During its reign of more than 2 million years, Tyrannosaurus rex persisted for more than 125,000 generations and ultimately spawned roughly 2.5 billion tyrant lizards, scientists reported this week.

The researchers drew upon information from the fossil record and from present-day animals to calculate the total number of T. rex that ever lived, and they say that the technique could be applied to other long-extinct species as well. The findings were reported April 15 in Science.

After they die, very few members of any given species will be preserved as fossils. Charles Marshall, director of the University of California Museum of Paleontology and first author of the study, was curious about just how rare an occurrence this is. He and his colleagues decided to calculate the total population size of T. rex, which lived during the Cretaceous, near the end of the age of dinosaurs. 

The first step was to determine the average size of an adult T. rex. Based on how many T. rex fossils of different ages and sizes have been found, the researchers worked out an average mass of 5.2 metric tons, or about 11,464 pounds. They also calculated that the average time between generations was 19 years.

"There's a very strong relationship in the living world between body mass and population density," Marshall said. "So in a given area in Africa, there would be relatively few elephants, there will be more zebras, and there will be a bucketload of rabbits and mice."

The tendency for larger animals to be relatively less abundant in a particular area is known as Damuth's law. Generally, carnivores, such as T. rex, are much less common than grazers; mammalian herbivores have population densities that average about 35 times higher than those of flesh-eating mammals. 

Whether an animal is warm-blooded, meaning it must maintain a constant body temperature, is also important. Reptiles generally have population densities 30 times higher than those of similarly sized mammals. 

"The cooler the blood, the less energy you need to keep alive," Marshall said, and "the more of you there can be."

For their calculations, he and his colleagues settled on a physiology midway between mammalian carnivores such as lions and Komodo dragons, which are "quite a lot warmer-blooded than an average lizard," Marshall said.  

He and his team estimated that T. rex had a population density of roughly one individual per about 110 square kilometers, an area around the size of San Francisco. That means an area the size of California would have a population of 3,800 T. rex, while an area the size of Washington, D.C., would have just two.

The researchers next had to work out how much land the species occupied. Judging by the sites where T. rex fossils have been found, it would have had a minimum geographic area about the size of Mongolia, which is approximately 604,200 square miles.

Scientists have previously used climate models to determine what other locations might have had appealing conditions for T. rex during the Cretaceous. These estimates suggest that its maximum range might have reached into the eastern United States, up into Alaska and down into Mexico. 

Based on the dinosaur's plausible population densities and geographic ranges, Marshall and his colleagues estimated that, on average, 20,000 T. rex were alive at any one time. 

Gaps in the fossil record make it difficult to determine how long T. rex was around, he says. Given the ages of T. rex specimens, though, Marshall and his team estimated that the species lasted for about 2.4 million years. 

This meant that T. rex existed for around 127,000 generations. Finally, the researchers were able to estimate that around 2.5 billion T. rex in total roamed the planet. 

There are about 32 T. rex specimens in museums, which works out to around one in 80 million adults discovered as fossils. However, when considering only the site in Montana where T. rex fossils are most abundant, the preservation rate jumps to an impressive one in 16,000 individuals. 

The true population of T. rex might have been 10 times larger or smaller than his team's average estimate, Marshall said. The biggest source of uncertainty is that population density can vary tremendously among living species.

"Spotted hyenas have about the same body mass as jaguars, they're both top carnivores [and] they're both mammals," Marshall noted — but the population density of hyenas is about 50 times that of jaguars. 

Polar bears dwell in frigid habitats with little food, so they are even sparser than their status as the largest terrestrial carnivore would suggest, he added. In general, carnivorous mammal species of the same body mass vary 150 times over in population density.

"If we want to narrow our estimate down, we need to have a better understanding of the ecology of T. rex, and that is going to be difficult," Marshall said.

One possibility is that T. rex gained enough bite force to crush bone as it matured, allowing it to extract more nutrition from the marrow and support higher population densities. 

"But flowering plants aren't very abundant yet, so there may be just less energy in the ecosystem, which means there will be less herbivores, which means there will be less food to eat, so maybe population density is actually lower," Marshall speculated.

Still, the findings open up the possibility of establishing the population sizes of other ancient species, which could give paleontologists a better sense of the ecosystem to which T. rex belonged.

Additionally, understanding how often well-documented dinosaurs were preserved in the fossil record could offer hints about rarer species.

"We can use the information to start to predict how many species might have been present that are simply not detectable because the preservation rates are too low," Marshall said. "Maybe it's a way of beginning to know the unknowns — the things that we don't see in the fossil record."

The study, "Absolute abundance and preservation rate of Tyrannosaurus rex," published April 15 in Science, was authored by Charles R. Marshall, Daniel V. Latorre, Connor J. Wilson, Tanner M. Frank, Katherine M. Magoulick and Joshua B. Zimmt, University of California, Berkeley; and Ashley W. Poust, University of California, Berkeley and San Diego Natural History Museum.