Reevaluating Body Size in Fossil Physeteroids Using Cranial Proportions

1. Introduction

Extant physeteroids are represented by a single species in the family Physeteridae and two species in the family Kogiidae (Vélez-Juarbe et al., 2015). Among them, Physeter macrocephalus is the largest living odontocete, with mature males commonly reaching approximately 16 m in total length, while exceptionally larger individuals have also been reported. In contrast, the two species of Kogia are much smaller, generally ranging from approximately 2.7 to 3.8 m in body length (McAlpine, 2009).

During the Miocene, however, physeteroids were considerably more diverse than they are today, occupying a broader range of ecological niches and exhibiting a wider distribution of body sizes (Bianucci & Landini, 2006; Lambert et al., 2017). Macroraptorial physeteroids, in particular, differed markedly from extant suction-feeding physeteroids. They possessed large, functional teeth in both the upper and lower jaws, together with robust jaw apparatuses well suited for capturing and processing relatively large prey (Bianucci & Landini, 2006; Lambert et al., 2010; Lambert et al., 2014). Dental wear and damage documented in some Miocene physeteroids further support the interpretation of these animals as predators capable of exerting substantial forces during prey capture and processing (Lambert & Bianucci, 2019). In addition, several extinct physeterids may have employed a broader range of feeding strategies than their extant relatives, and this ecological diversity was accompanied by considerable variation in body size.

One of the approaches used in previous studies to estimate body length in extinct physeteroids has been to compare bizygomatic width (BZW) with cranial dimensions and total body length in related taxa. Using this approach, Livyatan melvillei, one of the largest known extinct physeteroids, was estimated to have reached approximately 13.5 m when scaled from Physeter macrocephalus and approximately 16.2–17.5 m when scaled from Zygophyseter varolai (Lambert et al., 2010; Lambert et al., 2017). However, the latter estimates depend directly on the assumed body length of Z. varolai. In its original description, Z. varolai was estimated from the preserved postcranial skeleton to have reached approximately 6.5–7.0 m in total length (Bianucci & Landini, 2006). Although the holotype of Zygophyseter varolai is relatively well preserved, detailed vertebral measurements are not fully available and much of the posterior vertebral series is missing. These limitations make it difficult to constrain total length within a narrow range and introduce additional uncertainty into previously proposed estimates. Nevertheless, this estimate has not been extensively reassessed, and the potential use of more complete skeletons, such as that of Brygmophyseter shigensis, as comparative reference material has received limited attention. The present study therefore aims to reassess the body-size estimates of Z. varolai and B. shigensis and to use these revised estimates as a basis for generating updated body-size estimates for other extinct physeteroids.

The broader objective of this study is to provide a more consistent framework for reassessing and refining body-size estimates across numerous extinct physeteroids.

2. Materials and Methods

To obtain revised total-length estimates for the taxa used as comparative body-size proxies, measurements of condylobasal length (CBL), vertebral dimensions, and bizygomatic width (BZW) were compiled from the original descriptions and relevant literature of Zygophyseter varolai and Brygmophyseter shigensis (Bianucci & Landini, 2006; Hirota & Barnes, 1994; Kimura et al., 2006).

However, detailed measurements of the preserved vertebral series of Z. varolai were not available. Therefore, an approximate preserved vertebral series was estimated from a photograph published in a 2023 guide of the Natural History Museum of the University of Pisa, in which the preserved vertebral series is shown together with a 1 m scale bar (Collareta & Bianucci, 2023, fig. 10g). Because this estimate was derived from a photograph, it was treated as an approximate value rather than a precise anatomical measurement. The extracted measurements yielded reference total lengths of approximately 6.5 m for Z. varolai and 6 m for B. shigensis. The corresponding CBL values were 148 cm and ≥150 cm, respectively, and the BZW values were 74.5 cm and 70.5 cm (Hirota & Barnes, 1994, fig. 5). Detailed vertebral measurements for Brygmophyseter shigensis used in this study are provided in Supplementary Material 1.

2.1. Taxonomic Sampling

The analyzed sample included Acrophyseter, Albicetus, Aulophyseter, Brygmophyseter, Eophyseter, Idiorophus, Livyatan, Miophyseter, Physeter, Physeterula, Zygophyseter, and additional fossil physeteroid taxa for which adequate cranial or postcranial measurements were available.

