Tyrannosaurs as long-lived species

Abstract

Biodemographic analysis would be essential to understand population ecology and aging of tyrannosaurs. Here we address a methodology that quantifies tyrannosaur survival and mortality curves by utilizing modified stretched exponential survival functions. Our analysis clearly shows that mortality patterns for tyrannosaurs are seemingly analogous to those for 18th-century humans. This result suggests that tyrannosaurs would live long to undergo aging before maximum lifespans, while their longevity strategy is more alike to big birds rather than 18th-century humans.

Figure 1. Survival curves of tyrannosaurs.

The demographic data for tyrannosaurs were adapted from the survival curves by calibrating the 60% neonate mortality (the dots). The data were fit by the modified stretched exponential functions (the solid lines) as s(x) = exp(−(x/α)^β(x)) by measuring the characteristic life α and the stretched exponent β(x). The reduced age x/ω is taken by dividing the tyrannosaur age x by their maximum lifespan ω.

Figure 2. Age-dependent patterns of stretched exponents for tyrannosaurs.

The age-dependent stretched exponents β(x) for each survival curve were formulated by polynomial functions (the solid lines).

Figure 3. Mortality curves of tyrannosaurs and 18th-century humans.

Suitable descriptions of mortality curves were obtained from s(x) (Fig. 1) and β(x) (Fig. 2). We compared mortality patterns for tyrannosaurs (the solid lines) and 18th-century humans (the closed squares for the 1751 Swedish cohorts of males and females; the lowest solid line for the modeled mortality curve).

Figure 4. Species-dependent sensitivity of stretched exponents.

The age-dependent stretched exponents β(x) with respect to the normalized age x/α for various species exhibit a significant difference between 18th-century humans and tyrannosaurs. The species-dependent scale effect can be ruled out by using the normalized age x/α. Assessing the β(x) patterns is useful in understanding longevity strategy across species.