The headline that 2.5 *billon* *T. Rex* dinosaurs walked the Earth was definitely something that caught my attention. It turns out that that number was just the average with a massive variation in possible values. What I was more interested in was how one sets about even making an estimate of the number of animals in a species that has been extinct for 65 million years. The paper lays out the problem and basic method they used.

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 postjuvenile 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.

A basic problem with estimating the number of individuals in an extinct species is that the fossil record in incomplete and fossilization rates are unknown which makes the number of fossils a poor guide to the numbers that existed. So researchers had to find other means using data from *living* species. And what they used is the strong correlation between population density ρ and body mass M given by something called Damuth’s law that is given by the equation log_{10}(ρ) = log_{10}(a) − b × log_{10}(M) with values of b = −3/4 for the slope, leaving just a and M to be estimated. The above equation is equivalent to the power law ρ=aM^{-b}.

Once they get the population density, they multiply it by the plausible geographic areas to get the abundance. The average value of the abundance they get is 20,000 with a 95% interval from 1,300 to 328,000 individuals. To get the total number that ever existed they multiply this number by the number of generations that it persisted which they estimate as 127,000. This gives the range of the total number from 165 million to 42 billion, with an average value of 2.5 billion. Given the difficulty of estimating the parameters involved, the wide range of possible numbers is not surprising. Even the lower end is pretty big.

When you realize that only 32 adult *T. Rex* fossils have ever been found, you get an idea of how rarely fossilization occurs.

Bruce says

I’ll just note here that, like creationists, I’ve never found a fossil homo sapiens, so I can’t be sure they exist.

Pierce R. Butler says

… the strong correlation between population density ρ and body mass M given by something called Damuth’s law ..Which may be upended by something extraneous such as a possible higher oxygen level in the Cretaceous, or a different rate of maturation, or factors influencing, say, cannibalism among hatchlings. Does this sort of analysis even attempt to consider whether eggs should count as individual organisms?

sonofrojblake says

Biologist makes harmless but wild speculation based on massive assumptions. Physicist response: how interesting, let’s tell people about this.

Physicist makes harmless but wild speculation based on massive assumptions. Biologist response: how do physicists get away with publishing this crap? https://freethoughtblogs.com/pharyngula/2020/06/15/how-do-physicists-get-away-with-publishing-this-crap/

Interesting difference in attitude.

Sam N says

@3, maybe fair.

Biologists do get frustrated for good reasons. We have interacted with physicists on a regular basis, and the stereotype, based somewhat accurately, but, of course, simplified, is that when confronted by a biological problem will ignore all of the masses of evidence (i.e. variance) and propose a very simple, already considered, and incorrect idea. If we had not been confronted by such so regularly, maybe biologists wouldn’t be so defensive. I’m not defending PZ’s post (I haven’t read it). I’m just giving you context. If you ever actually worked as an academic biologist for a substantial amount of time, who very likely would have run into this. Neurosciences was so interdisciplinary I encountered many physicists who actually did become maddened by the variance and difficulty of clean conclusions.

Most physicists I have chosen to interact with are rather self-aware of this. I remember some guy at Johns Hopkins where we would go talking about whatever interested us until the lights were turned off at the happy hour. I wish I could remember his name. I know his face so clearly.

Sam N says

As a simple extension. Physicists are still yearning for a unified general physics theory. I long ago discarded any hope of such regarding the human brain, and realized, for systems neuroscience, one must adopt scattered bits and pieces of models and hope for the best.

Physicists are much more likely to believe some unified single theory of how brains work is presently feasible. They have no idea how clueless the best of the experts truly are.

Some group of science took neural networks of 5. Just 5 neurons, that could be examined completely. These neural nets were created to perform very simple operations. The success rate of researchers with access to precisely how the neural nets operated, every single feature, for understanding the intended operation was about 20% if I recall correctly.

Let that sink in for a while. I often will throw up my hands. I can give you some ideas, but I don’t know a damned thing.

Personal experience. But I would be sincerely interested in a poll based on undergraduate disciplines: Do you believe the brain can be explained, today, with a single unified theory?

sonofrojblake says

I can’t imagine anyone, from any discipline, answering that question with a yes.

Sam N says

You’ve never met Robert Hecht Nielsen (widely and accurately considered a crank, but well-cited despite that). Michael Graziano. I do not consider him a crank, but he oversimplifies.

Sam N says

Oh wow. I’m sharing a photo of myself now. I was just looking to set up a blog for myself. Another neuroscientist, friend helped me. I am extremely ignorant about how to use wordpress/the blog.