Table 1. Physeteroid taxa included in the body-length analysis.

Taxa	Material used	Estimation basis
Zygophyseter varolai	Skull + vertebrae	Vertebral reconstruction / reference taxon
Brygmophyseter shigensis	Skull + vertebrae	Vertebral reconstruction / reference taxon
Livyatan melvillei	Skull	BZW/CBL scaling + supplementary regression
Eophyseter damarcoi	Vertebrae	Vertebral-based estimation
Acrophyseter spp.	Skull	BZW/CBL scaling + supplementary regression
Albicetus	Skull	BZW/CBL scaling + supplementary regression
Idiophyseter	Skull	BZW/CBL scaling + supplementary regression
Idiorophus	Skull	BZW/CBL scaling + supplementary regression
Physeterula	Skull	BZW/CBL scaling + supplementary regression
Eudelphis	Skull	BZW/CBL scaling + supplementary regression
Miophyseter gunmaensis	Skull + vertebrae	BZW/CBL scaling + vertebral evidence
Orycterocetus	Skull	BZW/CBL scaling + supplementary regression
Placoziphius	Skull	BZW/CBL scaling + supplementary regression
Rhaphicetus	Skull	BZW/CBL scaling + supplementary regression
Diaphorocetus	Skull	BZW/CBL scaling + supplementary regression
Cozzuoliphyseter	Skull	BZW/CBL scaling + supplementary regression
Aulophyseter	Skull	BZW/CBL scaling + supplementary regression
Angelocetus	Skull	BZW/CBL scaling + supplementary regression
Kogiidae	Cranial and/or postcranial material	BZW/CBL scaling + supplementary regression

Table 1. Physeteroid taxa included in the body-length analysis.

Taxa	Material used	Estimation basis
Zygophyseter varolai	Skull + vertebrae	Vertebral reconstruction / reference taxon
Brygmophyseter shigensis	Skull + vertebrae	Vertebral reconstruction / reference taxon
Livyatan melvillei	Skull	BZW/CBL scaling + supplementary regression
Eophyseter damarcoi	Vertebrae	Vertebral-based estimation
Acrophyseter spp.	Skull	BZW/CBL scaling + supplementary regression
Albicetus	Skull	BZW/CBL scaling + supplementary regression
Idiophyseter	Skull	BZW/CBL scaling + supplementary regression
Idiorophus	Skull	BZW/CBL scaling + supplementary regression
Physeterula	Skull	BZW/CBL scaling + supplementary regression
Eudelphis	Skull	BZW/CBL scaling + supplementary regression
Miophyseter gunmaensis	Skull + vertebrae	BZW/CBL scaling + vertebral evidence
Orycterocetus	Skull	BZW/CBL scaling + supplementary regression
Placoziphius	Skull	BZW/CBL scaling + supplementary regression
Rhaphicetus	Skull	BZW/CBL scaling + supplementary regression
Diaphorocetus	Skull	BZW/CBL scaling + supplementary regression
Cozzuoliphyseter	Skull	BZW/CBL scaling + supplementary regression
Aulophyseter	Skull	BZW/CBL scaling + supplementary regression
Angelocetus	Skull	BZW/CBL scaling + supplementary regression
Kogiidae	Cranial and/or postcranial material	BZW/CBL scaling + supplementary regression

2.2. Body-Length Estimation

Total length (TL) was estimated using revised reference taxa whose body lengths were reconstructed from vertebral measurements and scale-bar-based skeletal data. The postcranial length of each target taxon was estimated by scaling the postcranial length of the reference taxon according to the ratio of bizygomatic width (BZW). The condylobasal length (CBL) of the target taxon was then added to the estimated postcranial length to obtain total length:

$$T{L}_{\mathit{target}}={\displaystyle \frac{T{L}_{\mathit{ref}}-{\mathit{CBL}}_{\mathit{ref}}}{{\mathit{BZW}}_{\mathit{ref}}}}\times {\mathit{BZW}}_{\mathit{target}}+{\mathit{CBL}}_{\mathit{target}}$$

$$T{L}_{\mathit{target}}=\left({\displaystyle \frac{T{L}_{\mathit{Zyg}}-{\mathit{CBL}}_{\mathit{Zyg}}}{{\mathit{BZW}}_{\mathit{Zyg}}}}\right){\mathit{BZW}}_{\mathit{target}}+{\mathit{CBL}}_{\mathit{target}}$$

BZW_target, BZW_ref, CBL_target, CBL_ref: represent the corresponding bizygomatic widths and condylobasal lengths, TL_target: is the estimated total length of the target taxon, TL_ref: is the total length of the reference taxon.

