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 log10(ρ) = log10(a) − b × log10(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.