Journal of

Anatomy

J. Anat. (2010) 216, pp37–47

doi: 10.1111/j.1469-7580.2009.01172.x

Semicircular canals and agility: the influence of size and shape measures Philip G. Cox and Nathan Jeffery Division of Human Anatomy and Cell Biology, School of Biomedical Sciences, University of Liverpool, Sherrington Buildings, Liverpool, UK

Abstract The semicircular canals of the inner ear sense angular accelerations and decelerations of the head and enable co-ordination of posture and body movement, as well as visual stability. Differences of agility and spatial sensitivity among species have been linked to interspecific differences in the relative size of the canals, particularly the radius of curvature (R) and the ratio of the canal plane area to streamline length (P ⁄ L). Here we investigate the scaling relationships of these two size variables and also out-of-plane torsion in the three semicircular canals (anterior, posterior and lateral), in order to assess which is more closely correlated with body size and locomotor agility. Measurements were computed from 3D landmarks taken from magnetic resonance images of a diverse sample of placental mammals encompassing 16 eutherian orders. Body masses were collected from the literature and an agility score was assigned to each species. The R and P ⁄ L of all three semicircular canals were found to have highly significant positive correlations with each other and no statistical difference was found between the slope of 2P ⁄ L against R and 1. This indicated that, contrary to initial hypotheses, there is little difference between 2P ⁄ L and R as measures of semicircular canal size. A measure of the in-plane circularity of the canal was obtained by dividing 2P ⁄ L by R and out-of-plane torsion was measured as angular deviation from a plane of best fit. It was predicted that deviations from in-plane and out-of-plane circularity would increase at small body size due to the constraints of fitting a proportionately larger canal into a smaller petrous bone. However, neither measurement was found to have a significant correlation with body mass, indicating that deviations from circularity (both in-plane and out-of-plane) are not sufficient to alter P ⁄ L to an extent that would impact the sensitivity of the canals. 2P ⁄ L and R were both shown to be significantly correlated with locomotor agility. The posterior canal was the least correlated with agility, suggesting that it may be generally less closely aligned to the direction of movement than the anterior canal. Of the three canals, the lateral canal was the most highly correlated with agility. In particular, it could be used to distinguish between species that move in a largely 2D environment and those that locomote in 3D space (aerial, arboreal and aquatic species). This complements previous work suggesting that the lateral canal primarily commands navigation, whereas the vertical canals control reflex adjustments. It was also found that 2P ⁄ L is substantially better correlated with agility than is R in the lateral canal. This result is intriguing given the above finding that there is no statistical difference between 2P ⁄ L and R, and requires further investigation. Key words circumference; labyrinth; semicircular canal; torsion.

Introduction The semicircular canals of the vertebrate inner ear, located within the petrous part of the temporal bone of the skull, are responsible for sensing angular accelerations and decel-

Correspondence Philip Cox, Division of Human Anatomy and Cell Biology, School of Biomedical Sciences, University of Liverpool, Sherrington Buildings, Ashton Street, Liverpool L69 3GE, UK. T: +44 151 794 5454; F: +44 151 794 5517; E: [email protected] Accepted for publication 13 October 2009

erations of the head. The output from the canals supplies information about how an animal is moving within its environment and enables it to co-ordinate posture, body movements and gaze direction during locomotion. Mammals, like most gnathostomes, possess three semicircular canals on each side of the head: two vertical (anterior and posterior canals) and one horizontal (lateral canal). These three semicircular canals show substantial variation in size across the mammals and these variations have been linked to functional differences of locomotion (e.g. Spoor & Zonneveld, 1998; Spoor et al. 2002, 2007). Here we investigate canal size and possibly more bio-physiologically realistic

ª 2009 The Authors Journal compilation ª 2009 Anatomical Society of Great Britain and Ireland

38 Semicircular canal size and shape, P. G. Cox and N. Jeffery

shape measurements in relation to patterns of locomotion as well as covariation with body size. The aim of this study was to see whether the more realistic measurements yield any tangible improvement in reconstructing patterns of locomotion.

