Statistical methods for paleodemography on fossil assemblages having small numbers of specimens: an investigation of dinosaur survival rates

We describe statistical methods to formulate and validate statements about survival rates given a small number of individuals. These methods allow one to estimate the age-specific survival rate and assess its uncertainty, to assess whether the survival rates during some age range differ from the survival rates during another age range, and to assess whether the survivorship curve has a particular shape. We illustrate these methods by applying them to a sample of 22 Albertosaurus sarcophagus individuals. We show that this sample is too small to provide any confidence in the claim that this species had a “convex” survivorship curve arising from age-specific survival rates that decreased monotonically with age. However, we show that a sample of 50 to 100 individuals has reasonable statistical power to support such a claim. There is evidence for the much weaker claim that average survival rates for ages 2 to 15 were higher than survival rates for later ages. Finally, we describe one way to account for size-dependent fossilization rates and show that a plausible positively-size-dependent fossilization rate results in a substantially non-convex survivorship curve for A. sarcophagus .