Statistical power analysis: application to an investigation of dinosaur thermal physiology

Abstract

It has been postulated that the variation in an animal's body temperature during different phases of bone deposition can be estimated from the variation in the ratio of two oxygen isotopes in phosphate recovered from its fossil. Using data from a fossil Tyrannosaurus rex skeleton, the previous researchers failed to reject the null hypothesis that the variation found in bones from the body core is signi®cantly less than that found in the extremities; they also failed to reject the null hypothesis that the coldest and hottest parts of the body differed by less than 4 8C. This suggests that either both null hypotheses are true, or that they are false but the statistical tests used were not powerful enough to detect this. Here I use calculation of con®dence intervals to differentiate between these two alternatives. In the ®rst case, I ®nd that the data are consistent with the variance in both the core and the extremity being up to 2.5 times that of the other. In the second case, I show that observations are consistent with temperature differences ranging from 2.6 8C to 6.4 8C. Hence, neither case provides any real support for the hypothesis that bone deposition in this specimen occurred under essentially thermostable conditions.

Respiratory and Reproductive Paleophysiology of Dinosaurs and Early Birds

“…However, there are abundant data demonstrating that many birds and mammals often maintain extremity temperatures well below deep-body, or core, temperatures (Ruben 1995). Additionally, fossil bone oxygen isotope ratios may be strongly influenced by ground water temperatures (Kolodny et al 1996) and, in any case, the conclusions reached by Barrick and Showers (1994) are not statistically supported by their own data (Ruxton 2000). Fossilized bone oxygen isotope ratios in dinosaurs are likely to reveal little, if any, definitive information about dinosaur metabolic physiology.…”

Stable Isotope Compositions of Biological Apatite

“…From these data Barrick and coworkers conclude that dinosaurs were basically endothermic, and that endothermy was accomplished by high metabolisms, but that metabolisms were perhaps not as high as in modern day birds or mammals. Others have criticized their results, partly because of issues regarding the potential for alteration of PO 4 oxygen in bones (Kolodny et al 1996), and partly because a > ± 2 ˚C temperature variability for the "dinosaurian endotherms" cannot be rejected statistically (Ruxton 2000). Nonetheless, the apparent preservation of isotopic differences among bones of an ecotherm, but not in dinosaurs, does suggest that dinosaurs had a different metabolism, and were capable of at least crude endothermy.…”

Historical biogeography of scarabaeine dung beetles

“…Further studies maintain that dinosaurs, in general, grew rapidly (Padian et al ., 2001) but that these rates fall between the slower rates in modern reptiles or marsupials and thefaster rates in modern birds or Eutherian mammals (Erickson & Tumanova, 2000). There is inconclusive support for thermostable conditions in Tyrannosaurus rex provided by comparisons between body core and body periphery bone deposition using oxygen isotopes (Ruxton, 2000). Additional studies show: (1) unmodified reptilian lung structure in theropod dinosaurs which is indicative of slower gas‐exchange rates compared with modern birds and mammals (Ruben et al ., 1997); (2) narrow nasal passages in theropod and ornithischian dinosaurs which are indicative of low ventilation and low metabolic rates compared with those in extant endotherms in which the cross‐sectional area of nasal passages is four times that in extant ectotherms (Ruben et al ., 1996); (3) the absence of respiratory maxillo‐turbinate nasal bones in dinosaurs (Ruben et al ., 1996) and early birds whose presence are indicative of endothermy in mammals (Monastersky, 1994); and (4) likely ectothermic patterns of thermoregulation in early birds (Ruben et al ., 1998) which are consistent with ectothermy in their dinosaur ancestors.…”