Canal size Semicircular canal size has historically been measured as the radius of curvature of the osseous canal (R). This measurement is distinct from the radius of the membranous duct seen in a cross-sectional slice through the canal (r). R has been measured from fixed, dissected specimens by superimposing a circle of best fit (estimated by eye) over the course of the canal either directly (Lindenlaub et al. 1995; McVean, 1999) or from photographs (Curthoys & Oman, 1986, 1987). More recently, semicircular canals have been imaged using computed tomography, obviating the need for dissection (Spoor & Zonneveld, 1998; Spoor et al. 2002, 2007). Here, the radius of curvature has typically been calculated from the width (w) and height (h) of each canal (R = 0.5[h+w] ⁄ 2). Fitted circles and calculated R measurements reveal notable size differences between the three semicircular canals. Generally, amongst mammals, the anterior canal is larger than the posterior and lateral canals. This has been demonstrated in rats (Cummins, 1925), mice (Calabrese & Hullar, 2006), chinchillas (Hullar & Williams, 2006), little brown bats (Ramprashad et al. 1980), rhesus and squirrel monkeys (Blanks et al. 1985), as well as guinea pigs, cats and humans (Curthoys et al. 1977). This relationship is also seen in most of the wide range of mammals studied by Ramprashad et al. (1984) and the large number of primates examined by Spoor & Zonneveld (1998) although the anterior and posterior canals are often very close in size and, in some cases, the radius of the posterior canal exceeds that of the anterior canal (e.g. Cercopithecus aethiops and Callithrix jacchus). As well as variation between the semicircular canals within an individual animal, there is also a great deal of variation in the relative size and shape of each semicircular canal between mammal species. Numerous studies (Jones & Spells, 1963; Spoor & Zonneveld, 1998; Spoor et al. 2007) have found that the canal dimensions increase with body size but with strong negative allometry, i.e. the relative size of the canals tends to decrease as body mass increases. Spoor & Zonneveld (1998) calculated the regression slope of a double logarithmic plot between body mass and mean radius of curvature of all three canals to be around 0.14, well below the value of 0.33 that would indicate an isometric relationship. This result was confirmed by Spoor et al. (2007) with the data adjusted using phylogenetic least squares regression. The relative size of the semicircular canals has long been assumed to be related to the method or speed of locomotion of an animal. For example, Gray (1907), in his compre-

hensive study of the vertebrate labyrinth, unequivocally attributed the diminished size of the canals in the sloth to its sluggish movements. This hypothesis was tested by Spoor et al. (2007) who, after controlling for body size, found a significant positive correlation between semicircular canal radius and agility across a wide sample of mammals. It is likely that this correlation is a result of the increased sensitivity to angular acceleration conferred by a larger radius of curvature. A relationship between canal radius and afferent sensitivity has been demonstrated between different canals of the same labyrinth in cats (Blanks et al. 1975; Curthoys et al. 1977) and pigeons (Dickman, 1996), and also between corresponding canals of different individuals in neonatal rats (Curthoys, 1982) and mice (Yang & Hullar, 2007), as well as across different species of mammals (Yang & Hullar, 2007).

Canal shape Despite its frequent use in studies of the semicircular canals (Jones & Spells, 1963; Curthoys et al. 1977; Spoor et al. 2007), R is limited in that it provides information on canal size but not on canal shape. This is important as deviation from circularity will affect the area enclosed by the canal, a parameter that has been shown to be closely related to canal sensitivity (McVean, 1999). A more useful measure may be 2P ⁄ L, referred to as the ‘average radius’ of the canal by Oman et al. (1987), in which L is the streamline length of fluid flow, encompassing the entire membranous duct, ampulla and utricle, and P is the plane area enclosed by L (Curthoys & Oman, 1986, 1987; Lindenlaub et al. 1995). This measure takes shape into account as, for a given streamline length, the greater the deviation from circularity, the smaller the value of P and hence P ⁄ L. A perfectly circular canal should have a value of 2P ⁄ L that equals R (because P = pR2 and L = 2pR). Therefore, the dimensionless variable (2P ⁄ L) ⁄ R gives a measure of circularity; a perfect circle will have a value of 1 and an ellipse will have a value of 0.960, P < 0.001 for all three canals after phylogenetic correction). However, it can be seen that the slopes of the RMA regression lines for the vertical canals, after phylogenetic correction, are not significantly different from 1. Although the slope of the RMA for

