Downsizing a heavyweight: factors and methods that revise weight estimates of the giant fossil whale Perucetus colossus

Body mass of the largest blue whale

The body mass of the largest blue whale has never been measured, although there is a good basis for estimating this value. Total length (TL) has been historically used by cetologists and marine mammalogists since the early twentieth century, and it was widely adopted as a standard by the early 20th century whaling industry (Mackintosh & Wheeler, 1929), which had abundant access to large, intact cetacean carcasses. By contrast, cetacean body mass is extremely difficult to measure reliably for cetaceans heavier than ~100 kg (Gambell, 1970; Lockyer, 1976); total length is also more invariant to fluid loss and distortion once the specimen close to weighing equipment.

We used Lockyer’s (1976) compilation of records for TL and weights for large cetaceans as a starting point for the primary literature, along with select records published in a narrative by Small (1971:31–34). Following Scheffer’s (1974) line of reasoning for identifying the largest blue whale ever, we focused on females from the Southern Hemisphere (owing to sex and geographic size biases; Branch et al., 2007) and a timeframe before the mid-twentieth century conclusion of large-scale pelagic whaling. Accordingly, the longest reliably measured blue whale was a female 33.26 m long (109.12 feet long; see Risting, 1928). Winston (1950) enumerated the piecemeal weighing of a 27.1 m female blue whale that was at least 136.4 tons, although additional reputable, but less comprehensive records point to blue whales minimally weighing between 140 tons and 160.4 tons (Lockyer, 1976). While other methods exist to measure large cetacean body weights (see Gambell, 1970 for sperm whales [Physeter macrocephalus]), TL provides the most consistently comparable and widely sampled value for this aim.

For the purposes of this study, we used five body lengths—17 m that was used as the minimum length for Perucetus, 25 m that was used by Bianucci et al. (2023), 30 m as convenient benchmark for blue whale length maxima, 33 m after Risting (1928), and lastly an arbitrary value of 15 m (half the latter benchmark) for data exploration purposes—to validate the implication by Bianucci et al. (2023) that Perucetus was larger than the largest blue whales. We employed both length-based on volumetric approaches so that the results can be cross-examined. For length-based estimation, we used the data set Nishiwaki (1950) and Ohno & Fujino (1952), who collectively reported the body mass and length of 34 individuals of blue whales, spanning from 21.3 to 27.1 m in length. The individual mentioned by Winston (1950), whale No. 319, is included in Nishiwaki’s (1950) dataset. Of the 34, we removed three pregnant individuals and retained the rest. Lockyer (1976) added some data to those mentioned above but we did not include these data because the weight data summarized in that work were inconsistently collected and the sample size is small. We ran an ordinary least square analysis on the data using R (R-Core-Team, 2020), with body mass as dependent and length as independent variables. We used the resulting regression relationships to extrapolate the body mass of a blue whale with a body length of 15, 17, 25, 30, and 33 m, with confidence and prediction intervals (Table 1).

Data from Nishiwaki (1950) and Ohno & Fujino (1952) were collected by cutting large whale carcasses into measurable pieces (as described by Winston, 1950), leading to blood (and other fluid) loss, despite the best efforts to retain them for weighing. Therefore, we sought to account for blood loss in our regressions. There is a general relationship between body to blood volume ratios and deep diving in whales (Bernaldo De Quirós et al., 2019). Blue whales are not deep diving taxa (Schreer & Kovacs, 1997), and non-deep-diving cetaceans fit in a range of 7 to 14% for this ratio. We therefore used this range of ratios to bracket for blood loss.

The logic of estimation explained above is not fundamentally different from one used by Lockyer (1976), who proposed two equations for estimating blue whale body mass from TL. However, we did not use these equations because one has an unspecified degree of blood loss compensation embedded, whereas the other is based on mixed data from inconsistent methods. The equations also lack confidence and prediction intervals.

