We tested if growth rates of recent taxa are unequivocally separated between endotherms and ectotherms, and compared these to dinosaurian growth rates. We therefore performed linear regression analyses on the log-transformed maximum growth rate against log-transformed body mass at maximum growth for extant altricial birds, precocial birds, eutherians, marsupials, reptiles, fishes and dinosaurs. Regression models of precocial birds (and fishes) strongly differed from Case’s study (1978), which is often used to compare dinosaurian growth rates to those of extant vertebrates. For all taxonomic groups, the slope of 0.75 expected from the Metabolic Theory of Ecology was statistically supported. To compare growth rates between taxonomic groups we therefore used regressions with this fixed slope and group-specific intercepts. On average, maximum growth rates of ectotherms were about 10 (reptiles) to 20 (fishes) times (in comparison to mammals) or even 45 (reptiles) to 100 (fishes) times (in comparison to birds) lower than in endotherms. While on average all taxa were clearly separated from each other, individual growth rates overlapped between several taxa and even between endotherms and ectotherms. Dinosaurs had growth rates intermediate between similar sized/scaled-up reptiles and mammals, but a much lower rate than scaled-up birds. All dinosaurian growth rates were within the range of extant reptiles and mammals, and were lower than those of birds. Under the assumption that growth rate and metabolic rate are indeed linked, our results suggest two alternative interpretations. Compared to other sauropsids, the growth rates of studied dinosaurs clearly indicate that they had an ectothermic rather than an endothermic metabolic rate. Compared to other vertebrate growth rates, the overall high variability in growth rates of extant groups and the high overlap between individual growth rates of endothermic and ectothermic extant species make it impossible to rule out either of the two thermoregulation strategies for studied dinosaurs.

How anatomical, physiological and ecological (life history) features scale with body mass is a fundamental question in biology. There is an ongoing debate in the scientific literature whether allometric scaling follows a universal pattern that can be described in a single model, or diff ers between groups. However, recently some analyses were published demonstrating a change in scaling across the body mass range: brain-size allometry of mammals indicates that scaling follows a curvilinear pattern in double-logarithmic space, and a quadratic pattern in double-logarithmic space was found in one of the largest physiological datasets, on basal metabolic rate (MR) in mammals. Here, we analysed a variety of independent datasets on anatomical, physiological and ecological characteristics in mammals, birds and reptiles to answer the question whether the quadratic scaling is a universal biological law, or a pattern unique to mammals. Th e pattern was present in mammalian basal and field MR, brain size, and reproduction parameters, but neither in other organ allometries in mammals, nor in the scaling of MR in birds and reptiles. However, the curvature was better explained by separate allometric scaling of three different mammalian reproduction strategies: marsupials, and eutherian mammals with one and with many off spring. The two latter strategies are distributed unequally over the body mass range in eutherian mammals. Our fi ndings show that a quadratic model, as well as a traditional allometric model with a universal scaling exponent (such as 0.67 or 0.75), may be inappropriate in mammals as they are a result of different scalings within these three reproductive groups. We propose that the observed distribution pattern is the result of the eutherian mammal clade's uniquely pronounced dichotomy of reproductive strategies. DOI: https://doi.org/10.1111/j. 1600-0706.2011.19505 64 and log-transformation gives the quadratic function 65(5) 66 Equation (4) reflects that the exponent term changes systematically with M 67 (Kolokotrones et al. 2010). In this approach the magnitude of the parameter estimates for a 68 and b 1 (but not b 2 ) depend on the unit of M; however, the full exponent term [is constant for a given M independent of the unit of M, and increases in a consistent manner 70 with M (Fig. 1b in Kolokotrones et al. 2010). 71In relaxing the assumption of a fixed allometric exponent, quadratic approaches to 72 metabolic scaling have the potential to unravel new trends in the evolution of life history 73 traits. A convenient interpretation of the quadratic scaling pattern is that, as mammals become 74 smaller or larger than some hypothetical M mid-point, they both increase their MR beyond 75 the general simple power allometry. Bats -which we will use repeatedly as an example here -76 appear to be one exception (of several) to that pattern, with lower BMR than many mammals 77 of similar M (Fig. 1a). We analysed datasets (see Table 1 for sources) for BMR in mammals, birds and reptiles, as 94 well as datasets fo...