ª 2009 The Authors Journal compilation ª 2009 Anatomical Society of Great Britain and Ireland

Semicircular canal size and shape, P. G. Cox and N. Jeffery 41

Table 1 Semicircular canal dimensions and torsion, plus body mass and agility of the 58 mammal species under study. ASC

PSC

LSC

Species

R

P⁄L

Torsion

R

P⁄L

Torsion

R

P⁄L

Torsion

BM

Agility

Capra hircus Hemitragus jemlahicus Ovis aries Naemorhaedus caudatus Hydropotes inermis Giraffa camelopardalis Tragulus javanicus Sus scrofa Vicugna vicugna Camelus bactrianus Equus caballus Equus grevyi Tapirus terrestris Tapirus indicus Galidia elegans Felis catus Neovison vison Lutra lutra Halichoerus grypus Vulpes vulpes Manis tricuspis Pteropus rodricensis Epomophorus gambianus Molossus molossus Scotophilus robustus Erinaceus europaeus Solenodon paradoxurus Pan troglodytes Pan paniscus Homo sapiens Gorilla gorilla Pongo pygmaeus Symphalangus syndactylus Hylobates lar Tarsius bancanus Perodicticus potto Loris tardigradus Nycticebus coucang Lemur catta Galeopterus variegatus Tupaia glis Sciurus carolinensis Glaucomys volans Mus musculus Rattus norvegicus Cavia porcellus Chinchilla lanigera Heterocephalus glaber Oryctolagus cuniculus Ochotona macrotis Choloepus didactylus Cyclopes didactylus Chlamyphorus truncatus Limnogale mergulus Tenrec ecaudatus

2.93 3.32 2.61 1.80 2.49 4.23 1.77 2.58 3.15 4.32 4.17 3.19 3.79 3.59 1.84 1.82 1.42 1.50 4.53 2.26 1.64 1.40 1.29 0.95 1.06 1.40 1.75 2.55 2.59 3.29 2.85 3.11 2.55 3.34 1.49 2.10 1.57 1.93 2.45 1.80 1.78 2.09 1.15 1.00 1.27 1.80 2.02 0.85 2.65 1.73 2.06 1.59 0.87 1.34 1.28

1.49 1.64 1.33 0.94 1.30 2.16 0.87 1.41 1.57 2.33 2.07 1.65 1.97 1.84 0.91 0.93 0.79 0.81 2.45 1.13 0.80 0.69 0.64 0.46 0.51 0.73 0.88 1.36 1.37 1.65 1.37 1.48 1.24 1.54 0.76 1.11 0.78 0.95 1.18 0.92 0.93 1.11 0.67 0.50 0.67 0.93 1.04 0.41 1.44 0.89 1.09 0.78 0.41 0.66 0.65

5.04 6.38 5.74 4.91 3.97 8.15 3.46 4.34 3.84 7.79 3.90 2.25 4.80 7.79 4.34 7.13 5.17 6.10 5.48 3.29 1.61 4.93 5.93 2.77 4.16 6.08 2.85 8.17 10.50 4.94 8.50 11.53 9.44 2.28 4.34 4.07 4.75 6.74 2.97 5.19 10.28 4.70 4.40 3.70 3.76 8.49 3.80 4.10 5.92 3.36 6.11 3.22 7.81 5.66 3.38

3.14 2.98 2.56 1.83 1.82 3.44 1.87 2.08 2.70 4.16 3.80 3.10 3.29 3.41 1.66 1.83 1.47 1.67 4.39 2.33 1.45 1.17 1.28 0.72 0.79 1.21 1.61 2.45 2.17 2.89 2.54 2.57 2.06 2.36 1.36 1.70 1.31 1.44 1.94 1.69 1.56 1.94 1.04 0.74 1.03 1.51 1.35 0.73 1.92 1.46 1.88 1.23 0.88 1.06 1.03

