Allometric equations for predicting body mass of dinosaurs

We use data from the literature to compare two statistical procedures for estimating mass (or size) of quadrupedal dinosaurs and other extraordinarily large animals in extinct lineages. Both methods entail extrapolation from allometric equations fitted to data for a reference group of contemporary animals having a body form similar to that of the dinosaurs. The first method is the familiar one of fitting a straight line to logarithmic transformations, followed by back-transformation of the resulting equation to a two-parameter power function in the arithmetic scale. The second procedure entails fitting a two-parameter power function directly to arithmetic data for the extant forms by nonlinear regression. In the example presented here, the summed circumferences for humerus plus femur for 33 species of quadrupedal mammals was the predictor variable in the reference sample and body mass was the response variable. The allometric equation obtained by back-transformation from logarithms was not a good fit to the largest species in the reference sample and presumably led to grossly inaccurate estimates for body mass of several large dinosaurs. In contrast, the allometric equation obtained by nonlinear regression described data in the reference sample quite well, and it presumably resulted in better estimates for body mass of the dinosaurs. The problem with the traditional analysis can be traced to change in the relationship between predictor and response variables attending transformation, thereby causing measurements for large animals not to be weighted appropriately in fitting models by least squares regression. Extrapolations from statistical models obtained by back-transformation from lines fitted to logarithms are unlikely to yield reliable predictions for body size in extinct animals. Numerous reports on the biology of dinosaurs, including recent studies of growth, may need to be reconsidered in light of our findings.     

Trabecular bone scales allometrically in mammals and birds

Many bones are supported internally by a latticework of trabeculae. Scaling of whole bone length and diameter has been extensively investigated, but scaling of the trabecular network is not well characterized. We analysed trabecular geometry in the femora of 90 terrestrial mammalian and avian species with body masses ranging from 3 g to 3400 kg. We found that bone volume fraction does not scale substantially with animal size, while trabeculae in larger animals' femora are thicker, further apart and fewer per unit volume than in smaller animals. Finite element modelling indicates that trabecular scaling does not alter the bulk stiffness of trabecular bone, but does alter strain within trabeculae under equal applied loads. Allometry of bone's trabecular tissue may contribute to the skeleton's ability to withstand load, without incurring the physiological or mechanical costs of increasing bone mass.     

Dynamics of haemopoiesis across mammals

Haemopoiesis is a fundamental physiologic process found in many animals. Among mammals, the diversity in size and function required suitable adaptations of this process. In this work, we use allometric principles to determine whether this required a change in the basic architecture of haemopoiesis. We show that it is possible to express both the number and rate with which haemopoietic stem cells replicate as well as total marrow output across all mammals as a function of adult mass. This unified view, which is compatible with the existing data, suggests that there was no need for major adaptations in the architecture of haemopoiesis across mammals.     

Scaling of rectal gland mass in the European lesser-spotted dogfish

In the European lesser-spotted dogfish Scyliorhinus canicula , rectal gland mass in mg ( M _Rg) followed the allometric relationship: M _Rg = 1·15 M ^0·68, where M is body mass (g). The concept of allometric scaling is an important consideration in studies investigating the function of osmoregulatory organs.     

Shrinking to fit: fluid jettison from a haemocoelic hydrostatic skeleton during defensive withdrawals of a gastropod larva

Although most of the basic animal body plans are supported by hydrostatic skeletons consisting of fluid maintained at constant volume, studies on how animals have solved biomechanical scaling dilemmas during evolution of large body size have emphasized cases where skeletons are formed by rigid solids. Larvae of gastropod molluscs swim using ciliated velar lobes supported by a constant volume hydrostatic skeleton. Defensive behaviour involves rapid withdrawal of the velar lobes and foot into a protective biomineralized shell. Some gastropod larvae grow to giant size and the velar lobes enlarge allometrically, but the lobes and foot of many can still withdraw completely into the mineral-stiffened shell. I dyed internal fluid of a large gastropod larva with fluorescein to show that fluid supporting the extended velar lobes is expelled from discrete release sites during defensive withdrawals. Scanning electron microscopy suggested that release sites are distinctive papillae on the upper velar epidermis. Ultrathin sections revealed that branched tracks of microvilli-free membrane on the surface of these papillae were formed by very thin epithelial cells, which may rupture and re-anneal during and after defensive withdrawals. Behaviours facilitated by fluid discharge from a haemocoelic (non-coelomic) body compartment have been rarely reported among aquatic invertebrates, but may be more widespread than currently recognized.     

