Body mass estimates of an exceptionally complete Stegosaurus (Ornithischia: Thyreophora): comparing volumetric and linear bivariate mass estimation methods

Body mass is a key biological variable, but difficult to assess from fossils. Various techniques exist for estimating body mass from skeletal parameters, but few studies have compared outputs from different methods. Here, we apply several mass estimation methods to an exceptionally complete skeleton of the dinosaur Stegosaurus. Applying a volumetric convex-hulling technique to a digital model of Stegosaurus, we estimate a mass of 1560 kg (95% prediction interval 1082–2256 kg) for this individual. By contrast, bivariate equations based on limb dimensions predict values between 2355 and 3751 kg and require implausible amounts of soft tissue and/or high body densities. When corrected for ontogenetic scaling, however, volumetric and linear equations are brought into close agreement. Our results raise concerns regarding the application of predictive equations to extinct taxa with no living analogues in terms of overall morphology and highlight the sensitivity of bivariate predictive equations to the ontogenetic status of the specimen. We emphasize the significance of rare, complete fossil skeletons in validating widely applied mass estimation equations based on incomplete skeletal material and stress the importance of accurately determining specimen age prior to further analyses.     

The extinct,giant giraffid Sivatherium giganteum: skeletal reconstruction and body mass estimation

Sivatherium giganteum is an extinct giraffid from the Plio–Pleistocene boundary of the Himalayan foothills. To date, there has been no rigorous skeletal reconstruction of this unusual mammal. Historical and contemporary accounts anecdotally state that Sivatherium rivalled the African elephant in terms of its body mass, but this statement has never been tested. Here, we present a three-dimensional composite skeletal reconstruction and calculate a representative body mass estimate for this species using a volumetric method. We find that the estimated adult body mass of 1246 kg (857—1812 kg range) does not approach that of an African elephant, but confirms that Sivatherium was certainly a large giraffid, and may have been the largest ruminant mammal that has ever existed. We contrast this volumetric estimate with a bivariate scaling estimate derived from Sivatherium''s humeral circumference and find that there is a discrepancy between the two. The difference implies that the humeral circumference of Sivatherium is greater than expected for an animal of this size, and we speculate this may be linked to a cranial shift in centre of mass.     

Scaling of Soaring Seabirds and Implications for Flight Abilities of Giant Pterosaurs

The flight ability of animals is restricted by the scaling effects imposed by physical and physiological factors. In comparisons of the power available from muscle and the mechanical power required to fly, it is predicted that the margin between the powers should decrease with body size and that flying animals have a maximum body size. However, predicting the absolute value of this upper limit has proven difficult because wing morphology and flight styles varies among species. Albatrosses and petrels have long, narrow, aerodynamically efficient wings and are considered soaring birds. Here, using animal-borne accelerometers, we show that soaring seabirds have two modes of flapping frequencies under natural conditions: vigorous flapping during takeoff and sporadic flapping during cruising flight. In these species, high and low flapping frequencies were found to scale with body mass (mass ^−0.30 and mass ^−0.18) in a manner similar to the predictions from biomechanical flight models (mass ^−1/3 and mass ^−1/6). These scaling relationships predicted that the maximum limits on the body size of soaring animals are a body mass of 41 kg and a wingspan of 5.1 m. Albatross-like animals larger than the limit will not be able to flap fast enough to stay aloft under unfavourable wind conditions. Our result therefore casts doubt on the flying ability of large, extinct pterosaurs. The largest extant soarer, the wandering albatross, weighs about 12 kg, which might be a pragmatic limit to maintain a safety margin for sustainable flight and to survive in a variable environment.     

