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.

SignificanceRed Queen (RQ) theory predicts that competition among species should cause extinction risk to be independent of species age, but recent analyses have refuted this central prediction. To fill the resulting theoretical vacuum, we used ecological neutral theory to build a model of the lifespans of incompletely sampled species evolving under zero-sum competition. This model predicts survivorship among fossil zooplankton with surprising accuracy and accounts for empirical deviations from the predictions of RQ more generally. A neutral model of background extinction allows for interpreting survivorship curves in terms of biological process, suggests a novel understanding of mass extinctions, and supports a role for competition in extinction.

Interested in the absolute preservation rate of one of the best understood dinosaurs, Tyrannosaurus rex, Marshall et al. (2021) estimated the total number that ever lived. This required estimating its geographic range, longevity, and population density, which required estimating its body mass and physiology. Meiri (2021) questions the precision of our estimates, emphasizing the difficulties in estimating population densities and geographic ranges for living species, and in error propagation. He posits that estimating population sizes of extinct species is 'extremely unlikely'. While we agree that we did not quantify some sources of uncertainty (for example, in the physiology of T. rex), our calculations do not depend on short-term changes in population density and geographic range, but rather on their long-term averages, rendering many of Meiri's (2021) concerns moot. We also note that Monte Carlo Simulation propagates uncertainties robustly. That is, we feel we have, in fact, developed a general method for estimating population sizes for extinct species, regardless of any shortfalls in implementation.