Ontogenetic phase shifts in metabolism: links to development and anti-predator adaptation

The allometric relationships between resting metabolism (VO₂) and body mass (M), VO₂ = a_iM^b, are considered a fundamental law of nature. A distinction though needs to be made between the ontogeny (within a species) and phylogeny (among species) of metabolism. However, the nature and significance of the intraspecific allometry (ontogeny of metabolism) have not been established in fishes. In this study, we present experimental evidence that a puffer fish ranging 0.0008–3 g in wet body mass has four distinct allometric phases in which three stepwise increases in scaling constants (a_i, i = 1–4), i.e. ontogenetic phase shifts in metabolism, occur with growth during its early life stages at around 0.002, 0.01 and 0.1 g, keeping each scaling exponent constant in each phase (b = 0.795). Three stepwise increases in a_i accompanied behavioural and morphological changes and three peaks of severe cannibalism, in which the majority of predation occurred on smaller fish that had a lower value of a_i. Though fishes are generally highly fecund, producing a large number of small eggs, their survivability is very low. These results suggest that individuals with the ability to rapidly grow and step up ‘a_i’ develop more anti-predator adaptation as a result of the decreased predatory risk.     

Scaling of gas exchange cycle frequency in insects

Previously, it has been suggested that insect gas exchange cycle frequency (fC) is mass independent, making insects different from most other animals where periods typically scale as mass-0.25. However, the claim for insects is based on studies of only a few closely related taxa encompassing a relatively small size range. Moreover, it is not known whether the type of gas exchange pattern (discontinuous versus cyclic) influences the fC-mass scaling relationship. Here, we analyse a large database to examine interspecific fC-mass scaling. In addition, we investigate the effect of mode of gas exchange on the fC-scaling relationship using both conventional and phylogenetically independent approaches. Cycle frequency is scaled as mass(-0.280) (when accounting for phylogenetic non-independence and gas exchange pattern), which did not differ significantly from mass(-0.25). The slope of the fC-mass relationship was shallower with a significantly lower intercept for the species showing discontinuous gas exchange than for those showing the cyclic pattern, probably due to lower metabolic rates in the former. Insects therefore appear no different from other animals insofar as the scaling of gas exchange fC is concerned, although gas exchange fC may scale in distinct ways for different patterns.     

Fecundity and fertility in a freshwater population of the neotropical amphidromous shrimp Macrobrachium acanthurus from the southeastern Atlantic

The neotropical amphidromous shrimp Macrobrachium acanthurus is one of various freshwater crustaceans heavily exploited in the southwestern Atlantic. Fecundity (nº early embryos female^?1) was examined during 2007 at four different localities (Iguape, Registro, Sete Barras, and Eldorado) along a stretch of river extending over 85?km (Ribeira de Iguape, São Paulo State, Brazil). Also, fertility (nº hatched larvae female^?1) was examined at one locality (Registro) during 2009–2010. Fecundity (mean?±?SD: 5191?±?2635; range: 1086–13,014 embryos female^?1) did not vary throughout the segment of river studied. Fecundity increased with female body size (carapace length, CL). However, fecundity scaled negatively with shrimp body size; females produce disproportionably fewer eggs with a unit increase in CL. The conditions explaining the negative allometric relationship between fecundity and female body size in M. acanthurus remain to be addressed. Nevertheless, natural food constraints limiting the ability of large but not small females to acquire enough resources to produce and fill their gonads with oocytes represents a plausible explanation for the negative scaling of fecundity with body size. Fertility varied between 545 and 12,465 hatched larvae female^?1 with an average (±SD) of 3981 (± 2693) and increased isometrically with a unit increase in female body size. M. acanthurus has an average fecundity and fertility that represents one of the extremes regarding the trade-off between fecundity/fertility and egg-size reported for caridean shrimps. All of this information needs to be considered in assessing shrimp stocks and establishing a sustainable management plan for this exploited species in the southwestern Atlantic.