-protected. Spanish King Alfonso XII claimed the jungle as a 19th-century royal preserve. Decades later, Theodore Roosevelt made it a national reserve, and El Yunque remains the only tropical rain forest in the National Forest system.

“We went down in ’76, ’77 expressly to measure the resources: the insects and the insectivores in the rain forest, the birds, the frogs, the lizards,” Lister said.

He came back nearly 40 years later, with his colleague Andres Garcia, an ecologist at the National Autonomous University of Mexico. What the scientists did not see on their return troubled them. “Boy, it was immediately obvious when we went into that forest,” Lister said. Fewer birds flitted overhead. The butterflies, once abundant, had all but vanished.

Garcia and Lister once again measured the forest’s insects and other invertebrates, a group called arthropods that includes spiders and centipedes. The researchers trapped arthropods on the ground in plates covered in a sticky glue, and raised several more plates about 3 feet into the canopy. They also swept nets over the brush hundreds of times, collecting the critters that crawled through the vegetation.

Each technique revealed the biomass (the dry weight of all the captured invertebrates) had significantly decreased from 1976 to the present day.