Janis and Carrano (1992) suggested that large dinosaurs might have faced a lower risk of extinction under ecological changes than similar-sized mammals because large dinosaurs had a higher potential reproductive output than similar-sized mammals (JC hypothesis). First, we tested the assumption underlying the JC hypothesis. We therefore analysed the potential reproductive output (reflected in clutch/litter size and annual offspring number) of extant terrestrial mammals and birds (as “dinosaur analogs”) and of extinct dinosaurs. With the exception of rodents, the differences in the reproductive output of similar-sized birds and mammals proposed by Janis and Carrano (1992) existed even at the level of single orders. Fossil dinosaur clutches were larger than litters of similar-sized mammals, and dinosaur clutch sizes were comparable to those of similar-sized birds. Because the extinction risk of extant species often correlates with a low reproductive output, the latter difference suggests a lower risk of population extinction in dinosaurs than in mammals. Second, we present a very simple, mathematical model that demonstrates the advantage of a high reproductive output underlying the JC hypothesis. It predicts that a species with a high reproductive output that usually faces very high juvenile mortalities will benefit more strongly in terms of population size from reduced juvenile mortalities (e.g., resulting from a stochastic reduction in population size) than a species with a low reproductive output that usually comprises low juvenile mortalities. Based on our results, we suggest that reproductive strategy could have contributed to the evolution of the exceptional gigantism seen in dinosaurs that does not exist in extant terrestrial mammals. Large dinosaurs, e.g., the sauropods, may have easily sustained populations of very large-bodied species over evolutionary time.

It has been hypothesized that a high reproductive output contributes to the unique gigantism in large dinosaur taxa. In order to infer more information on dinosaur reproduction, we established allometries between body mass and different reproductive traits (egg mass, clutch mass, annual clutch mass) for extant phylogenetic brackets (birds, crocodiles and tortoises) of extinct non-avian dinosaurs. Allometries were applied to nine non-avian dinosaur taxa (theropods, hadrosaurs, and sauropodomorphs) for which fossil estimates on relevant traits are currently available. We found that the reproductive traits of most dinosaurs conformed to similar-sized or scaled-up extant reptiles or birds. The reproductive traits of theropods, which are considered more bird-like, were indeed consistent with birds, while the traits of sauropodomorphs conformed better to reptiles. Reproductive traits of hadrosaurs corresponded to both reptiles and birds. Excluding Massospondylus carinatus , all dinosaurs studied had an intermediary egg to body mass relationship to reptiles and birds. In contrast, dinosaur clutch masses fitted with either the masses predicted from allometries of birds (theropods) or to the masses of reptiles (all other taxa). Theropods studied had probably one clutch per year. For sauropodomorphs and hadrosaurs, more than one clutch per year was predicted. Contrary to current hypotheses, large dinosaurs did not have exceptionally high annual egg numbers (AEN). Independent of the extant model, the estimated dinosaur AEN did not exceed 850 eggs (75,000 kg sauropod) for any of the taxa studied. This estimated maximum is probably an overestimation due to unrealistic assumptions. According to most AEN estimations, the dinosaurs studied laid less than 200 eggs per year. Only some AEN estimates obtained for medium to large sized sauropods were higher (200-400 eggs). Our results provide new (testable) hypotheses, especially for reproductive traits that are insufficiently documented or lacking from the fossil record. This contributes to the understanding of their evolution.

Osteocytes harbour much potential for paleobiological studies. Synchrotron radiation and spectroscopic analyses are providing fascinating data on osteocyte density, size and orientation in fossil taxa. However, such studies may be costly and time consuming. Here we describe an uncomplicated and inexpensive method to measure osteocyte lacunar densities in bone thin sections. We report on cell lacunar densities in the long bones of various extant and extinct tetrapods, with a focus on sauropodomorph dinosaurs, and how lacunar densities can help us understand bone formation rates in the iconic sauropod dinosaurs. Ordinary least square and phylogenetic generalized least square regressions suggest that sauropodomorphs have lacunar densities higher than scaled up or comparably sized mammals. We also found normal mammalian-like osteocyte densities for the extinct bovid Myotragus, questioning its crocodilian-like physiology. When accounting for body mass effects and phylogeny, growth rates are a main factor determining the density of the lacunocanalicular network. However, functional aspects most likely play an important role as well. Observed differences in cell strategies between mammals and dinosaurs likely illustrate the convergent nature of fast growing bone tissues in these groups.