For the volumetric approach, we used an R package Paleomass (Motani, 2023), which brackets the true body mass of marine vertebrates using 3D models built from orthogonal silhouettes. The method has a high accuracy, with a mean absolute error of 1.33% when the silhouettes are accurate. We built Paleomass models based on a dorsal view photograph (https://commons.wikimedia.org/wiki/File:Blue_Whale_001_body_bw.jpg) and lateral view reconstruction (https://commons.wikimedia.org/wiki/File:Balaenoptera_musculus_NOAA.jpg) derived from NOAA (National Oceanic and Atmospheric Administration), and assumed a whole body density of 1.027 g/cm³, which is the density of seawater at surface (Stewart, 2008). We used a superelliptical exponent range of 2.0 to 2.3, which was found to be suitable for cetaceans (Motani, 2023). Given that the two images are from different individuals which are most likely smaller than 30 m, the error level is probably higher than 1.33%. Nevertheless, it provides sufficient accuracy to cross-examine the length-based estimates, which tends to have a much larger error margin.

Volumetric mass estimation of Perucetus

It is impossible to accurately estimate the body mass of Perucetus volumetrically, given the lack of accurate body outline reconstructions from both ventral and lateral views. However, it is still possible to bracket the upper bound of its body mass based on the data from Bianucci et al. (2023). There are two difficulties involved: that only the lateral view was reconstructed (Bianucci et al., 2023; Fig. 2), with the vertebral column curled down toward the tail, and that the accuracy of the published body outline reconstruction is unknown.

We addressed the first difficulty in two steps. First, we straightened the published body reconstruction of Perucetus colossus along the vertebral column, as seen in Fig. 2. Lines perpendicular to the vertebral column were drawn at the center of every second vertebral centrum, spanning the dorsal and ventral margins of the body (Fig. 2). Then the vertebral column was straightened posteriorly by rotating each segment from the previous step, leaving some curvature near the fluke that approaches similar curves in extant whales (Buchholtz, 2001). The ends of the perpendicular lines were connected to draw the new dorsal and ventral margins (Fig. 2, black curves). Second, we used the straightened lateral view outline to bracket the upper bound of the body in the R package Paleomass. Extant cetaceans have a more slender profile in dorsal view rather than lateral view (Bierlich et al., 2022), so using the lateral view in place of ventral view constantly leads to overestimation of the true body volume (compare Figs. 1C and 1D). The largest distortion is caused by the tail stock, which is strongly compressed laterally. We tested this observation with Paleomass based on the blue whale silhouettes discussed above, as well those from three other species in Motani (2023). The overestimation rate was 26% in harbor porpoises (Phocoena phocoena), 23% in Heaviside’s dolphins (Cephalorhynchus heavisidii), 14% in bottlenose dolphins (Tursiops truncatus), and 5% in blue whales. In particular, blue whales have an exceptionally low value because they have heads sufficiently large and flattened to counterbalance the tail, which is laterally compressed, so using the value of 5% for non-mysticetes would likely lead to errors. We therefore assume that the body mass of Perucetus was overestimated by 14 to 26% by using only the lateral body silhouette.

The second difficulty cannot be addressed easily. However, it is evident that the published body outline reconstruction of Perucetus is already very fat for its length—its body depth, assuming a body length of 20 m, is already as deep as that of a 30 m blue whale (Figs. 1B vs. 1C). We therefore infer that the published reconstruction is close to the upper limit of how fat Perucetus could have been for its length. In combination with the factors explained above, the resulting volumetric estimate of body mass is expected to overestimate true mass, allowing bracketing of the upper bound.

Perucetus was estimated to be 17 to 20 m in total length, a value that is well-constrained by comparison with closely related basilosaurid whales (e.g., Basilosaurus) that are known from complete skeletons e.g. (Gingerich, Smith & Simons, 1990). We therefore used this range for volumetric estimates of body mass. We also experimented with slightly smaller sizes of down to 15 m, which is an arbitrary decision, but nonetheless useful for the purposes of exploring possible outcomes for estimating body mass.