Euclidean geometry explains why lengths allow precise body mass estimates in terrestrial invertebrates: the case of oribatid mites

Indirect measures of soil invertebrate body mass M based on equations relating the latter to body length (l) are becoming increasingly used due to the required painstaking laboratory work and the technical difficulties involved in obtaining some thousands of reliable weight estimates for animals that can be very small. The implicit assumption of such equations is that dM/dV=δ, where V is body volume and δ is a constant density value. Classical Euclidean scaling implies that V∝l³∝M. One may thus derive M from l when the latter can provide a good estimate of V and the assumption of a constant δ is respected. In invertebrates, equations relating weight to length indicate that the power model always provides the best fit. However, authors only focused on the empirical estimation of slopes linking the body mass to the length measure variables, sometimes fitting exponential and linear models that are not theoretically grounded. This paper explicates how power laws derive from fundamental Euclidean scaling and describes the expected allometric exponents under the above assumptions. Based on the classical Euclidean scaling theory, an equivalent sphere is defined as a theoretical sphere with a volume equal to that of the organism whose body mass must be estimated. The illustrated application to a data set on soil oribatid mites helps clarify all these issues. Lastly, a general procedure for more precise estimation of M from V and δ is suggested.     

Shape shifting predicts ontogenetic changes in metabolic scaling in diverse aquatic invertebrates

Metabolism fuels all biological activities, and thus understanding its variation is fundamentally important. Much of this variation is related to body size, which is commonly believed to follow a 3/4-power scaling law. However, during ontogeny, many kinds of animals and plants show marked shifts in metabolic scaling that deviate from 3/4-power scaling predicted by general models. Here, we show that in diverse aquatic invertebrates, ontogenetic shifts in the scaling of routine metabolic rate from near isometry (b_R = scaling exponent approx. 1) to negative allometry (b_R < 1), or the reverse, are associated with significant changes in body shape (indexed by b_L = the scaling exponent of the relationship between body mass and body length). The observed inverse correlations between b_R and b_L are predicted by metabolic scaling theory that emphasizes resource/waste fluxes across external body surfaces, but contradict theory that emphasizes resource transport through internal networks. Geometric estimates of the scaling of surface area (SA) with body mass (b_A) further show that ontogenetic shifts in b_R and b_A are positively correlated. These results support new metabolic scaling theory based on SA influences that may be applied to ontogenetic shifts in b_R shown by many kinds of animals and plants.     

Lower limits of ornithischian dinosaur body size inferred from a new Upper Jurassic heterodontosaurid from North America

The extremes of dinosaur body size have long fascinated scientists. The smallest (<1 m length) known dinosaurs are carnivorous saurischian theropods, and similarly diminutive herbivorous or omnivorous ornithischians (the other major group of dinosaurs) are unknown. We report a new ornithischian dinosaur, Fruitadens haagarorum, from the Late Jurassic of western North America that rivals the smallest theropods in size. The largest specimens of Fruitadens represent young adults in their fifth year of development and are estimated at just 65–75 cm in total body length and 0.5–0.75 kg body mass. They are thus the smallest known ornithischians. Fruitadens is a late-surviving member of the basal dinosaur clade Heterodontosauridae, and is the first member of this clade to be described from North America. The craniodental anatomy and diminutive body size of Fruitadens suggest that this taxon was an ecological generalist with an omnivorous diet, thus providing new insights into morphological and palaeoecological diversity within Dinosauria. Late-surviving (Late Jurassic and Early Cretaceous) heterodontosaurids are smaller and less ecologically specialized than Early (Late Triassic and Early Jurassic) heterodontosaurids, and this ecological generalization may account in part for the remarkable 100-million-year-long longevity of the clade.     

Giants on the landscape: modelling the abundance of megaherbivorous dinosaurs of the Morrison Formation (Late Jurassic,western USA)

The ecosystem impact of megaherbivorous dinosaurs of the Morrison Formation would have depended on their abundance (number of animals per unit of habitat area) on the landscape. We constrain Morrison megaherbivore abundance by modelling dinosaur abundance in terms of carrying capacity (K), average body mass (ABM) and animal's energy needs. Two kinds of model are presented: ‘demand-side’ models that estimate K in terms of the aggregate energy demand of the dinosaur community, and ‘supply-side’ models that estimate K in terms of retrodicted primary productivity. Baseline values of K, ABM and energy needs for the models are further derived from comparisons with modern large herbivores, and from the composition of the megaherbivore fauna from a particular stratigraphic interval of the Morrison, but in all models a broad range of fractions and multiples of these baseline parameters are considered. ‘Best-guess’ estimates of Morrison megaherbivore abundance suggest an upper limit of a few hundred animals across all taxa and size classes per square kilometre, and up to a few tens of individuals of large subadults and adults.     