For several taxa, total-length estimates were additionally refined using the BZW-based regression equation of Pyenson and Sponberg (2011):

log₁₀(TL) = 0.92[log₁₀(BZW) − 1.68] + 2.64

TL: estimated total length, BZW: bizygomatic width, this equation was used as a supplementary estimator rather than as the primary body-length reconstruction method.

Table 2. Reference body-size measurements used for proportional scaling in this study.

Taxa	TL (m)	CBL (cm)	BZW (cm)	Source
Zygophyseter varolai	6.5	148	74.5	Bianucci & Landini, 2006; Collareta & Bianucci, 2023
Brygmophyseter shigensis	ca. 6.0	≥150	70.5	Hirota & Barnes, 1994; Kimura et al., 2006

Abbreviations: TL, total length; CBL, condylobasal length; BZW, bizygomatic width.

Table 2. Reference body-size measurements used for proportional scaling in this study.

Taxa	TL (m)	CBL (cm)	BZW (cm)	Source
Zygophyseter varolai	6.5	148	74.5	Bianucci & Landini, 2006; Collareta & Bianucci, 2023
Brygmophyseter shigensis	ca. 6.0	≥150	70.5	Hirota & Barnes, 1994; Kimura et al., 2006

Abbreviations: TL, total length; CBL, condylobasal length; BZW, bizygomatic width.

2.3. Detailed Methodology

When the bizygomatic width (BZW) or condylobasal length (CBL) of a target taxon was unknown or incompletely preserved, the missing measurement was estimated using the cranial proportions of the phylogenetically closest taxon with a broadly similar body size and morphology.

For taxa with well-preserved vertebral and postcranial remains, direct skeletal evidence was prioritized over indirect estimates based solely on cranial proportions. Accordingly, in taxa such as Zygophyseter varolai, where a substantial portion of the postcranial skeleton is preserved, body-length reconstruction based on the preserved skeletal series and vertebral measurements was given precedence, whereas cranial proportional scaling was treated as supplementary evidence.

In addition, alternative body-length estimates were generated by applying several candidate body-proportion ratios to CBL. Among these, the ratios considered most appropriate for the morphology and phylogenetic position of each target taxon were retained as supplementary estimates. To better account for the body proportions of some crown physeterids, the extant Physeter macrocephalus was also included as an additional reference taxon. Final body-length estimates were calculated as the mean of several estimates considered most appropriate on morphological and phylogenetic grounds. Estimates were selected before averaging according to predefined criteria, including phylogenetic proximity, cranial similarity, preservation quality, and compatibility with available postcranial evidence.

3. Results

Revised body-length estimates were generated for all examined fossil physeteroids using BZW- and CBL-based scaling. The complete set of calculations is provided in Supplementary Material 2, whereas only the principal results are summarized here.

None of the kogiids examined reached the medium-sized category. Orycterocetus, Idiophyseter, Angelocetus, Diaphorocetus, and Placoziphius were classified as small and were broadly similar in body size. Specimens assigned to Acrophyseter, together with Rhaphicetus, Physeterula, and Albicetus (approaching the large-sized category), fell within the medium-sized category. Brygmophyseter, Aulophyseter, Zygophyseter, and Idiorophus reached the large-sized category, whereas Eophyseter, Livyatan, and Physeter were classified as gigantic.

Estimated total lengths among macroraptorial physeteroids ranged from approximately 4.0–4.3 m in middle taxa to approximately 15–16 m in Livyatan melvillei. Acrophyseter robustus was estimated at approximately 4.0 m, whereas A. deinodon and Acrophyseter sp. were estimated at approximately 4.1–4.3 m. The medium-to-large-sized Albicetus oxymycterus yielded an estimated total length of approximately 5.9 m.

