In recent decades, scientists have looked for better ways to determine how many species are left to find. In 1988, Robert May, an evolutionary biologist at the University of Oxford, observed that the diversity of land animals increases as they get smaller. He reasoned that we probably have found most of the species of big animals, like mammals and birds, so he used their diversity to calculate the diversity of smaller animals. He ended up with an estimate 10 to 50 million species of land animals.

Other estimates have ranged from as few as 3 million to as many as 100 million. Dr. Mora and his colleagues believed that all of these estimates were flawed in one way or another. Most seriously, there was no way to validate the methods used, to be sure they were reliable.

For the new estimate, the scientists came up with a method of their own, based on how taxonomists classify species. Each species belongs to a larger group called a genus, which belongs to a larger group called a family, and so on. We humans, for example, belong to the class of mammals, along with about 5,500 other species.

In 2002, researchers at the University of Rome published a paper in which they used these higher groups to estimate the diversity of plants around Italy. At three different sites, they noted the number of genera, families and so on. There were fewer higher-level groups than lower ones at each site, like the layers of a pyramid. The scientists could estimate how many species there were at each site, much as it’s possible to estimate how big the bottom layer of a pyramid based on the rest of it.

The paper drew little notice at the time, but Dr. Mora and his colleagues seized on it, hoping to use the method to estimate all the species on Earth. They charted the discovery of new classes of animals since 1750. The total number climbed steeply for the first 150 years and then began to crest — a sign that we’re getting close to finding all the classes of animal. They found that the discovery rate of other high-level groups has also been slowing down. The scientists built a taxonomic pyramid to estimate the total number of species in well-studied groups, like mammals and birds. They consistently made good predictions.

Confident in their method, the scientists then used it on all major groups of species, coming up with estimates of 7.7 million species of animals, for example, and 298,000 species of plants. Although the land makes up 29 percent of the Earth’s surface, the scientists concluded that it is home to 86 percent of the world’s species.

“I think it is an interesting and imaginative new approach to the important question of how many species actually are alive on earth today,” said Lord May.