What is winter? Modeling spatial variation in bat host traits and hibernation and their implications for overwintering energetics

White‐nose syndrome (WNS) has decimated hibernating bat populations across eastern and central North America for over a decade. Disease severity is driven by the interaction between bat characteristics, the cold‐loving fungal agent, and the hibernation environment. While we further improve hibernation energetics models, we have yet to examine how spatial heterogeneity in host traits is linked to survival in this disease system. Here, we develop predictive spatial models of body mass for the little brown myotis (Myotis lucifugus) and reassess previous definitions of the duration of hibernation of this species. Using data from published literature, public databases, local experts, and our own fieldwork, we fit a series of generalized linear models with hypothesized abiotic drivers to create distribution‐wide predictions of prehibernation body fat and hibernation duration. Our results provide improved estimations of hibernation duration and identify a scaling relationship between body mass and body fat; this relationship allows for the first continuous estimates of prehibernation body mass and fat across the species'' distribution. We used these results to inform a hibernation energetic model to create spatially varying fat use estimates for M. lucifugus. These results predict WNS mortality of M. lucifugus populations in western North America may be comparable to the substantial die‐off observed in eastern and central populations.     

Body mass estimation in xenarthra: A predictive equation suitable for all quadrupedal terrestrial placentals?

The Magnorder Xenarthra includes strange extinct groups, like glyptodonts, similar to large armadillos, and ground sloths, terrestrial relatives of the extant tree sloths. They have created considerable paleobiological interest in the last decades; however, the ecology of most of these species is still controversial or unknown. The body mass estimation of extinct species has great importance for paleobiological reconstructions. The commonest way to estimate body mass from fossils is through linear regression. However, if the studied species does not have similar extant relatives, the allometric pattern described by the regression could differ from those shown by the extinct group. That is the case for glyptodonts and ground sloths. Thus, stepwise multiple regression were developed including extant xenarthrans (their taxonomic relatives) and ungulates (their size and ecological relatives). Cases were weighted to maximize the taxonomic evenness. Twenty‐eight equations were obtained. The distribution of the percent of prediction error (%PE) was analyzed between taxonomic groups (Perissodactyla, Artiodactyla, and Xenarthra) and size groups (0–20 kg, 20–300 kg, and more than 300 kg). To assess the predictive power of the functions, equations were applied to species not included in the regression development [test set cross validation, (TSCV)]. Only five equations had a homogeneous %PE between the aforementioned groups. These were applied to five extinct species. A mean body mass of 80 kg was estimated for Propalaehoplophorus australis (Cingulata: Glyptodontidae), 594 kg for Scelidotherium leptocephalum (Phyllophaga: Mylodontidae), and 3,550.7 kg for Lestodon armatus (Phyllophaga: Mylodontidae). The high scatter of the body mass estimations obtained for Catonyx tarijensis (Phyllophaga: Mylodontidae) and Thalassocnus natans (Phyllophaga: Megatheriidae), probably due to different specializations, prevented us from predicting its body mass. Surprisingly, although obtained from ungulates and xenarthrans, these five selected equations were also able to predict the body mass of species from groups as different as rodents, carnivores, hyracoideans, or tubulidentates. This result suggests the presence of a complex common allometric pattern for all quadrupedal placentals. J. Morphol., 2008. © 2008 Wiley‐Liss, Inc.     

Evidence for a Mass Dependent Step-Change in the Scaling of Efficiency in Terrestrial Locomotion