We assumed a density of surface seawater (1.027 g/cm³) for Perucetus, as with blue whales. Although marine tetrapods alter their body density during the course of a day, depending on their behavior, the body density range always includes neutral buoyancy (Domning & de Buffrénil, 1991; Watanabe et al., 2006; Aoki et al., 2011; Sato et al., 2013; Gordine, Fedak & Boehme, 2015). This density consistency is partly because marine tetrapods need to breathe at sea surface, during which they are neutrally or positively buoyant. We note that this consistency is also true for pachyostotic marine mammals, such as sirenians (Domning & de Buffrénil, 1991; Kipps et al., 2002; Lefebvre, 2023). Therefore, our use of the surface seawater density is justified.

Effect of assumed isometry in extrapolation

Bianucci et al. (2023) tested the isometry between skeletal and bone masses with a positive result and used this result as the justification for using a simple ratio instead of an allometric regression line to estimate body mass. However, the test of isometry only demonstrates that the difference between the isometric line through the mean, representing a constant ratio, and the corresponding allometric regression line is very small in the range of observation. Notably, it does not guarantee that the two are identical, especially outside of the data range. It is therefore necessary to examine if the isometric line from a ratio and the corresponding allometric regression lines are sufficiently close to each other outside of the data range.

We took the following steps in examining this question. We started by downloading the data and R scripts used by the authors from their GitHub site (https://GitHub.com/eliamson/ColossalCode). The site did not contain the phylogenetic tree used in computation, named MamPhy_fullPosterior_BDvr_DNAonly_4098sp_topoFree_NDexp_MCC_v2_target.tre, so we located it in another GitHub site (https://github.com/n8upham/MamPhy_v1/tree/master/_DATA) and downloaded it. Upon examination of the tree, however, we noticed that the topology of Mysticeti placed Megaptera at the base of the clade, a relationship that is not supported by current phylogenetic consensus (e.g., McGowen et al., 2020). We therefore used Timetree.org to download a time-calibrated phylogeny of Cetacea in Newick format to be used as an alternative tree. The tree is provided in Supplemental Information.

We made four subsets of data, representing terrestrial mammals, Cetacea, Odontoceti, and Mysticeti, respectively, and regressed the body mass against skeletal mass for each subset, with Phylogenetic Generalized Least Square (PGLS). This step is the opposite of Fig. 4 in Bianucci et al. (2023) because the aim is to estimate body mass from skeletal mass. We used the same tree as Bianucci et al. (2023) for terrestrial mammals, and the above stated trees for cetaceans. We then plotted isometric lines, i.e., of slope 1, though the means of these four subsets, respectively. Lastly, we assessed the differences between isometric and allometric lines in the part of the graph extrapolated to accommodate Perucetus.

Effect of pachyostosis

The data used by Bianucci et al. (2023) contained 11 individuals belonging to Florida manatees (Trichechus manatus) selected from Domning & de Buffrénil (1991), which clearly have much lighter body mass for their skeletal mass compared to cetaceans. Manatees are known for pachyostosis, which thickens cortical bones that gives them greater density than in typical vertebrates (Houssaye, 2013). It is reasonable for pachyostotic mammals to have lighter body mass for skeletal mass because they are not necessarily much fatter than non-osteosclerotic species despite the added bone weight. Given that Perucetus was also pachyostotic, it is possible that it also had a lighter body mass for skeletal mass compared to modern cetaceans. We therefore estimated the body mass of Perucetus based on the regression relationships of skeletal mass against body mass in manatees. We used ordinary least square regression given that the data are monospecific.