1.63 1.56 1.38 0.92 1.02 1.79 0.88 1.08 1.44 2.18 1.97 1.60 1.74 1.76 0.84 0.95 0.78 0.80 2.12 1.06 0.75 0.57 0.63 0.39 0.41 0.53 0.83 1.19 1.10 1.50 1.27 1.50 1.17 1.17 0.69 0.80 0.67 0.83 1.05 0.81 0.79 0.98 0.54 0.39 0.55 0.79 0.74 0.37 1.04 0.74 1.02 0.63 0.44 0.54 0.55

6.34 4.83 4.07 8.02 6.88 6.77 5.98 6.37 7.98 4.44 3.12 2.55 1.66 4.37 3.32 8.43 3.75 10.13 3.61 7.99 3.93 4.72 8.37 4.11 7.39 5.67 4.54 6.52 10.58 7.11 3.74 3.80 10.44 3.94 2.16 4.49 6.41 11.96 5.23 3.95 3.21 5.11 11.22 3.62 4.77 12.50 3.00 7.89 7.35 5.86 4.79 9.83 3.35 2.25 6.94

2.39 2.89 2.35 1.64 1.68 3.41 1.37 1.76 2.42 3.55 3.23 2.55 2.93 2.93 1.32 1.63 1.48 1.89 3.44 2.56 1.25 1.03 1.08 0.49 0.76 1.19 1.39 2.39 2.41 2.40 3.05 2.43 2.21 2.28 1.39 1.29 1.08 1.18 1.94 1.37 1.40 1.69 1.15 0.66 0.91 1.46 1.55 0.73 2.23 1.25 1.45 1.06 0.82 0.87 1.07

1.31 1.40 1.27 0.98 0.88 2.05 0.54 1.01 1.33 1.97 1.68 1.34 1.59 1.53 0.71 0.85 0.74 1.04 1.87 1.17 0.67 0.57 0.62 0.37 0.46 0.67 0.72 1.21 1.34 1.26 1.60 1.18 1.18 1.27 0.76 0.69 0.57 0.61 1.01 0.73 0.76 0.95 0.62 0.38 0.55 0.81 0.80 0.37 1.14 0.70 0.72 0.53 0.41 0.49 0.56

4.74 10.30 6.16 5.50 5.11 5.32 2.64 8.58 2.15 7.95 6.33 2.91 6.02 4.19 2.14 7.41 9.52 7.77 7.32 4.47 3.04 6.53 5.59 4.14 7.59 9.81 4.11 7.32 5.13 8.50 7.41 10.81 7.81 6.65 5.21 7.36 3.95 17.50 4.50 7.17 7.93 5.01 9.60 4.76 3.06 9.77 14.31 6.71 8.65 6.88 7.53 7.64 5.05 7.23 6.39

46 750 14 700 33 750 27 000 1285 1 190 000 2000 101 900 45 000 415 000 250 000 341 000 207 500 296 250 900 3713 1045 9600 233 000 4380 2000 350 83 14 83 780 900 43 820 39 100 58 313 109 790 35 700 11 300 5340 123 1230 193 679 2210 1000 165 519 62 14 279 728 485 60 1437 143 4150 400 130 80 832

4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 5 5 4 3 6 6 6 6 4 4 4 4 4 2 2 4 6 6 2 2 2 4 6 4 6 6 4 4 4 6 2 5 5 2 3 5 4 5

ª 2009 The Authors Journal compilation ª 2009 Anatomical Society of Great Britain and Ireland

42 Semicircular canal size and shape, P. G. Cox and N. Jeffery

Table 1 (Continued). ASC

PSC

LSC

Species

R

P⁄L

Torsion

R

P⁄L

Torsion

R

P⁄L

Torsion

BM

Agility

Potamogale velox Rhynchocyon cirnei Procavia capensis

2.00 2.13 1.87

1.07 1.06 1.02

2.67 6.73 4.82

1.41 1.89 2.35

0.66 0.99 1.16

5.27 6.78 7.21

1.43 1.79 1.64

0.73 0.88 0.92

6.45 5.34 6.78

660 490 3140

5 4 4

ASC, anterior semicircular canal; BM, body mass (g); L, streamline length (mm); LSC, lateral semicircular canal; P, canal plane area (mm2); PSC, posterior semicircular canal; R, radius of curvature (mm).