A reanalysis of existing data suggests that the established tenet of increasing efficiency of transport with body size in terrestrial locomotion requires re-evaluation. Here, the statistical model that described the data best indicated a dichotomy between the data for small (<1 kg) and large animals (>1 kg). Within and between these two size groups there was no detectable difference in the scaling exponents (slopes) relating metabolic (E _met) and mechanical costs (E _{mech, CM}) of locomotion to body mass (M _b). Therefore, no scaling of efficiency (E _{mech, CM}/E _met) with M _b was evident within each size group. Small animals, however, appeared to be generally less efficient than larger animals (7% and 26% respectively). Consequently, it is possible that the relationship between efficiency and M _b is not continuous, but, rather, involves a step-change. This step-change in the efficiency of locomotion mirrors previous findings suggesting a postural cause for an apparent size dichotomy in the relationship between E _met and M _b. Currently data for E _{mech, CM} is lacking, but the relationship between efficiency in terrestrial locomotion and M _b is likely to be determined by posture and kinematics rather than body size alone. Hence, scaling of efficiency is likely to be more complex than a simple linear relationship across body sizes. A homogenous study of the mechanical cost of terrestrial locomotion across a broad range of species, body sizes, and importantly locomotor postures is a priority for future research.     

A computational analysis of limb and body dimensions in Tyrannosaurus rex with implications for locomotion, ontogeny, and growth

The large theropod dinosaur Tyrannosaurus rex underwent remarkable changes during its growth from <10 kg hatchlings to >6000 kg adults in <20 years. These changes raise fascinating questions about the morphological transformations involved, peak growth rates, and scaling of limb muscle sizes as well as the body's centre of mass that could have influenced ontogenetic changes of locomotion in T. rex. Here we address these questions using three-dimensionally scanned computer models of four large, well-preserved fossil specimens as well as a putative juvenile individual. Furthermore we quantify the variations of estimated body mass, centre of mass and segment dimensions, to characterize inaccuracies in our reconstructions. These inaccuracies include not only subjectivity but also incomplete preservation and inconsistent articulations of museum skeletons. Although those problems cause ambiguity, we conclude that adult T. rex had body masses around 6000-8000 kg, with the largest known specimen ("Sue") perhaps ～9500 kg. Our results show that during T. rex ontogeny, the torso became longer and heavier whereas the limbs became proportionately shorter and lighter. Our estimates of peak growth rates are about twice as rapid as previous ones but generally support previous methods, despite biases caused by the usage of scale models and equations that underestimate body masses. We tentatively infer that the hindlimb extensor muscles masses, including the large tail muscle M. caudofemoralis longus, may have decreased in their relative size as the centre of mass shifted craniodorsally during T. rex ontogeny. Such ontogenetic changes would have worsened any relative or absolute decline of maximal locomotor performance. Regardless, T. rex probably had hip and thigh muscles relatively larger than any extant animal's. Overall, the limb "antigravity" muscles may have been as large as or even larger than those of ratite birds, which themselves have the most muscular limbs of any living animal.     

Body size and body shape in early hominins - implications of the Gona Pelvis

Discovery of the first complete Early Pleistocene hominin pelvis, Gona BSN49/P27, attributed to Homo erectus, raises a number of issues regarding early hominin body size and shape variation. Here, acetabular breadth, femoral head breadth, and body mass calculated from femoral head breadth are compared in 37 early hominin (6.0-0.26 Ma) specimens, including BSN49/P27. Acetabular and estimated femoral head sizes in the Gona specimen fall close to the means for non-Homo specimens (Orrorin tugenesis, Australopithecus africanus, Paranthropus robustus), and well below the ranges of all previously described Early and Middle Pleistocene Homo specimens. The Gona specimen has an estimated body mass of 33.2 kg, close to the mean for the non-Homo sample (34.1 kg, range 24-51.5 kg, n = 19) and far outside the range for any previously known Homo specimen (mean = 70.5 kg; range 52-82 kg, n = 17). Inclusion of the Gona specimen within H. erectus increases inferred sexual dimorphism in body mass in this taxon to a level greater than that observed here for any other hominin taxon, and increases variation in body mass within H. erectus females to a level much greater than that observed for any living primate species. This raises questions regarding the taxonomic attribution of the Gona specimen. When considered within the context of overall variation in body breadth among early hominins, the mediolaterally very wide Gona pelvis fits within the distribution of other lower latitude Early and Middle Pleistocene specimens, and below that of higher latitude specimens. Thus, ecogeographic variation in body breadth was present among earlier hominins as it is in living humans. The increased M-L pelvic breadth in all earlier hominins relative to modern humans is related to an increase in ellipticity of the birth canal, possibly as a result of a non-rotational birth mechanism that was common to both australopithecines and archaic Homo.     

