IRA FLATOW: This is Science Friday. I’m Ira Flatow. Who doesn’t know or want to know more about T-rex? And that’s good because there’s still a lot we don’t know about the charismatic carnivore. One of the questions a team of researchers had was how many total T-rexes– how many individual dinos actually existed? And how would you calculate that?

That group of scientists did some back-of-the-envelope calculations and came up with a rough estimate of 2 and 1/2 billion T-rexes over 2 and 1/2 million years. That’s plus or minus a factor of 10. The results were published in the journal Science.

My next guest is one of the authors on that study here to quench those Cretaceous stats with us. Charles Marshall, director of the University of California Museum of Paleontology in Berkeley, California. Welcome to Science Friday.

CHARLES MARSHALL: Good morning. Thank you.

IRA FLATOW: This sounds like a crazy idea. I mean, not really. But what made you come up with this?

CHARLES MARSHALL: Ever since I was a kid, I was struck by how rare fossils were. If I had a fossil in my hand or I see a T. Rex skeleton, I know that it’s rare, but I’ve always asked myself, how rare? One in a million? One a billion? One in a trillion? And then I realized, I think I know how to calculate that number.

IRA FLATOW: Fill us in on how you did that.

CHARLES MARSHALL: With the fossil record alone, it’s simply not possible. However, on the landscape today, the bigger the animal, the rarer it is. There are fewer elephants than there are zebras compared to rabbits or mice. So it turns out there’s a very strong relationship between body mass and population density.

And I realized that relationship is strong enough that if we had an estimate of T. Rex body mass, which we do, we could estimate density. All we need to do is multiply that density by the geographic area over which T-rex lives and that would give us the total number of T-rex that lives at any one time. And then all I need to know is the geologic longevity and the number of generations that represents. Multiply that and I get the total number of T-rex that ever lived.

IRA FLATOW: You know, 2 and 1/2 billion sounds like a lot of T-rex.

CHARLES MARSHALL: It’s a lot of T-rex. We were surprised by the size of that number. At any one time, it’s pretty small– 20,000, a few tens of thousands. I remind you that our human population now we have about 5 billion adults alive right now. So it’s tiny compared to the human population sizes.

IRA FLATOW: So can you give us an idea of how many lived per square mile, for example?

CHARLES MARSHALL: So it looks like the density is about one T-rex per 40 square miles. I believe that Manhattan is about 23 square miles. So there’d be about one T-rex in the area of Manhattan, except I think they were probably clumpy. They were probably following prey. So that over time, the average would be about one per Manhattan.

IRA FLATOW: Sounds like a lot of number crunching. How did you get all of this data?

CHARLES MARSHALL: So it turns out, particularly in the last 10 or 15 years, our knowledge of T-rex has increased enormously. Not only is that the iconic dinosaur, it’s probably one of the best-known dinosaurs, period.

And so what we needed for that, we needed to know roughly its maximum age– about 28 years. We needed to know how it grew. We have growth curves, you can cut a bone you can look at the growth rings, and you can estimate its age. You can estimate its body mass, therefore estimate a growth curve. That enabled us to calculate the generation time.

There are enough fossils that you can plot out the geographic area. That’s a minimum estimate because the fossil record is incomplete. Someone has done some climate modeling. Taking it back for the Cretaceous, and using the known distribution of fossils, you can estimate what the climate was that it preferred and then map that out to the rest of North America, it looks like T-rex may have lived as far north as southern Alaska, Mexico, and perhaps all the way across the eastern, southern eastern United States. And that gave us a maximum estimate of geographic range, for example.

IRA FLATOW: And one of the variables you had to figure out, I imagine, was how warm-blooded was T-rex?

CHARLES MARSHALL: Ah, yes, very good. The density of animals on the ground is proportional to how warm-blooded they are. Warm-bloodedness takes a lot of energy. So there are less animals. So I think there are about 35 times more lizards, for example, than small mammals of the same size that have the same diet.

Everybody agrees that T-rex was warm blooded. Most people agree that it was probably a little less warm blooded than say, a lion or a tiger. Some people think the only way they could get so large so fast was if they had a metabolism similar to that of a Komodo dragon.

Komodo dragons turn out to be a lot more energetic than the average lizard. A lot of paleontologist feel like a Komodo dragon is just too cool-blooded to be a T-rex. And so what we did is we split the difference. And said it’s somewhere between a Komodo dragon and a lion.

I would add that ecological differences for a given body mass are so large that it actually swamps out that uncertainty. For example, spotted hyenas are 50 times denser than jaguars even though they both have about the same body mass. The difference between our estimate of T-rex and a Komodo dragon and our estimate of T-rex and a mammal is just a factor of 2.

IRA FLATOW: I understand that you ignored juvenile T-rexes. Why is that?

CHARLES MARSHALL: So we ignored juvenile T-rexes for two reasons. We hoped we could ignore them. If I start off with 100 eggs and they hatch, it’s very hard to get any evidence in the fossil record of them and to account for them. The main reason we ignored them is it looks like as they cross into sexual maturity that the increase in bite force, they’re changing the ecological role.

Moreover, when we go to places like Hell Creek where T-rex are most common, even though you’d expect more than half of those fossils to be juveniles, it turns out that only 15% are. That suggests they’re living somewhere else where they’re not being fossilized and ecologically playing a different role. And therefore, in effect, they’re almost like a different species. So we just considered the adult T-rex.

IRA FLATOW: Now why is figuring out the population density of T-rex so important to you? And did you learn stuff that you thought you knew but turned out to be wrong or some new things you never heard of before?

CHARLES MARSHALL: The fossil record is the only way we know about things like T-rex and Triceratops, mass extinctions, the history of our own species. But it’s incomplete and it’s past. It’s gone. So one of my major interests is how much can we know and how do we go about knowing it.

So this is partly an exercise in just seeing how much we can know. I had no idea how much we knew about T-rex when I began this study. A lot of creative work, a lot of fossils discovered, a lot of clever ways of analyzing those fossils.

I was very surprised at the ecological shift. I didn’t know about that. I was surprised that we could get a very tight number for the generation time, 19 years, plus or minus 1. I was surprised at how many T-rex ever lived. That really surprises me a lot, the size of that number.

We also did the calculation of the preservation rate where T-rex are most common. Across the whole geologic and geographic range, it looks like we have about 1 in every 80 million individuals that ever walked the Earth. In Hell Creek, it looks like we have about 1 in 16,000. And that strikes me as being an incredible fossil recovery rate.

IRA FLATOW: Good happy hunting to everybody who’s looking for more T-rex because they’re still out there.

CHARLES MARSHALL: Indeed.

IRA FLATOW: Thank you very much for taking time to be with us today.

CHARLES MARSHALL: You are most welcome.

IRA FLATOW: We all learned a lot. Charles Marshall, director of the University of California Museum of Paleontology in Berkeley, California.

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