How many T. rexes ever lived? If you think a billion, go higher

While movies like Jurassic Park make an attempt, it’s difficult to imagine what life would be like if the Tyrannosaurus rex was still running around.

“In terms of the T. rex’s physiology, there is no animal alive today that is anything like it,” Charles Marshall tells Inverse. “It was midway between a carnivorous mammal and the Komodo dragon.”

But while we don’t have a creature that compares to the “king of the tyrant lizards,” Marshall, the director of the University of California Museum of Paleontology and a U.C. Berkeley professor, does have a sense of what North America looked like during its reign: at least one T. rex thriving within a 100 square kilometers radius.

In a study published Thursday in Science Marshall and colleagues estimate about 20,000 T. rexes lived at any one time in North America. This suggests some 2.5 billion of these dinosaurs lived on Earth over the course of 2.5 million years.

The background — While it’s known the world’s most popular dinosaur used to live in North America, the question about how many of them wandered within the continent weighed heavily on Marshall’s mind for several years.

After teaming up with his students to find answers, the group realized the answer could emerge if they calculated in an essential fact: there’s a strong relationship between the body mass of any animal and the geographical range of its population density.

For example, considering an animal’s body mass in any location explains why there are relatively few elephants, comparatively more zebras, and loads of rabbits and mice, explains Marshall.

“If you know whether the animal was a carnivore or herbivore, its geographic range of population density, warm or cold-blooded, it is possible to compute with some degree of accuracy or precision about their population density,” he says.

When it comes to the T. rex, experts hypothesize it was relatively warm-blooded, despite its reputation as “king of the tyrant lizards.”

“Most [experts] agree that the Tyrannosaurus rex was a little less warm-blooded than average mammals,” Marshall says.

These factors made the T. rex similar to Komodo dragons, which are about seven or eight times more energetic than the average lizard

With this in mind, the team crunched the numbers and found that around 20,000 adult T. rexes lived at any given time. This data informs the estimation that, over the course of their existence, there were 2.5 billion T. rexes overall.

Digging into the details — While Marshall and his students were brainstorming over how to calculate the approximate population size of the T. rex, he realized that a colleague at UC Berkeley, Wayne Getz, had already been successful in computing the population densities of lions in South Africa.

“That was an ‘aha’ moment,” says Marshall. “I realized if I could use the data from living animals, that makes the calculations easy even for long-extinct animals like the T. rex.”

In addition to what’s known about the Tyrannosaurus rex from fossil records, the researchers incorporated data published by research biologist John Damuth of the University of California, Santa Barbara. Damuth came up with “Damuth’s law”, which states there is a mathematical relationship between an animal’s body mass and its population density.

“... the Tyrannosaurus rex is a lot like a lion.”

After the researchers scoured the scientific literature and consulted experts, they came up with the estimate that the T. rex likely achieved sexual maturity at 15.5 years. Meanwhile, it’s theorized their maximum lifespan was up to their late 20s. Each generation lived up to an average of 19 years.

Throughout their lifespan, the body mass of an adult was around 5.2 tons. The dinosaurs had another growth spurt during sexual maturity and could weigh around 7 tons after that.

“From our calculations, we found that in terms of its population density, the Tyrannosaurus rex is a lot like a lion,” Marshall says.

“In Africa, scientists estimate that there are around 20,000 lions at present as humans have eliminated 95 percent of their geographic range. In comparison, tigers have two to three times lesser population density.”

Predator science — In some respects, the population numbers of adult T. rexes are unusual. Not only was it the only super large predator but there is also a big gap between them and the next apex predators.

“At first, we thought as the only carnivore, adult T. rexes might have been more abundant than you might expect because they were not sharing resources with another species,” says Marshall. “Or maybe the ecosystem just can’t support very much, as flowering plants aren’t as abundant for herbivores.”

For example, in the Arctic region, the population density of polar bears is quite low because of the lack of food sources.

“We simply don’t know whether there was sufficient food availability for the T. rex adults,” Marshall says.

The biggest uncertainty — When it comes to any carnivore’s body mass, there is a lot of ecological variation involved, the study team writes.

For instance, the population density of spotted hyenas is 50 times denser than jaguars — although they are the same size.

“So, when we transfer that ecological variation across to our T. rex study, that gives us an over 100-fold uncertainty in our estimates,” Marshall says.

While the study estimates that there were 20,000 T. rex adults alive at a time, there could have been as few as 1,000, Marshall says. There’s also a chance there were more.

“But that seems way too small,” he says. “It could be as high as almost 330,000. That seems a little more plausible.”

Abstract: Although much can be deduced from fossils alone, estimating abundance and preservation rates of extinct species requires data from living species. Here, we use the relationship between population density and body mass among living species combined with our substantial knowledge of Tyrannosaurus rex to calculate population variables and preservation rates for post-juvenile T. rex. We estimate that its abundance at any one time was ~20,000 individuals, that it persisted for ~127,000 generations, and that the total number of T. rex that ever lived was ~2.5 billion individuals, with a fossil recovery rate of 1 per ~80 million individuals or 1 per 16,000 individuals where its fossils are most abundant. The uncertainties in these values span more than two orders of magnitude, largely because of the variance in the density–body mass relationship rather than variance in the paleobiological input variables.