Of the 19 non-kogiid physeteroid genera examined, only seven reached or exceeded 6 m in estimated total length. Of these, three genera (B. shigensis, Z. varolai, Eophyseter damarcoi) were represented by body-length estimates based primarily on vertebral measurements rather than cranial proportional scaling, while one genus was the extant Physeter. Among the three genera classified as giant-bodied in the present study, only Livyatan and Physeter exceeded 15 m in estimated total length, indicating that extreme gigantism was restricted to a very small number of physeteroid lineages.

4. Discussion

4.1. Review of the Selection of Calculation Formulas

The body-length scaling approach proposed by Lambert et al. (2010) was also employed in the present study. However, this method may be prone to overestimation, a tendency also noted by Paolucci et al. (2025). In the present interpretation, this potential bias may partly result from the use of an upper-end body-length estimate for Zygophyseter varolai as the comparative reference. By contrast, the equation of Boersma and Pyenson (2015) has been suggested to underestimate total length (Paolucci et al., 2025), as illustrated by estimates of approximately 11–13 m for Livyatan melvillei when this equation is applied. Accordingly, the present study sought to reduce the risk of overestimation by using revised reference body lengths, while the Boersma and Pyenson (2015) equation was excluded from the final estimates because of its apparent tendency toward underestimation (Paolucci et al., 2025, Table S1). This is further supported by the fact that the condylobasal length (CBL) of Brygmophyseter is at least 150 cm, whereas the equation proposed by Boersma and Pyenson (2015) yields an estimated CBL of less than 120 cm (Kimura & Hasegawa, 2026).

4.2. Body-Size Distribution in Physeteroids

The final estimates indicate that large-bodied physeteroids, defined here as taxa reaching or exceeding 6 m in total length, represented a relatively small proportion of the genera examined. Albicetus, estimated at approximately 5.9 m, and Physeterula, estimated to exceed 5.5 m, approached the large-bodied category but remained within the medium-sized class under the present criteria. Consequently, the number of genera classified as large or larger was reduced from nine to seven. These category assignments reflect the representative body-length estimates and size thresholds adopted in this study. Depending on the estimation method used, Albicetus may exceed 6 m in total length.

Among these, the body-length estimates of Brygmophyseter (c. 6 m) and Zygophyseter (6.5 m) are based primarily on vertebral measurements or preserved skeletal length, whereas Physeter represents the only extant genus. The remaining large-bodied genera include Livyatan (15–16 m), Eophyseter (11.6 m), Idiorophus (6.64 m), and the adult specimen of Aulophyseter. Notably, Livyatan and Eophyseter were the only fossil physeteroids in this study to exceed 9.5 m in estimated total length, placing them in the giant body-size category.

However, no kogiid included in this study reached the medium-sized category. The largest extant pygmy sperm whale (Kogia breviceps) attained a total length of approximately 3.8 m, whereas Platyscaphokogia, the largest fossil kogiid examined here, reached only about 3.5 m. Thus, even the largest known kogiids remained substantially smaller than the medium- to large-bodied physeteroids considered above.

4.3. Challenges of Vertebral-Based Estimation

Brygmophyseter shigensis is comparatively well suited for vertebral-based body-length analysis because detailed vertebral measurements are publicly available. However, several aspects of the preserved skeleton remain incomplete, and estimates based solely on the published vertebral dimensions may therefore underestimate its original total length. No cervical vertebrae are preserved, so the length of this region must be reconstructed indirectly, and much of the thoracic series is damaged. Fifteen caudal vertebrae are preserved, but additional posterior caudals appear to be missing, with approximately seven vertebrae potentially absent from the preserved series. The skull is also incomplete anteriorly, with the rostral portion of the maxilla missing; consequently, the condylobasal length can only be constrained to a minimum of approximately 150 cm, preventing a more precise reconstruction of total skull length. Thus, even though vertebral measurements are available, estimates of the living animal’s total length remain subject to substantial uncertainty. Owing to these preservation-related limitations, the present study adopts a conservative total-length estimate of approximately 6 m for B. shigensis.