Scaling of standard metabolic rate in estuarine crocodiles Crocodylus porosus

Standard metabolic rate (SMR, ml O₂ min^?1) of captive Crocodylus porosus at 30 °C scales with body mass (kg) according to the equation, SMR = 1.01 M^0.829, in animals ranging in body mass of 3.3 orders of magnitude (0.19–389 kg). The exponent is significantly higher than 0.75, so does not conform to quarter-power scaling theory, but rather is likely an emergent property with no single explanation. SMR at 1 kg body mass is similar to the literature for C. porosus and for alligators. The high exponent is not related to feeding, growth, or obesity of captive animals. The log-transformed data appear slightly curved, mainly because SMR is somewhat low in many of the largest animals (291–389 kg). A 3-parameter model is scarcely different from the linear one, but reveals a declining exponent between 0.862 and 0.798. A non-linear model on arithmetic axes overestimates SMR in 70 % of the smallest animals and does not satisfactorily represent the data.     

Body shape shifting during growth permits tests that distinguish between competing geometric theories of metabolic scaling

Metabolism fuels all of life's activities, from biochemical reactions to ecological interactions. According to two intensely debated theories, body size affects metabolism via geometrical influences on the transport of resources and wastes. However, these theories differ crucially in whether the size dependence of metabolism is derived from material transport across external surfaces, or through internal resource‐transport networks. We show that when body shape changes during growth, these models make opposing predictions. These models are tested using pelagic invertebrates, because these animals exhibit highly variable intraspecific scaling relationships for metabolic rate and body shape. Metabolic scaling slopes of diverse integument‐breathing species were significantly positively correlated with degree of body flattening or elongation during ontogeny, as expected from surface area theory, but contradicting the negative correlations predicted by resource‐transport network models. This finding explains strong deviations from predictions of widely adopted theory, and underpins a new explanation for mass‐invariant metabolic scaling during ontogeny in animals and plants.     

Use of bioelectrical impedance spectroscopy to provide a measure of body composition in sows

The ability to accurately estimate fat mass and fat-free mass (FFM) has the potential to improve the way in which sow body condition can be managed in a breeding herd. Bioelectrical impedance spectroscopy (BIS) has been evaluated as a practical technique for assessment of body composition in several livestock species, but similar work is lacking in sows. Bioelectrical impedance uses population-specific algorithms that require values for the apparent resistivities of body fluids and body proportion factors. This study comprised three major aims: (i) to derive apparent resistivity coefficients for extracellular water (ECW) and intracellular water (ICW) required for validation of BIS predictions of total body water (TBW) in live sows against standard reference tracer dilution methods; (ii) to develop predictions of TBW to body composition prediction algorithms, namely FFM, by developing a body geometry correction factor (Kb) and (iii) to compare the BIS predictions of FFM against existing impedance predictors and published prediction equations for use in sows, based on physical measurements of back-fat depth and BW (P2-based predictors). Whole body impedance measurements and the determination of TBW by deuterium dilution and ECW by bromide dilution were performed on 40 Large White x Landrace sows. Mean apparent resistivity coefficients of body fluids were 431.1 Ω.cm for ECW and 1827.8 Ω.cm for ICW. Using these coefficients, TBW and ECW were over-estimated by 6.5 and 3.3%, respectively, compared to measured reference values, although these differences were not statistically different (P > 0.05). Mean Kb was 1.09 ± 0.14. Fat-free mass predictions were 194.9 kg, which equates to 60.9% of total sow weight, and 183.0 kg for BIS and the deuterium dilution method, respectively. Mean differences between the predicted and measured FFM values ranged from − 8.2 to 32.7%, but were not statistically different (P > 0.05). Method validation (leave-one-out procedure) revealed that mean differences between predicted and measured values were not statistically significant (P > 0.05). Of the impedance-based predictors, equivalence testing revealed that BIS displayed the lowest test bias of 11.9 kg (8.2%), although the P2-based prediction equations exhibited the lowest bias and percentage equivalence, with narrow limits of agreement. Results indicate although differences between mean predicted and measured values were not significantly different, relatively wide limits of agreement suggest BIS as an impractical option for assessing body composition in individual sows compared to the use of existing prediction equations based on BW and back fat.     

