Absolute abundance and preservation rate of Tyrannosaurus rex - Science Magazine

used a relationship established between body size and population density in extant species to estimate traits such as density, distribution, total biomass, and species persistence for one of the best-known dinosaurs, Tyrannosaurus rex, revealing previously hidden aspects of its population ecology.

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.

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.

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.

(M) Estimate of total number of T.

Our calculations depend on the ability to estimate the population density (ρ) of T.

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.

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).

There is general agreement that dinosaurs were broadly endothermic (7, 16–21) but that different species had different physiologies (19–21) with metabolisms equal to or lower than those of living mammals (20, 21).

This translates into population densities 2.1 times as large as the population densities of the average mammalian carnivore and population densities 1/2.1 times the size of population densities of large varanids for the same body mass.

By contrast, mammalian herbivores average ~35-fold higher population densities than those of flesh-eating mammals (11), and reptiles have, on average, ~30-fold higher population densities than those of mammals for the same body mass (8).

For the body mass estimate of T.

rex, we computed the average body mass of postjuvenile individuals (Fig. 1B and Table 1) [see (11) for why we used this cutoff], which we call the ecological body mass.

This was estimated by summing, over all postjuvenile age cohorts, the product of the average mass of individuals in each cohort, using a T.

rex’s population density (Eq. 1) was between 0.00058 and 0.14 postjuvenile individuals/km2 (with 95% confidence), with a median of 0.0091 individuals/km2 (Fig. 2E and Table 2).

This agrees well with Farlow’s (7) estimate of 0.01 individuals/km2 and is ~0.16 times the population density of tigers and ~0.07 times the population density of lions (8).

The median estimate translates into a population size of 3800 T.

Multiplying the plausible population densities by the plausible geographic areas yielded an average population size of 20,000 individuals, with a 95% interval from 1300 to 328,000 individuals (Fig. 2G and Table 2).

Our median estimate of postjuvenile T.

rex biomass alive at any one time—the population size multiplied by the ecological body mass—is 1.1 × 105 tonnes with a 95% interval from 6.6 × 103 to 1.7 × 106 tonnes.

To estimate the total number of T.

rex that ever lived, we multiplied the standing population size by the total number of generations that T.

The generation time was calculated using the proportion of individuals living to age x years (lx), derived from its cohort survivorship curve (4), and the average number of progeny produced at each age (bx), which requires an estimate of the onset of sexual maturity and its maximum lifetime (eq. S25) (11).

The median estimate, although large, is about half of the total number of adult humans currently alive.

This translates into a median total postjuvenile biomass for all T.

rex that ever existed and the minimum number of described postjuvenile fossil individuals curated in public repositories (10, 11), which consists of 32 individuals, the minimum median per-individual fossil recovery rate is 1 fossil individual for every 80 million individuals (Fig. 2N and Table 2), with a 95% interval ranging from 1 in every 4.5 million to 1 in every 1.3 billion individuals (Fig. 2N and Table 2).

The estimated total number of postjuvenile individuals of T.

The largest source of uncertainty in our analysis stems from the scatter in the body mass–population density relationship from living species, which is about two orders of magnitude larger than the paleobiological uncertainties (Table 2).

This capacity has been enabled by the discovery of many more fossils and the ability to establish growth and survivorship curves from age and body mass estimates.

It also opens the door for other types of analysis—for example, determining how rare, geographically restricted, or short-lived a species had to be to escape discovery in the fossil record or combining population size estimates with measured rates of morphological evolution to infer selection coefficients.

Relationship between body mass and population density elucidates the potential population biology of Tyrannosaurus rex.

Relationship between body mass and population density elucidates the potential population biology of Tyrannosaurus rex