What are the limits on whale ear bone size? Non-isometric scaling of the cetacean bulla

Anatomical measurements

We measured the bizygomatic width (BZW), tympanic bulla length (BL), and tympanic bulla width (BW) of cetacean skulls using handheld calipers (±1 mm). Bizygomatic width was defined as the maximum distance between the lateral edges of the zygomatic processes and was used as a proxy for cetacean body size (Pyenson & Sponberg, 2011). In the case of incomplete skulls, the bizygomatic width was measured from the lateral edge of one zygomatic process to the midline and doubled. BL was measured in the dorsal and lateral views from the outer posterior prominence to the edge of the involucral ridge following previous authors and as documented by Tsai & Fordyce (2015) and references therein. Bulla width was measured in ventral views from the mallear ridge to the involucrum following Tsai & Fordyce (2015) and Tanaka, Ando & Sawamura (2018) (Fig. 1). Where possible, we measured both the right and left bulla and used the mean value in this study. Only complete and intact specimens were included in the final dataset. Other studies have used the periotic, specifically inner ear structures such as the spiral cochlea and the bony labyrinth, to test for changes in acoustic ecology through whale evolutionary history. Here, we elect to focus on the tympanic bulla because it is an external structure that can be measured with minimal resource allocations and because tympanic bullae preserve readily in the fossil record, making it easier to amass a large dataset that can be easily replicated.

Data acquisition and taxonomic selection

We measured the bizygomatic width, bulla length, and bulla width for specimens that preserve both skulls and at least one complete tympanic bulla. Our data set includes fossil cetaceans from the UMMP and USNM; we then supplemented this dataset with additional measurements from published specimens from the literature. Juvenile and subadult specimens were excluded as examining ontogenetic growth is beyond the scope of this study. The final dataset (Table S1) includes 267 representatives of nearly every known cetacean taxon (n = 135) with pairable bizygomatic widths and tympanic bulla.

Phylogenetic analysis

To test for potential phylogenetic signal, we constructed a composite tree using previously established phylogenetic relationships and their heuristic searches with accepted support values (Lambert, Bianucci & De Muizon, 2017; Tanaka & Fordyce, 2017; Marx & Fordyce, 2015; Peredo & Uhen, 2016; Gatesy et al., 2013; O’Leary, 2001). The composite matrix, constructed in MESQUITE 3.6 (Maddison & Maddison, 2018), included three new continuous characters: BZW, BL, and BW. Phylogenetic Independent Contrasts (PICs) correlated continuous size variable traits with corresponding taxa using non-transformed data in PDTREE. Branch lengths were set to 1.0 and colors were allocated by character value (Pyenson, Goldbogen & Shadwick, 2013). PIC axes were set as follows: Y-the character for exploration (|BL:BZW|) and X-the tree character ( $\sqrt{\mathrm{\Sigma }\rho \left(X,Y\right)}$, the square root of the sum of the correlated branch lengths). To assess the phylogenetic underpinnings of non-isometric scaling relationships, we regressed the PICs of the continuous character traits and mapped them back onto the original composite tree (Garland & Ives, 2000; Pyenson, Goldbogen & Shadwick, 2013). The dataset exhibited a normal distribution and character trait ranges were spread across families.

Allometry of cetacean tympanic bullae

Scaling relationships of tympanic bulla length (Fig. 2A slope = 0.5488×, R² = 0.7055) and bulla width (Fig. 2B slope = 0.5644×, R² = 0.6824) vs bizygomatic width were positively allometric (Fig. 2). This trend suggests that body size is the predominant correlate influencing ear size, with roughly 70% of the bullae dimensional variation being explained by changes in body size. We used log-transformed plots to display linear regressions across the sample, allowing size extremes to be shown with minimal axis compression (Fig. 2). The smallest cetaceans (e.g., Cephalorhynchus hectori, Pontoporia blainvillei, and Phocoena phocoena) had bullae that were about twice as long as they were wide (BL:BW 1.7–2.2). Conversely, the largest cetaceans (e.g., Eubalaena glacialis, Megaptera novaeangliae, Balaenoptera physalus) exhibited bullae nearly as wide as they were long (BL:BW 1.1–1.7). At smaller body sizes (BZW < 185 mm), the tympanic bulla length was consistently 15–41% of bizygomatic width. However, at larger body sizes (BZW > 407 mm) bulla length was closer to 10% and as low as 4% of bizygomatic width in some specimens of Megaptera novaeangliae and Balaenoptera physalus, indicating that tympanic bullae are proportionally smaller at the largest body sizes.

The patterns observed in the cumulative dataset remain consistent within taxonomic groupings (stem cetaceans, odontocetes, and mysticetes). Larger body sizes were correlated with longer tympanic bulla in all three groups (Fig. 3): stem cetaceans (slope = 0.1626×, R² = 0.7166), mysticetes (slope = 0.0248×, R² = 0.4635), and odontocetes (slope = 0.049×, R² = 0.5868). Similar patterns were observed for body size and tympanic bulla width in stem cetaceans (slope= 0.0034×, R² = 0.7719), mysticetes (slope= 0.0217×, R² = 0.4100), and odontocetes (slope = 0.04×, R² = 0.5293).