This limitation also applies to the present study itself. Because the exact total length of Brygmophyseter shigensis, one of the principal reference taxa used for body-proportion reconstruction, cannot be fully restored, the present analysis necessarily relies on a conservative estimate of approximately 6 m. Consequently, body-length estimates derived using B. shigensis as a reference also inherit a degree of uncertainty from this baseline value. Nevertheless, because this estimate is reconstructed from published vertebral measurements and preserved skeletal evidence, it was retained as one of the most anatomically direct reference values currently available and was therefore used in the final body-proportion analysis.

Furthermore, although much of the anterior skeleton of Zygophyseter varolai is preserved, severe sedimentary compression prevents meaningful measurements from being obtained, making it impossible to reconstruct total body length from vertebral dimensions (Bianucci & Landini, 2006). Consequently, body-length estimation must rely on a scale-bearing image of the museum reconstruction, in which the vertebrae are arranged in sequence (Collareta & Bianucci, 2023).

4.4. Palaeoecological Implications of Body-Size Variation

Figure 1. Body size and feeding ecology of physeteroids through time. Description: Symbols indicate inferred feeding ecology: diamonds (◆), macroraptorial; triangles (▲), intermediate; circles (●), complex feeding; and squares (■), Physeter-type. The vertical axis represents estimated total body length (m), and the horizontal axis represents geological age (Ma).

Figure 1. Body size and feeding ecology of physeteroids through time. Description: Symbols indicate inferred feeding ecology: diamonds (◆), macroraptorial; triangles (▲), intermediate; circles (●), complex feeding; and squares (■), Physeter-type. The vertical axis represents estimated total body length (m), and the horizontal axis represents geological age (Ma).

Body size can provide a supplementary indication of the range of prey sizes that physeteroids were potentially capable of exploiting. Macroraptorial physeteroids, for example, generally fall within medium to large body-size categories. Nevertheless, body size alone should not be treated as a primary indicator of feeding ecology. More direct evidence is provided by the morphology and functional structure of the jaws and dentition (Paolucci et al., 2025), while dental wear and pathological damage may offer additional information regarding prey capture and processing (Lambert & Bianucci, 2019).

Physeteroids of broadly similar body size may nevertheless differ substantially in cranial and dental morphology. For example, the largest known specimens of Aulophyseter fall within the large-bodied category in the present study, yet they differ markedly from macroraptorial physeteroids and other large-bodied forms such as Idiorophus. In particular, reduction of the upper dentition and the absence of enamel suggest that Aulophyseter was adapted to relatively small prey, possibly including small fishes and cephalopods. A comparable extant example is Physeter. Although Physeter represents one of the largest-bodied physeteroid genera, it is primarily a suction feeder that predominantly consumes cephalopods. Accordingly, large body size alone cannot be regarded as direct evidence of predation on large prey, and body-length estimates should be interpreted together with cranial morphology, dentition, jaw structure, and patterns of dental wear.

In the phylogenetic analysis of Kimura and Hasegawa (2026), Miophyseter was placed within an unresolved polytomy involving crown physeteroids, macroraptorial sperm whales, and other early-diverging lineages. Its suction-assisted feeding adaptations therefore provide further evidence that similar feeding mechanisms may have arisen independently within Physeteroidea. The known specimen of M. gunmaensis is interpreted as a subadult and has an estimated total length of approximately 3–4 m (Kimura & Hasegawa, 2026). Although the adult body size was presumably somewhat larger, the available evidence does not suggest that it would have reached the large-bodied category defined in the present study.

Kogiids also exhibited considerable ecological diversity, and their body sizes varied within the small-bodied category. However, none of the genera reached the medium-sized category. Platyscaphokogia was relatively large for a kogiid and possessed an elongated rostrum, a well-developed temporal fossa, functional upper alveoli, and comparatively large teeth, all of which have been interpreted as evidence for active prey capture (Collareta et al., 2020). By contrast, the unusual jaw morphology of Scaphokogia has been interpreted as indicative of benthic feeding. These morphologies differ markedly from the predominantly suction-feeding ecology of the two extant species of Kogia, suggesting that extinct kogiids occupied a substantially broader range of feeding niches than their living relatives.

4.5. Evolutionary Implications of Body-Size Increase

Among the seven genera classified as large-bodied in the present study, at least two, or possibly three if the uncertain case of Eophyseter is included, appear to have been suction feeders or predators specialized on relatively small prey. This strongly suggests that increases in body size among physeteroids did not necessarily reflect a single evolutionary pathway toward giant macroraptorial predators such as Livyatan, but may instead have arisen independently under different ecological regimes.