Mechanics of posture and gait of some large dinosaurs

Dimensions of dinosaur bones and of models of dinosaurs have been used as the basis for calculations designed to throw light on the posture and gaits of dinosaurs.
Estimates of the masses of some dinosaurs, obtained from the volumes of models, are compared with previous estimates. The positions of dinosaurs' centres of mass, derived from models, show that some large quadrupedal dinosaurs supported most of their weight on their hind legs and were probably capable of rearing up on their hind legs.
Distributions of bending moments along the backs of large dinosaurs are derived from measurements on models. The tensions required in epaxial muscles to enable Diplodocus to stand are calculated. It is likely that the long neck of this dinosaur was supported by some structure running through the notches in the neural spines of its cervical and dorsal vertebrae. The nature of this hypothetical structure is discussed.
An attempt is made to reconstruct the walking gait of sauropod dinosaurs, from the pattern of footprints in fossil tracks.
The dimensions of dinosaur leg bones are compared to predictions for mammals of equal body mass, obtained by extrapolation of allometric equations. Their dimensions are also used to calculate a quantity which is used as an indicator of strength in bending. Comparisons with values for modern animals lead to speculations about the athletic performance of dinosaurs.
Estimates of pressures exerted on the ground by the feet of dinosaurs are used in a discussion of the ability of dinosaurs to walk over soft ground.     

New Insights into Non-Avian Dinosaur Reproduction and Their Evolutionary and Ecological Implications: Linking Fossil Evidence to Allometries of Extant Close Relatives

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.     

A test of genetic models for the evolutionary maintenance of same-sex sexual behaviour

The evolutionary maintenance of same-sex sexual behaviour (SSB) has received increasing attention because it is perceived to be an evolutionary paradox. The genetic basis of SSB is almost wholly unknown in non-human animals, though this is key to understanding its persistence. Recent theoretical work has yielded broadly applicable predictions centred on two genetic models for SSB: overdominance and sexual antagonism. Using Drosophila melanogaster, we assayed natural genetic variation for male SSB and empirically tested predictions about the mode of inheritance and fitness consequences of alleles influencing its expression. We screened 50 inbred lines derived from a wild population for male–male courtship and copulation behaviour, and examined crosses between the lines for evidence of overdominance and antagonistic fecundity selection. Consistent variation among lines revealed heritable genetic variation for SSB, but the nature of the genetic variation was complex. Phenotypic and fitness variation was consistent with expectations under overdominance, although predictions of the sexual antagonism model were also supported. We found an unexpected and strong paternal effect on the expression of SSB, suggesting possible Y-linkage of the trait. Our results inform evolutionary genetic mechanisms that might maintain low but persistently observed levels of male SSB in D. melanogaster, but highlight a need for broader taxonomic representation in studies of its evolutionary causes.     

Scaling in Free-Swimming Fish and Implications for Measuring Size-at-Time in the Wild

This study was motivated by the need to measure size-at-age, and thus growth rate, in fish in the wild. We postulated that this could be achieved using accelerometer tags based first on early isometric scaling models that hypothesize that similar animals should move at the same speed with a stroke frequency that scales with length^-1, and second on observations that the speed of primarily air-breathing free-swimming animals, presumably swimming ‘efficiently’, is independent of size, confirming that stroke frequency scales as length^-1. However, such scaling relations between size and swimming parameters for fish remain mostly theoretical. Based on free-swimming saithe and sturgeon tagged with accelerometers, we introduce a species-specific scaling relationship between dominant tail beat frequency (TBF) and fork length. Dominant TBF was proportional to length^-1 (r² = 0.73, n = 40), and estimated swimming speed within species was independent of length. Similar scaling relations accrued in relation to body mass^-0.29. We demonstrate that the dominant TBF can be used to estimate size-at-time and that accelerometer tags with onboard processing may be able to provide size-at-time estimates among free-swimming fish and thus the estimation of growth rate (change in size-at-time) in the wild.