Within groups, our data demonstrated insignificant linear growth trajectories, with stem cetaceans and odontocetes constrained to the left side of the graph likely as a result of their smaller body sizes, and mysticetes occupying a wide range of ear and body sizes (Figs. 2 and 3). As a paraphyletic group, stem cetaceans resemble the tympanic bullae size and proportions of odontocetes despite larger body sizes comparable to those of smaller mysticetes (Fig. 3). The composite dataset includes a diverse assortment of bulla and bizygomatic sizes.

Tympanic bullae and bizygomatic width seemingly conform to the same scaling coefficient, regardless of taxonomic grouping (Figs. 2 and 3). Our phylogenetic independent contrasts (PIC) yielded no genus-level clustering in both branch proximity and corresponding character traits, indicating that tympanic bulla size is not governed by phylogeny (Fig. S1).

Scaling and function

Tympanic bullae play a fundamental role in cetaceans’ abilities to navigate, communicate, and feed within aquatic systems. Our results demonstrate that cetacean bulla dimensions increase in a positively allometric pattern irrespective of taxonomic identity or phylogenetic history. Nonetheless, the largest cetaceans (mysticetes) exhibit disproportionately small tympanic bullae, while small-bodied cetaceans (e.g., Pontoporia, Platanista, phocoenids, and extinct odontocetes such as Olympicetus and Echovenator) exhibit particularly large ears for their body sizes (Fig. 3). These small-bodied odontocetes all retain proportionately large tympanoperiotic complexes, possibly hinting at a lower limit for cetacean bulla size. Notably, the largest cetaceans are all extant (Rosel et al., 2020; Pyenson & Sponberg, 2011; Pyenson & Vermeij, 2016; Slater, Goldbogen & Pyenson, 2017). Whale body size persists near a lower bound for much of their evolutionary history and only reached extreme gigantism during the Plio-Pleistocene (Slater, Goldbogen & Pyenson, 2017). Such departures from linearity suggest that functional auditory capacity is not based on proportional congruences, but may instead be constrained by functional or biological auditory limits.

One such constraint may be osteological: the tympanic bulla functions by acoustically isolating the hearing apparatus from the rest of the skull (Luo & Gingerich, 1999; Nummela et al., 2004; Cozzi et al., 2015) and it remains unclear how acoustic isolation functions at proportionally larger body sizes. Another potential limitation may be ecological. The pachyosteosclerotic bulla enhances the reception of sound underwater, and may therefore be bound within a functional size range with upper and/or lower limits of effectiveness. This constraint is likely true for echolocating odontocetes, which rely on high frequency sounds not just for communication, but for navigation and feeding as well (Ketten, 1994). Future research is needed to determine how bulla size influences sound reception underwater. Finally, cetaceans often exhibit paedomorphic ear bone morphology at birth (Cozzi et al., 2015; Yamato & Pyenson, 2015), suggesting that future work examining changes in allometry across whale ontogeny may reveal developmental constraints on ear bone scaling. Such studies would necessarily focus on extant sampling, as developmental series are mostly lacking from the fossil record of cetaceans.

Evolutionary patterns

Cetaceans underwent major morphological transformations associated with an increasingly marine lifestyle, but our results demonstrate that tympanic bulla allometry remains relatively unchanged throughout 50 million years of cetacean evolutionary history. Stem cetaceans maintain a stronger consistent relationship between tympanic bulla dimensions and body size than either of the crown groups (Fig. 3). This pattern may hold because stem cetaceans exhibit small and medium body sizes overall, but generally not the gigantism observed in extant mysticetes (Fig. 3). Despite innovations that involve hearing, such as ultrasonic echolocation in odontocetes and extreme gigantism in mysticetes, neither extant lineage differs markedly from stem cetaceans in terms of tympanic bullae dimensions and scaling. This result is noteworthy given their seemingly disparate ecologies and suggests little functional selection on tympanic bulla dimensions. Instead, bulla dimensions converge around a common form. The consistency of tympanic bulla dimensions across the land-to-sea transition, even in stem cetaceans, reinforces the hypothesis that even the earliest cetaceans already had aquatic-adapted tympanic bullae (Luo & Gingerich, 1999; Nummela et al., 2004).

Notably, while our study examines the relationship between tympanic bullae size and body size, it does not directly test whether changes in tympanic bulla size are driven by ecological factors. Future studies might test specific ecological factors as potential drivers of bulla size to help elucidate the relationship between ear size and functional ecology. For example, it remains unclear whether bullae can reach substantially larger sizes, or if the observed values in extant whales represent an upper limit, as seems to be the case for body size (Slater, Goldbogen & Pyenson, 2017). Further study in this regard will reveal to what extent tympanic bulla size and shape are restrained by functional ecology. Recent authors have begun to elucidate the specific mechanism for infrasonic hearing in mysticetes (Park et al., 2017; Ekdale & Racicot, 2015), though it remains overall less understood than ultrasonic hearing in odontocetes. Consequently, future work in this area has the potential to inform a potential relationship between mysticete hearing and mysticete gigantism.