But the DNA of animals offers good reason to think that the roots of the kingdom extend much further back. Over generations, genetic mutations arise at a roughly steady rate. By comparing the mutations in different animal lineages, scientists can estimate how much earlier the common ancestor of those lineages lived. The studies suggest that the common ancestor of all living animals lived somewhere around 750 million years ago — well before the Cambrian.

That’s why the possibility that a 609-million-year-old fossil like Caveasphaera is an animal is so exciting, and provokes so much controversy.

Caveasphaera was first described in 2000 by Dr. Knoll and Shuhai Xiao , then a Harvard graduate student and now a paleobiologist at Virginia Tech. The creature was among a flood of new species emerging around then from an extraordinary site in southern China called the Doushantuo Formation.

Its limestone rocks were packed with microscopic remains. A single rock from the site, dissolved in a mild acid, can yield hundreds of thousands of fossils.

Scientists including Dr. Knoll and Dr. Xiao picked out a few of the most common species to examine closely. They noticed some striking similarities between some of them and animal embryos. Some fossils were spheres containing a pair of cells, or four cells, or more.

Those first reports attracted a flood of research, and a lot of debate. It turns out that early animal embryos can be hard to distinguish from other forms of life. Red algae, for example, divide into embryo-like clusters of cells before sprouting stalks and fronds.

“I would love them to be animals,” said Philip C.J. Donoghue , a paleontologist at the University of Bristol, in England, who has studied Doushantuo fossils for 15 years. “But they could well be lots of other things, too.”