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Absolute abundance and preservation rate of Tyrannosaurus rex

Despite the famed incompleteness of the fossil record, much can be inferred from fossil material, including cell sizes and thus genome sizes (1); individual longevities (2, 3); and growth and cohort survivorship curves (2, 4, 5). However, quantifying population-level variables such as population density and abundance is made difficult by the incompleteness of the fossil record (6, 7), largely because fossilization rates are unknown, which means that the number of fossils cannot be used to calculate these variables.

Nonetheless, data from living species indicate a strong relationship between population density and body mass (8), which makes it possible to estimate population-level variables. Here, for one of the best understood dinosaurs, Tyrannosaurus rex (Fig. 1) (9, 10), we use this relationship to estimate its population density, which we combine (Fig. 2) (11) with our rich knowledge of the species to estimate several population-level variables, including the total number of T. rex that ever lived and the species’ preservation rate. We assessed the impact of uncertainties in the data used with Monte Carlo simulations (11), but these simulations do not accommodate uncertainties that might stem from the choices made in the design of our approach (11).

Our calculations depend on the ability to estimate the population density (ρ) of T. rex (Fig. 2). Here, we use Damuth’s Law (8, 12, 13) to constrain that density. Derived from living species, Damuth found that ρ is negatively correlated with a species’ body mass (M) through a power law (8)log10(ρ) = log10(a) − b × log10(M)(1)In applying Eq. 1, we used the broadly accepted value of b = −3/4 for the slope (8, 11, 12, 14) [see (11) for b = −2/3], which leaves two unknowns: the intercept [log10(a)] and the body mass (M).

The intercept [log10(a)] depends on trophic level and physiology. Trophically, T. rex was clearly a carnivore, but establishing its physiology has proven challenging (7, 15). Among living species, a slower metabolism is reflected in larger population densities, hence larger values of the intercept. However, ecological differences between species within the same trophic level, regardless of physiology, translate into a large scatter in population densities, independent of the intercept (Fig. 2A). For example, flesh-eating mammals have a 150-fold variation (±1.96σ) in population density for species of the same body mass (11) (Fig. 2A).

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