the lateral canal is significantly > 1, even after phylogenetic correction, it appears that this result is being unduly influenced by one point (see Fig. 3C) that has a much larger value of 2P ⁄ L than any of the others. This point represents the node where the giraffe branches off from the cervids and bovids. Removal of this one point decreases the value of the slope from 1.15 to 1.05, which is not significantly different from 1. Therefore, it is implied by these results that there is little difference between R and 2P ⁄ L as measures of canal size.

Size scaling constraints The second hypothesis given in the Introduction states that, owing to the need to pack a relatively larger canal into a smaller volume in the petrous bone, smaller species will show a greater deviation from circularity, i.e. they will have smaller values of 2P ⁄ L compared with R. Table 3 shows the product-moment correlation coefficients of (2P ⁄ L) ⁄ R against log10 body mass. It can be seen that this variable does not show a significant correlation with body mass in any of the three canals. Therefore, there seems to be no tendency for the semicircular canals of smaller species to become less circular and more elliptical. Analysis of the SD of the circularity measure across the entire sample (Table 3) indicates that there is very little variation in this measure throughout mammals as a whole, which is consistent with the previous result that showed that there is very little difference between R and 2P ⁄ L.

Out-of-plane torsion The degree of out-of-plane torsion of each canal as measured by angular deviation from the plane of best fit is given for each of the species under study in Table 1. Values ranged between 1.6 and 11.5 for the anterior canal, 1.7 and 12.5 for the posterior canal, and 2.1 and 17.5 for the lateral canal, with a minimum torsion of 1.6 being found in the anterior canal of the tree pangolin, Manis tricuspis, and a maximum torsion of 17.5 in the lateral canal of the slow loris, Nycticebus coucang. It was hypothesized that a high degree of out-of-plane torsion would be negatively correlated with 2P ⁄ L as a trade-off between maximizing in-

plane and out-of-plane sensitivity. Table 4 shows that no significant correlation was found between 2P ⁄ L and torsion. Therefore, it was hypothesized that the degree of out-ofplane torsion exhibited by a canal may be influenced by the volume available into which the canal can expand, i.e. a greater degree of torsion may be found in smaller species that have relatively larger semicircular canals in a more constrained space. This was tested by calculating correlation coefficients between torsion and log10 body mass (see Table 5). It can be seen that there is no correlation between out-of-plane torsion and body size for any of the three canals (the correlation seen initially in the anterior canal appears to be artefactual as it is lost under phylogenetic correction). As above, in the analysis of in-plane circularity, examination of the SD of the whole sample (Table 5) indicates that there is very little variation in torsion across placental mammals – mean torsion falls between 5 and 7 and the SD is between 2 and 3 for all three canals. Thus, although all mammals show some torsion in all three canals, the degree of torsion is reasonably small and does not change substantially between species.

Agility It is hypothesized in this investigation that the increased complexity of the variable P ⁄ L will make it a better predictor of locomotor ability than R. Table 6 gives the results of an ANOVA conducted to investigate whether the mean values of size-adjusted P ⁄ L and R are statistically different between the agility groups from 2 to 6. P ⁄ L and R were corrected for body size by dividing by the cube root of body mass. It can be seen that both P ⁄ L and R of all three semicircular canals could be used to distinguish between fast- and slowmoving mammals, even after phylogenetic correction. It can also be seen that the P-value is about five times smaller for P ⁄ L than R for the lateral canal, suggesting that this measure correlates substantially better with agility than does R. This is not true for the anterior or posterior canals – P ⁄ L and R have approximately the same power to discriminate between agility groups in these canals. In addition, the posterior canal appears to be less strongly correlated (P < 0.01) with agility than the anterior and lateral canals (P < 0.001). Post-hoc Duncan’s tests indicate that both P ⁄ L

ª 2009 The Authors Journal compilation ª 2009 Anatomical Society of Great Britain and Ireland

Semicircular canal size and shape, P. G. Cox and N. Jeffery 43

Fig. 2 Phylogeny of mammal species used in this analysis, constructed from Bininda-Emonds et al. (2007). Branch length scale is in millions of years.

and R can distinguish between the two most agile (5 and 6) and the three least agile (2, 3 and 4) groups but not within these groupings (e.g. there is no statistically significant difference between groups 5 and 6).