The original data of Domning & de Buffrénil (1991) contained 64 individuals from two species of manatees (Trichechus spp.), of which 50 had both body and skeletal mass data. Twelve of the 50 were less than 1.5 m in body length and considered perinates according to Ingle & Porter (2020), leaving 38 individuals in the complete manatee data. Bianucci et al. (2023) selected the largest 11 individuals of the 38, with body lengths greater than 3 m. The intention may have been to include only adults but this threshold value is too large—Domning & de Buffrénil (1991) used this value for a threshold for “large adults” (p. 337), citing Odell (1981), who said sexual maturity was reached at a body length of about 2.6 m in females and 2.75 m in males. More importantly, such subsetting of data based on size range often adds bias in the results of allometric regression, especailly if it is used for extrapolation (see Fig. S1 for how adult-based regression lines depart from the general trend when extrapolated to a whale size, potentially causing errors). We therefore tried including all 38 individuals in regression and compare the results with those from truncated data set with only 11 individuals.

Error rates of body mass estimation methods

Bianucci et al. (2023) did not test the accuracy of the new body mass estimation methods based on skeletal to body mass ratio. We estimated the body mass of cetaceans in their data with these methods and calculated the mean absolute error for each, together with the minimum and maximum absolute errors. We also use the methods to predict the body mass of the only pachyostotic marine mammal with a large sample size (manatees), and calculated the same error statistics. For comparison, we repeated the same with regression-based estimation methods.

Skeletal to body mass ratios in Cetacea

Bianucci et al. (2023) used the skeletal to body mass ratios calculated for six individuals of large whales from five species in a previous study (Robineau & de Buffrénil, 1993). However, these ratios are based on estimated body masses, casting some doubts on the accuracy. They also added Delphinus delphis from de Buffrénil, Collet & Pascal (1985) and seven species of smaller cetaceans. We therefore cross-examined the skeletal to body mass ratios using the wet bone mass data from other authors (Nishiwaki, 1950; Omura, 1950; Ohno & Fujino, 1952; Fujino, 1955; Omura et al., 1969).

Wet bone masses are substantially larger than dry bone masses that were used to calculate the skeletal to body mass ratio (de Buffrénil, Collet & Pascal, 1985), yet they are expected share scaling trends if the latter is approximated as a proportion of the former. Then, comparing the scaling patterns of the two may allow identification of outliers.

We fitted linear models to the data from the literature mentioned above to test if different species share a common intraspecific trend when regressing wet and dry bone masses against body mass. We tested the correlation between bone mass and body mass with a class variable, where species are separated into categories and, if a single species had both wet and dry bone mass data, they were also treated as separate categories. We also separated Antarctic and North Pacific populations of sperm whales into different categories within this class variable, given that they have vastly different bone masses for body mass. Lastly, we calculated the interspecific trend based on species means with PGLS to examine if it differed from the intraspecific trend.

Consensus between regression-based and volumetric mass estimates

For each mean body mass estimate from PGLS for Perucetus, we tested if it was compatible with any volumetric estimates from within the body length range of 15–20 m.

Body mass of the largest blue whale

Using a linear least square regression on log-transformed body length and mass, we calculated that a 33 m blue whale would weigh 234 (95% CI [187–294]) tons. Assuming that body fluid equivalent to 7% of the body volume was lost, the body mass of the whale would be 252 (CI [201–306]) tons and the value is 272 (CI [217–342]) tons with a ratio of 14%. In combination, the mass is estimated to be in the range of 252–272 (CI [201–342]) tons with the regression approach. The volumetric approach resulted in a body mass range of 266–279 tons, overlapping the regression-based confidence intervals. Although these volumetric estimates lack accuracy because of the factors discussed in Materials and Methods, it is sufficiently close to regression-based results to allow validation of the claim that the largest blue whales are in the vicinity of 270 tons. See Table 1 for corresponding prediction intervals and estimates at other body lengths.

Volumetric mass estimation of Perucetus

Based on the lateral view only, the body mass of a 20 m Perucetus is estimated to be about 98 to 114 tons. Results, including estimates for other body lengths, are summarized in Table 2.

