Body Size Predicts Echolocation Call Peak Frequency Better than Gape Height in Vespertilionid Bats

In most vocalizing vertebrates, lighter animals tend to produce acoustic signals of higher frequency than heavier animals. Two hypotheses propose to explain this negative relationship in vespertilionid bats: (i) mass-signal frequency allometry and (ii) emitter-limited (maximum gape) signal directionality. The first hypothesis, that lighter bats with smaller larynges are constrained to calls with higher frequencies, is supported at the species level. The second hypothesis proposes that in open space, small bats use higher frequencies to achieve narrow sonar beams, as beam directionality increases with both emitter size (maximum gape) and signal frequency. This hypothesis is supported within a comparative context but remains untested beyond a few species. We analyzed gape, body mass, and echolocation data under a phylogenetic comparative framework to test these hypotheses, and considered forearm length as both a proxy for wing design and an alternative measure of bat size. Controlling for mass, we found no support for the directionality hypothesis. Body mass and relative forearm length were negatively related to open space echolocation call peak frequency, reflecting species-specific size differences, but also the influence of wing design and preferred foraging habitat on size-independent species-specific differences in echolocation call design.

in bats can vary greatly over the course of a day and across the seasons) 12,13 . Forearm length is also a relative indicator of bat flight style and habitat use 14 , and thus can provide insight into acoustic specialization across preferred habitats. We predicted that the two proxies of body size (i.e. mass and forearm length) would be strong, independent predictors of PF due to size-signal allometry (as observed in non-echolocating vocalizing vertebrates) but that gape height (when corrected for mass) would not influence PF as strongly.

Discussion
Controlling for phylogeny, we found that in open space vespertilionids' call peak frequencies decrease significantly with body mass, forearm length, and maximum gape height. After correcting for mass, forearm length remains a significant, negative predictor of peak frequency, but maximum gape does not. These findings substantiate earlier results 2 and suggest that small vesper species are constrained to high frequencies by their smaller bodies and larynges 2, 6 . In other words, when accounting for the effects of size and shared ancestry, we find support for the hypothesis that peak frequency decreases with body size in vespertilionid bats (i.e. the mass-signal frequency allometry hypothesis) and little to no support for the emitter-limited (maximum gape) signal directionality hypothesis. However, even though peak frequency decreases significantly with the two proxies of body size, this still does not account for the incongruence between body mass and signal frequency relative to non-echolocating mammals (Fig. 1). Vespertilionids vocalize at much higher frequencies than do similarly sized non-echolocating mammals, despite having much larger larynges 15 (Fig. 1). Thus, although body size appears to be an important predictor of peak frequency, an allometric relationship alone is insufficient to explain their signal diversity 7,8 . Why the larynges of echolocating bats are larger than similar sized mammals and why, despite this, they call at much higher frequencies than these animals, is not entirely clear. Bats are louder than most mammals 16,17 , and larger larynges may be required to produce these loud sounds. Additionally, the unusually high frequencies emitted by laryngeal echolocating bats have been attributed to specialized vocal membranes found atop the vocal folds, only the latter are typical of other non-echolocating mammals (reviewed in Neuweiler 18 ; Ratcliffe et al. 19 ). More comparative research into echolocation call production mechanisms in vespertilionids should provide better insight into species-specific echolocation call frequency composition.
After controlling for species' size, we found no support for the emitter-limited directionality hypothesis. Mass and absolute gape height had both appeared to be good predictors of peak frequency 2, 8 , but in our study gape did not remain so after size-correction within a phylogenetic context. Thus, while directionality had been put forth as a potentially better predictor of open space PF than body size 8 , we do not find support for the directionality hypothesis. That is, when using 86 vespertilionid species and phylogenetically informed mass residuals (to account for common ancestry and size), the once apparent relationship between PF and gape essentially disappeared. Therefore, a single convergent open space field of view may not apply to all vespertilionids. Bats which preferentially hunt in cluttered habitat, for instance, may be constrained to relatively broad beams even when flying in open space as a result of other, perhaps competing, demands on overall call design. Other factors may also contribute to shape situation-specific optimal call design for bats. For instance, facial features such as nose leaves and exaggerated lip and tongue morphologies can affect sound emission patterns 20 . Indeed, facial musculature has recently been shown to alter beam formation in free-tailed bats 21 . Taking these various features into account may provide further insight into beam shape and size by echolocating vespertilionid bats.
Because small bats tend to call at higher frequencies than larger bats, it had once been thought that such high frequencies were specialized to detect prey of a preferred size class. This idea has since been largely rejected. First, the majority of echolocating bats call at frequencies 3 or more times higher than should be necessary to detect the smallest prey found in their diet 7,22 . Second, while larger bats do take larger prey than smaller bats, they can also detect and intercept small prey 23 . Instead, it is small bats that appear to be limited in the prey sizes they can take, as a result of handling effort and perhaps interspecific competition, not sensory system constraints 23 . Still, consideration of diet is important. For instance, some bats like the ~16 g spotted bat, Euderma maculatum, use call designs that circumvent insect defenses. E. maculatum calls at ~10.5 kHz, a PF (much lower than predicted by body size) and eats mostly eared moths that are mostly deaf to frequencies below 15 kHz 24 . Further, diet relates to jaw morphology: bats with long, gracile jaws are limited to soft bodied insects while the jaws of those species that can consume harder shelled prey (e.g., beetles) are relatively shorter and stronger 25 . More rigorous accounting of the relationships between diet, gape, size, call parameters, and beam directionality across laryngeal echolocating bats may provide further insight into active sensing and prey selection.
In keeping with the theme of ecological impacts, forearm length is a significant predictor of peak frequency, both before and after size correction. Interestingly, PF decreased more with absolute and mass-corrected forearm than it did with mass (i.e. had a steeper negative slope), suggesting that, for a given mass, bats with longer forearms use lower peak frequency echolocation calls in open space. Relative forearm length is also a proxy for different wing morphologies, which relate to different foraging ecologies. Insectivorous bats with relatively short forearms tend to have short, broad wings with low wing loadings 14,26,27 and aspect ratios 14,[28][29][30] . It has been suggested that this wing design is well suited for slow, maneuverable flight in cluttered habitat, but may be disadvantageous for successful prey capture in open space 14,29 . Bats with relatively long forearms, conversely, tend to have long, narrow wings of high wing loading and aspect ratio. This wing design demands fast, agile flight and may be best suited for aerial capture in open spaces 14 . All else being equal, in open space, bats that have long narrow wings are expected to use echolocation calls with lower PFs than those species with short, broad wings 29,30 . Our results support this prediction. Such calls maximize an echolocating bat's detection range [31][32][33] . The higher peak frequency calls of slower, more maneuverable fliers should translate into more precise information for object ranging and resolution 8,32 .