Discussion The results show that, as hypothesized, the radius of curvature and the ratio of canal plane area to streamline length

ª 2009 The Authors Journal compilation ª 2009 Anatomical Society of Great Britain and Ireland

44 Semicircular canal size and shape, P. G. Cox and N. Jeffery

Table 2 Product-moment correlation coefficients (r) and RMA line fittings (a, slope; b, intercept; 95% CI, 95% confidence interval on the slope) of 2P ⁄ L against R for uncorrected and phylogenetically corrected (PIC) data.

Standard ASC PSC LSC PIC ASC PSC LSC

r

P

a

95% CI

b

0.35 0.30

P (a = 1)

0.99 0.99 0.98

* * *

1.04 1.04 1.07

0.98 – 1.10 0.98 – 1.10 1.01 – 1.15

)0.03 )0.02 )0.01

NS NS ***

0.94 0.88 0.87

* * *

1.02 1.03 1.15

0.94 – 1.10 0.93 – 1.13 1.02 – 1.30

0.00 0.00 0.00

NS NS ***

0.25 2P/L (ASC)

Canal

A 0.40

0.20 0.15 0.10 0.05 0.00 0.00

0.05

0.10

0.15

–0.05

0.20

0.25

0.30

0.35

0.25

0.30

0.35

R (ASC)

B 0.35

*P < 0.001; ***P < 0.05. Abbreviations as for Table 1.

0.30

2P/L (PSC)

0.25 0.20 0.15 0.10 0.05 0.00 0.00

0.05

0.10

0.15 0.20 R (PSC)

C 0.35 0.30 0.25 2P/L (LSC)

are highly significantly correlated. This was expected as both R and 2P ⁄ L represent some form of the radius of the semicircular canals. However, the prediction that 2P ⁄ L would differ greatly from R was firmly rejected. Indeed, it has been shown that the slope of 2P ⁄ L against R is not significantly different from 1 for any of the three canals, indicating that R and 2P ⁄ L are two ways of expressing the same measure. This is particularly marked in the vertical semicircular canals. The lateral semicircular canal initially appears to show a slope >1 for 2P ⁄ L against R but further analysis indicates that this result is heavily influenced by one potentially spurious data point. The original hypothesis was formulated because it was inferred that deviations away from circularity in the semicircular canals would result in a smaller area and thus a smaller value of 2P ⁄ L but would not be accounted for in R. However, the findings reported here – that there is little difference between 2P ⁄ L and R – suggest that deviations from in-plane circularity are not great enough to produce a significant difference between 2P ⁄ L and R. Indeed, McVean (1999) notes that deviations from circularity have to be extremely severe (above 0.8 eccentricity) before any significant reduction of area occurs. Thus, small- and medium-sized deviations from perfect circularity are unlikely to be reflected in the value of 2P ⁄ L. It was hypothesized that 2P ⁄ L divided by R would give a dimensionless variable that would represent the degree of circularity of a semicircular canal, as it would indicate the discrepancy between the two input variables. Hypothesis 2 predicted an inverse relationship between (2P ⁄ L) ⁄ R and body mass as it was hypothesized that smaller species would need to have a greater deviation from circularity in order to fit their relatively larger semicircular canals (Jones & Spells, 1963; Spoor & Zonneveld, 1998) in the petrous part of the temporal bone. However, no correlation was found between this circularity measure and body mass. The correlation between body mass and (2P ⁄ L) ⁄ R in the anterior canal was found to be almost significant but even this weak relationship is likely to have been further weakened by phy-

0.20 0.15 0.10 0.05 0.00 0.00

–0.05

0.05

0.10

0.15

0.20

0.25

R (LSC)