Idiorophus, which appeared during the Early Miocene, falls within the large-bodied category and has been strongly interpreted as a raptorial feeder (Paolucci et al., 2025). By the Middle Miocene, large predatory physeteroids such as Brygmophyseter and the near-large-bodied Albicetus had appeared, while Aulophyseter also attained a large body size during a similar interval. However, the feeding adaptations of Aulophyseter differ markedly from those of macroraptorial forms, indicating that large body size evolved under more than one ecological regime.

Particularly notable is the occurrence of fossils attributed to Livyatan or a closely related lineage as early as the Burdigalian, in the Early Miocene (Piazza et al., 2018). This suggests that the Livyatan lineage may have undergone gigantism earlier and independently from the large predatory physeteroids that became prominent during the Middle Miocene. Thus, even among lineages with broadly similar raptorial or macroraptorial feeding strategies, increases in body size may have evolved independently. Fossil records attributed to the Livyatan lineage extending into the Early Pliocene further suggest that this large-bodied predatory ecomorph persisted for a substantial interval of time.

It is also noteworthy that the more secure fossil record of Physeter and closely related forms appears primarily from the Pliocene onward. Although Physeter antiquus has been reported from earlier deposits, its taxonomic status is uncertain and it is therefore excluded from the present discussion. One of the earliest giant forms associated with the Physeter lineage is Eophyseter damarcoi, which appeared in the Early Pliocene at approximately 3.2 Ma. Depending on the estimation method, its total length has been suggested to range from approximately 11–12 m (McClure, 2026) to as much as 15.1 m (Bisconti et al., 2025), placing it within the giant body-size category. An early Pleistocene physeterid specimen from Japan, dated to approximately 1.60–1.77 Ma, has been provisionally assigned to Physeter sp. (Kimura et al., 2023).

This temporal distribution suggests a potentially important evolutionary pattern. Giant macroraptorial lineages such as Livyatan had already achieved very large body size during the Miocene, whereas gigantism within Physeter and closely related lineages may have developed later, during the Pliocene–Pleistocene. Thus, gigantism in physeteroids may not represent a single continuous evolutionary trend, but rather multiple independent episodes of body-size increase occurring in lineages with different feeding ecologies.

5. Conclusions

This study presents a revised framework for estimating body size in fossil physeteroids using cranial proportions, particularly bizygomatic width (BZW) and condylobasal length (CBL), calibrated against reference taxa whose body lengths were reassessed using preserved skeletal and vertebral evidence. By revising the reference lengths of Zygophyseter varolai and Brygmophyseter shigensis, the present approach reduces reliance on previously proposed upper-end estimates and provides a more consistent basis for comparing body size across extinct physeteroids.

The resulting estimates indicate that large body size was relatively uncommon among the examined non-kogiid physeteroids. Only seven genera reached or exceeded 6 m in estimated total length, while Livyatan and Eophyseter were the only fossil genera in this study to exceed the 9.5 m threshold used here for the giant size category. Several taxa previously regarded as large-bodied, including Albicetus and Physeterula, instead fall near the upper end of the medium-sized range under the revised estimates.

The results also emphasize that body size alone cannot be used as a direct indicator of feeding ecology. Large-bodied physeteroids included both macroraptorial predators and taxa interpreted as suction feeders or predators of relatively small prey. Accordingly, cranial morphology, dentition, jaw structure, dental wear, and other functional traits remain more direct indicators of feeding ecology than total length alone.

Finally, the temporal distribution of large and giant physeteroids suggests that gigantism may have evolved independently in different ecological lineages. Giant macroraptorial forms such as Livyatan appeared during the Miocene, whereas very large forms associated with the Physeter lineage appear later in the fossil record. This pattern is consistent with multiple episodes of body-size increase rather than a single continuous trend toward gigantism within Physeteroidea.

Nevertheless, the present estimates remain limited by incomplete preservation, uncertainty in the total lengths of reference taxa, and the use of reconstructed cranial measurements in some species. Future discoveries of more complete skeletons and additional postcranial measurements will be necessary to further refine body-size estimates in fossil physeteroids.