Effect of assumed isometry in extrapolation

The results of PGLS extrapolation and its comparison with isometric extrapolation are given in Fig. 3 and Table 3. Although the differences among isometric lines and allometric regression lines may appear minor when viewing the entire span of the data (Figs. 3A and 3B), the actual bias in the extrapolated range is obvious when magnifying the part that is relevant to Perucetus (Fig. 3C). In this range, a minor deviation between lines results in a large difference in body mass because of the nature of log scale. For example, an isometric line results in body masses that are 100 to 150 tons larger than those from cetacean PGLS line when the minimum cetacean ratio is assumed, and 17 to 26 tons with the mean cetacean ratio (Fig. 3; Table 3). These two ratios were used by the original authors, so the published body masses were inflated by the assumption of isometry.

Effect of pachyostosis

The effect from pachyostosis on body mass estimation is not negligible. When using the regression line from manatees, the body mass of Perucetus is estimated to be 45.3 (35.3–52.1) tons based on a data set with 50 individuals (Table 3). These values are more than 100 tons less than 163 tons from the cetacean PGLS line, which does not consider the effect from pachyostosis.

Truncation of the dataset also led to a large difference in body mass estimates: for example, compare 74.2 (61.4–86.6) tons based on 11 individuals with the above-mentioned results. When comparing the regression results from the complete versus truncated manatee data sets, truncated data set gave less stable results than the complete one. The confidence and prediction intervals from the truncated data set are too wide whereas those from the complete data set are much narrower (Table 3).

Error rates of body mass estimation methods

The mean absolute error from each method is summarized in Table 4, together with the maximum and minimum absolute errors. The ratio-based methods, assuming isometry between the skeletal and body masses, generally have high error rates even when applied to the data from which the ratios were derived. The worst performance is when using the minimum skeletal to body mass ratio from cetaceans, which led to a mean absolute error of 61% and maximum absolute error of 127.9% even when applied to modern cetaceans from which the ratio was derived. The maximum error was 287% when applied to pachyostotic marine mammals. This method was used by Bianucci et al. (2023) to arrive at the maximum body mass of 343 tons. Regression-based methods generally performed better, although the error rates are not low.

Skeletal to body mass ratios in Cetacea

A linear model found a common intraspecific trend of 0.858, which was strongly significant (p-value < 2 × 10⁻¹⁶). Interspecific trends from PGLS were 1.02 (p < 2 × 10⁻¹⁶) for dry bone mass, and 1.11 (p < 2 × 10⁻¹⁶) for wet bone mass. Therefore, the intra- and interspecific trends are opposite, i.e., larger whales tend to have less skeletal mass for body mass within a single species whereas larger whale species tend to have more skeletal mass for body mass compared to smaller species. The interspecific trend is shared with patterns known for terrestrial mammals (Prange, Anderson & Rahn, 1979).

Distribution of species on the bone versus body mass space is given in Fig. 4. Data for blue whales exhibited a strange behavior. This species has the largest wet bone mass for body mass given the trend among whales examined, yet it has the smallest dry bone mass for body mass, again given the trend. It is unknown if this reflects the reality or is an artifact of the estimations involved in the dry bone data that were pointed out in Materials and Methods.

Consensus between regression-based and volumetric mass estimates

As seen in Fig. 3C and Tables 1 and 2, mass estimates from cetacean regression lines are too large to be validated by volumetric estimates, even at the maximum possible body length of 20 m (red horizontal band with arrow d in Fig. 3C). Therefore, it is impossible to pack the mass suggested by these lines into a whale that is 20 m or shorter. Within the body length range of 17–20 m suggested by Bianucci et al. (2023), only those regression-based estimates from the truncated manatees and terrestrial mammals yield a consensus result with volumetric estimates. Notably, estimates based on truncated manatee data matched the volumetric estimates assuming a body length of 18.0 m (overlap of arrow b and e in Fig. 3C). When considering body size smaller than 17 m, there was a match between volumetric estimates from a 15-m individual and regression-based estimates from the complete manatee data set (overlap of arrows c and f in Fig. 3C).