Fig. 3 Bivariate plot of independent contrasts of 2P ⁄ L against R for the (A) anterior semicircular canal (ASC), (B) posterior semicircular canal (PSC) and (C) lateral semicircular canal (LSC). Arrow marks potentially anomalous data point in the LSC data set.

logenetic adjustment. However, it was noted above that, unless the deviations from circularity were extremely pronounced, they would not greatly reduce 2P ⁄ L compared with R. Thus, the value of (2P ⁄ L) ⁄ R would be unlikely to vary much over the entire dataset. This was shown to be the case by the very small SDs seen for this measure in all three canals (Table 3).

ª 2009 The Authors Journal compilation ª 2009 Anatomical Society of Great Britain and Ireland

Semicircular canal size and shape, P. G. Cox and N. Jeffery 45

Table 3 Mean values (± SD) of (2P ⁄ L) ⁄ R and product-moment correlation coefficients (r) of (2P ⁄ L) ⁄ R against log10 body mass for each semicircular canal for non-phylogenetically corrected data. Canal

Mean±SD

r

P

ASC PSC LSC

1.02 ± 0.05 1.03 ± 0.06 1.07 ± 0.09

0.22 0.06 )0.10

NS NS NS

Table 6 Results of

ANOVA

between agility categories (2–6).

Dependent

F

P

Significant under PIC?

R(ASC) R(PSC) R(LSC) 2P ⁄ L(ASC) 2P ⁄ L(PSC) 2P ⁄ L(LSC)

5.63 5.10 5.77 5.71 4.82 7.00

0.00075 0.00150 0.00062 0.00067 0.00216 0.00013

Yes Yes Yes Yes Yes Yes

Abbreviations as for Table 1. R and 2P ⁄ L divided by 3BM to correct for size. Other abbreviations as for Table 1. Table 4 Product-moment correlation coefficients (r) of 2P ⁄ L against out-of-plane torsion for each semicircular canal for nonphylogenetically corrected data. Canal

r

P

ASC PSC LSC

0.20 )0.16 0.07

NS NS NS

ported by the low means and SDs calculated for all three canals across the entire data set. The ANOVA showed that both measures of semicircular canal size (P ⁄ L and R) are correlated with locomotor agility in all three canals in mammals. Spoor et al. (2007) found that this was true for the radius of curvature, treating agility as a quantitative measure. In this investigation, agility has been more realistically treated as a qualitative variable with discrete groups, hence the use of ANOVA here instead of least-squares regression. The results indicate that P ⁄ L has a greater power to distinguish between fast- and slow-moving species for the lateral canal. This is not the case for the anterior or posterior canal, the latter of which appears to be the least closely correlated with agility. It is difficult to see why the posterior canal should be less closely associated with agility of locomotion than the anterior canal but it may indicate that the posterior canal is positioned such that it is less closely aligned to the usual plane of movement (i.e. directly forwards) than the anterior canal. This would suggest that the vertical canals are not orientated at 45 to the midline (as noted by Simpson & Graf, 1981; Ezure & Graf, 1984; Cox & Jeffery, 2007). The most intriguing aspect of the results presented here is the outcome that 2P ⁄ L and R are very highly correlated, and have an RMA slope not significantly different from 1, yet 2P ⁄ L is more powerful than R at distinguishing between agility groups for the lateral canal. This suggests that, although over the entire mammalian sample deviations

Abbreviations as for Table 1.

Out-of-plane torsion was calculated as the mean angular deviation from the plane of best fit of the canal, measured from the centroid of the canal. It was predicted that torsion helps to optimize overall sensitivity by sacrificing in-plane mechanical sensitivity, as denoted by P ⁄ L, in order to shift the best fit plane closer to the plane of maximal sensitivity (Rabbitt, 1999). This predicts that P ⁄ L and torsion are negatively correlated. The alternative arguments are that the torsion is not sufficient to influence P ⁄ L (e.g. McVean, 1999) or that torsion is due to spatial constraints and will correlate negatively with body size (see hypothesis 2ii). No correlation was found between 2P ⁄ L and torsion and nor was a significant correlation between torsion and body mass found in any of the canals after phylogenetic correction. Thus, it was inferred that the degree of torsion found in the mammalian semicircular canals is not sufficient to substantially alter the value of P ⁄ L. This conclusion was sup-

