Charles Marshall had been bugging his paleontologist colleagues with this question for years before he eventually collaborated with his students to find an answer.
The team discovered, which will be published in the journal Science this week, is that about 20,000 adult T. rexes lived at any given time, give or take a factor of ten, which is close to most of his colleagues guessed.
Few paleontologists, including himself, had wholly understood that this meant that 2.5 billion people lived and died during the nearly 2 1/2 million years that dinosaurs roamed the planet.
No one has been able to calculate population estimates for long-extinct species until now. George Gaylord Simpson, one of the twentieth century’s most prominent paleontologists, believed it was impossible.
Marshall, the curator of the University of California Museum of Paleontology and the Philip Sandford Boone Chair of Paleontology at UC Berkeley, was also shocked that such an estimate was possible.
“In a way, the project started out as a lark,” he said. “If I hold a fossil in my lap, I can’t help but think about how unlikely it is that this particular beast was alive millions of years ago, and that I am holding a piece of its skeleton. ‘How improbable is it, exactly?’ I kept asking myself. Is it a one-in-a-thousand, a one-in-a-million, or a one-in-a-billion chance?’ Then it occurred to me that we might be able to guess how many were alive, and therefore I might be able to address that question. “
Marshall can point out that the figures have a lot of uncertainty. While the T. rexes population was most likely 20,000 adults at any given time, the 95 percent confidence range (the population range within which there’s a 95 percent probability that the actual number lies) is 1,300 to 328,000 people. As a result, the estimated number of individuals who existed during the lifespan may have ranged from 140 million to 42 billion.
“As Simpson pointed out, making quantitative calculations with the fossil record is extremely difficult,” he said. “In our research, rather than concentrating on making the best estimates, we focused on establishing rigorous constraints on the variables we needed to make our calculations.”
He and his team used Monte Carlo computer simulation to see how the data uncertainties transformed into results uncertainties.
The most significant question mark in these figures, according to Marshall, is the actual existence of the dinosaur’s ecology, including how warm-blooded T. rex was. The research relies on data from UC Santa Barbara’s John Damuth, who established a relationship between body mass and population density in living animals known as Damuth’s Law. While the link is close, ecological differences lead to vast differences in population densities for animals with the same physiology and environmental niche, he said. Jaguars and hyenas, for example, are around the same height, but hyenas have a 50-fold higher density in their population than jaguars.
“Our estimates are based on the relationship between body mass and population density for living organisms,” Marshall said, “but the relationship is uncertain by two orders of magnitude.” “Surprisingly, then, the ecological variability dominates the uncertainty in our predictions, rather than the uncertainty in the paleontological information we used.”
Marshall wanted to model T. rex as a predator with energy needs halfway between a lion and the Komodo dragon, the world’s most giant lizard.
Marshall and his team ignored juvenile T. rexes underrepresented in the fossil record and may have lived apart from adults and hunted different prey. T. rex’s jaws became stronger by order of magnitude as it matured, allowing it to crush bone. It implies that juveniles and adults ate different prey and were almost predator species in their own right.
The lack of medium-sized predators alongside the giant predatory T. rex during the Late Cretaceous was hypothesized to be because juvenile T. rex filled the ecological niche, according to a recent study led by evolutionary biologist Felicia Smith of the University of New Mexico.
What the fossils have to say
The UC Berkeley researchers used evidence from the scientific literature and the expertise of colleagues to calculate that a T. rex’s total body mass. An adult was around 5,200 kilograms or 5.2 tonnes; its maximum lifespan was possibly into its late 20s, and its average lifespan was probably into its late 20s. They also used information about how rapidly T. rexes evolved throughout their lives: they had a growth spurt during sexual maturity and could weigh up to 7,000 kilograms (7 tonnes).
They also determined that each generation lasted about 19 years and that the estimated population was about one dinosaur per 100 square kilometers based on these figures.
They then estimated fixed population size of 20,000 by calculating that T. rex’s entire geographic range was about 2.3 million square kilometers. The species had lived for about 2 1/2 million years. Throughout the species’ 127,000-generation existence, this equates to about 2.5 billion individuals.
Where did all those bones go with such a large number of post-juvenile dinosaurs in the species’ history, not to mention the juveniles that were supposedly more numerous? What percentage of these people have been found by paleontologists? Just about 100 T. rex individuals have been discovered so far, with all of them represented by a single fossilized bone.
“Today, public museums have about 32 reasonably well-preserved post-juvenile T. rexes,” he said. “This means we have around one in every 80 million post-juvenile adults who have ever existed.”
“If we limit our study of the fossil return rate to where T. rex fossils are most common, a portion of the popular Hell Creek Formation in Montana,” he continued, “we estimate we have recovered about one in 16,000 of the T. rexes that lived in that area during the time period that the rocks were deposited.” “We were taken aback by this figure; this fossil record contains a far higher proportion of living organisms than I had expected. Given the uncertainties in the beast’s projected growth rates, it may be as high as one in 1,000 or as low as one in a quarter million.”
Marshall anticipates that many, if not all, of the figures will be disputed by his colleagues. Still, he maintains that his calculational method for estimating extinct populations will hold up and help estimate people of other fossilized species.
“It’s been a paleontological experiment in how much we should discover and how we go about learning it,” he said. “It’s amazing how much we already know about dinosaurs and how much more we can deduce from that. More fossils, more ways of studying them, and improved ways of combining details from different fossils have all helped us learn a lot more about T. rex in the last few decades.”
The system, which the researchers also made accessible as computer code, lays the groundwork for calculating how many species paleontologists might have overlooked while excavating for fossils.
“We may start to guess how many short-lived, geographically specialised organisms we may be losing in the fossil record with these numbers,” he said. “This might be a way to start quantifying what we don’t know.”