Materials and Methods
Data assembly. We photographed, in lateral view, the cranium and the mandible of vespertilionid bat species at the Royal Ontario Museum (ROM) in Toronto, Canada using a Nikon D40x digital SLR camera. We also photographed skins (≤4 individuals/species) to obtain forearm measurements. Whenever possible, we selected skins and skulls from the same specimen, and included the same number of males and females per species. We imported all photos into Image J v. 1.49 34 to measure skull characteristics and forearm length 9 times (3 hypothesis-blind assistants, 3 times each) to obtain a single mean value for each measure for each species.
We measured the distances between the posterior-most point of the temporomandibular joint and the anterior-most point of the upper incisors (a), lower incisors (b), and origin (A) and insertion (B) of the superficial masseter to estimate the maximum gape for each individual (Fig. 3). We used a reported gape angle of 90° and A:B ratio of 2.1, as reported for Myotis lucifugus 35 , to estimate maximum gape height (GH) using equation (1).   (as described by Herring and Herring 36 , and modified by Jakobsen and colleagues 8 ; Fig. 3). This method of estimating gape height is robust for vespertilionids and other primarily insectivorous bat families 37 . For a given frequency, emitter size primarily determines signal directionality in vespertilionid bats 38 . This relationship among emitter size, maximum estimated gape, actual call emission gape, and call PF and directionality have been confirmed in Myotis daubentonii 8,10 . We used mass and forearm length as proxies for body size. We measured maximum forearm length as the length between the elbow and wrist 39 . Mass (g), species-specific open-space echolocation call peak frequency (PF; frequency with the maximum energy in first 'harmonic' in kHz) were obtained from a single, comprehensive review of the literature 40 . For raw data see Supplementary Figure S1. The data for all continuous variables used in this study were not normally distributed and were thus log-transformed in subsequent analyses.

Statistical analyses.
We found a significant phylogenetic signal in all variables (Pagel's λ not significantly different from 1; see Results). Thus, we conducted all subsequent statistical analyses using a lambda evolutionary model and a pruned version of a recent, time-calibrated, molecular phylogeny 41 (Fig. 4). For these analyses, we used all vespertilionid species (i) with call parameters in Collen 40 , (ii) included in the Shi and Rabosky 41 phylogeny, and (iii) for which the ROM had at least one intact adult skull or taxidermied specimen. This resulted in 86 species (260 specimens) with mass and gape data, and 69 species (200 specimens) with forearm data.
We used phylogenetic generalized least squares (PGLS) regressions by restricted maximum likelihood (REML) to test the relationship between peak frequency and (i) body mass, (ii) forearm length, and (iii) maximum gape height, respectively. However, since gape height is significantly and positively correlated with body size metrics (b = 0.263 ± 0.02, t = 12.09, p < 0.001, d.f. = 85, R 2 (Phylogenetic Independent Contrasts regression) = 0.63, we ran re-ran the analyses using size-corrected gape (residuals on mass or forearm length via PGLS regressions; Revell 42 )). Similarly, since PF was significantly negatively correlated with body size, we used size-corrected PF as well.