Estimation of maximum body size in fossil species: A case study using Tyrannosaurus rex

Among extant species, the ability to sample the extremes of body size-one of the most useful predictors of an individual's ecology-is highly unlikely. This improbability is further exaggerated when sampling the already incomplete fossil record. We quantify the likelihood of sampling the uppermost limits of body size in the fossil record using Tyrannosaurus rex Osborn, 1905 as a model, selected for its comparatively well-understood life history parameters. We computationally generate a population of 140 million T. rex (based on prior estimates), modelling variation about the growth curve both with and without sexual dimorphism (the former modelled after Alligator mississippiensis), and building in sampling limitations related to species survivorship and taphonomic bias, derived from fossil data. The 99th percentile of body mass in T. rex has likely already been sampled, but it will probably be millennia before much larger giants (99.99th percentile) are sampled at present collecting rates. Biomechanical and ecological limitations notwithstanding, we estimate that the absolute largest T. rex may have been 70% more massive than the currently largest known specimen (~15,000 vs. ~8800 kg). Body size comparisons of fossil species should be based on ontogenetically controlled statistical parameters, rather than simply comparing the largest known individuals whose recovery is highly subject to sampling intensity.