The science of tree-building took a significant step forward in the late 1900s. Biologists set up standard rules for comparing species and figuring out who was most closely related to whom. Once they were all speaking the same scientific language, they could test each other’s hypotheses with new evidence. They also began to get new kinds evidence for their trees. It became possible to compare not just the skeleton or color patterns of species, but also their proteins and genes.

At first biologists could draw only small trees, typically with a dozen branches at most. They were held back by the fact that a group of species may possibly be related in many different ways. If a biologist adds more species to a group, the possibilities explode. “For 25 species, there are more possible trees than there are stars in the known universe,” Dr. Westneat said. “For 80 species, there are more trees than there are atoms in the known universe.”

Simply comparing every single tree would be impossible. Fortunately, mathematicians developed statistical methods for searching quickly through potential trees to find the ones that do the best job of explaining all the evidence. Computers could do millions of calculations for biologists and store a growing database of information on Web sites. Trees grew hundreds of new branches, then thousands. “We’re overwhelmed with information,” Dr. Hillis said.

Today trees with thousands of branches, sometimes called “supertrees” or “megatrees,” are starting to appear in scientific literature. Their branches reveal patterns in evolution that were missed in smaller studies.

In 2007, for example, Olaf Bininda-Edmonds, a biologist at Carl von Ossietzky University in Germany, and his colleagues published a tree of 4,500 mammals  in other words, just about every known mammal species. The tree allowed researchers to estimate the rate at which mammals have evolved into new lineages. For decades, many researchers have argued that most major groups of living mammals evolved after the dinosaurs became extinct 65 million years ago. Based on their mammal supertree, Dr. Bininda-Emonds and his colleagues argued that mammals were diversifying millions of years earlier.

Less than two years later, the mammal supertree is looking puny. In a paper to be published in the journal BMC Evolutionary Biology, Stephen Smith of the National Evolutionary Synthesis Center in North Carolina and his colleagues have created a tree containing 13,533 species of plants. Their study shows that ferns  sometimes considered as living fossils that have changed little for hundreds of millions of years  have actually been evolving faster than younger groups of plants, like conifers and flowering plants.

Plants are not just related to one another. They’re also related to us animals, fungi, bacteria and all other living things on Earth. Over the past seven years, the National Science Foundation has been financing a project known as Assembling the Tree of Life, the goal of which is “to reconstruct the evolutionary origins of all living things,” according to its Web site. Research teams are analyzing slices of the tree, while mathematicians and computer scientists work on methods to combine them into a single analysis. “You can just imagine how Darwin would have enjoyed it,” Dr. Kohn said.