Table 5 Mean values (± SD) of out-of-plane torsion, product-moment coefficients (r) and RMA line fittings (a, slope; b, intercept; 95% CI, 95% confidence interval on the slope) of out-of-plane torsion against log10 body mass for each semicircular canal for uncorrected and phylogenetically corrected (PIC) data. Standard

PIC

Canal

Mean ± SD

r

P

a

95% CI

b

r

P

ASC PSC LSC

5.32 ± 2.19 5.87 ± 2.57 6.65 ± 2.73

0.30 )0.16 0.07

* NS NS

3.73

2.90 – 4.70

)0.62

0.22

NS

*P < 0.05. Abbreviations as for Table 1. ª 2009 The Authors Journal compilation ª 2009 Anatomical Society of Great Britain and Ireland

46 Semicircular canal size and shape, P. G. Cox and N. Jeffery

above and below an RMA slope of 1 cancel each other out, at the individual species level 2P ⁄ L is a better predictor of agility (at least in the case of the lateral canal). Investigations requiring a sensitive discrimination among agility types may benefit from using P ⁄ L as opposed to R. Overall, the lateral semicircular canal has been shown to be the only canal in which 2P ⁄ L and R are potentially significantly different, although it has been noted that this may be an artefact due to one erroneous data point. Of the three semicircular canals, it is also the most closely associated with the degree of locomotor agility (as also noted by Spoor et al. 2007). The post-hoc Duncan’s tests show that the canal variables in particular distinguish groups 2, 3 and 4 from groups 5 and 6. Mammals that have been classified in groups 5 and 6 are largely aerial, arboreal, aquatic or ricochetal, i.e. they have a strong 3D element to their locomotion. Thus, it appears that the lateral canal is especially important for movement in 3D space. This is consistent with the suggestion of Fitzpatrick et al. (2006) that the lateral canal primarily controls navigation, whereas the vertical canals are concerned with reflex adjustments in response to movement.

Acknowledgements Thanks are due to the following for allowing access to specimens: Rob Asher, Adrian Friday, Matt Lowe and Ray Symonds (University Museum of Zoology, Cambridge); Liz Chadwick (Cardiff University); Judith Chupasko (Museum of Comparative Zoology, Harvard University); Bob Connolly (University of Liverpool); Chris Faulkes and Haidee Price-Thomas (Queen Mary, University of London); Andrew Kitchener, Jerry Herman and Phil Howard (National Museums of Scotland); Fay Penrose (University of Liverpool Veterinary School); Rod Penrose (UK Cetacean Strandings Investigation Programme); and Fred Spoor (University College London). Additional magnetic resonance datasets of modern humans and apes were kindly provided by Dirk Bartz (University of Leipzig) and Jim Rilling (Emory University). We are grateful to the following for assistance with the imaging: Bill Bimson and Valerie Adams (Magnetic Resonance and Image Analysis Research Centre, University of Liverpool); Karen Davies and Steve Williams (Imaging Science and Biomedical Engineering, University of Manchester); Franklyn Howe (Cardiac and Vascular Sciences, St George’s, University of London); Alasdair Preston (Queen Mary, University of London and lately Preclinical Imaging Unit Institute of Psychiatry, King’s College London); and Andrew Webb and Thomas Neuberger (Huck Institute Magnetic Resonance Centre, Penn State University). We thank the British Heart Foundation for supporting the 7T MRI scanner at King’s College London. We also thank Fred Spoor and two anonymous referees for many helpful comments on the manuscript. This work was funded by the Biotechnology and Biological Sciences Research Council (grant no. BBD0000681).

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Supporting Information Additional Supporting Information may be found in the online version of this article. Table S1 Number, sex, source and imaging details of species used in this analysis. As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer-reviewed and may be reorganized for online delivery but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.

ª 2009 The Authors Journal compilation ª 2009 Anatomical Society of Great Britain and Ireland