Poster - Yapuncich and Boyer 2014 AAPA

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Gabriel S. Yapuncich¹ and Doug M. Boyer¹
Talar articular surface curvature decreases allometrically among primates
Department of Evolutionary Anthropology, Duke University, Durham, NC; New York Consortium in Evolutionary Primatology (NYCEP), New York, NY
INTRODUCTION
Surveying mammals of various body sizes, it can be observed that larger taxa reduce the use
of flexed-limb postures in favor of more extended-limb postures, effectively trading decreased
joint mobility for increased stability and stress reduction1,2,3,4,5 (though it should be noted this
relationship has not been supported in intraspecific studies6,7 or among small-bodied primates8).
Greater joint mobility has been associated with greater facet curvature9,10,11,12. Therefore,
allometric postural differences should also correlate with articular curvature: larger animals
should have flatter joint surfaces that limit range of motion. The curvature of convex or male-type
facets has been linked to mobility, while the curvature of concave or female-type facets has
been linked to stability11,12. Thus, if the range of motion of joints decreases allometrically relative
to body mass, convex facets should display reduced curvature as body mass increases. The
curvature of concave facets is not expected to alter allometrically with increasing body mass.
Here we test the hypothesis that joint curvature reflects the correlation of joint mobility and
body size by examining the relationship between body size and curvature of three articular
surfaces of the primate talus: the ectal (or posterior calcaneal), lateral tibial, and navicular facets.
Our predictions are as follows:
• P1: Convex facets (lateral tibial and navicular) will become flatter as body mass increases.
• P2: Curvature of concave facets (ectal facet) will scale with isometry relative to body mass.
DISCUSSION
• The lateral tibial facet is a convex facet and thus should promote joint mobility with greater curvature11,12. For the
groups examined here, the lateral tibal facet becomes flatter with increasing body mass, confirming P1.
• The ectal facet is a concave facet and should promote joint stability with increased curvature. Its curvature
scales isometrically for all groups, confirming P2. While curvature does not change allometrically, the ectal facet
becomes disproportionally large as body size increases21. This would appear to confirm Hamrick’s hypothesis that
concave facets promote joint stability.
• The navicular facet is a convex facet and should promote mobility. However, it does not scale with negative
allometry as expected by P1. This may be the result of a poor match between the sphere of best fit and the
navicular facet: of the three facets examined here, the sphere of best fit for the navicular has the highest average
standard deviation relative to the volume of the sphere (LTF SD/Vol=0.000153, ectal SD/Vol=0.000098, navicular
SD/Vol=0.000264). Alternatively, since this facet is not primarily involved in flexion and extension of the foot (as
the lateral tibial facet is), it may not follow the same scaling pattern. Similarly, no significant relationship between
facet curvature and body size has been observed in the wrists of strepsirrhines11. Body mass may have different
impacts on the scaling of limb and intertarsal/carpal joint surfaces.
• Lorisids are unusual in having relatively small and flat talar articular surfaces. Joint surfaces with these
properties would be at risk of displacement under high loads11. However, slow-climbing and suspensory behaviors
may reduce talar joint stresses, or lorisids may recruit more soft tissue structures to stabilize talar joints22,23. A high
degree of mobility could be achieved with highly incongruent joint curvature of two mating articular surfaces24.
Dermopterans, another suspensory group, show similar volume/area ratios.
RESULTS cont.
Scaling of ratio of sphere volume/facet area
Because talar facet areas often scale with positive allometry
relative to body mass21, allometric increases of the best-fit
sphere may not represent changes in curvature if facet area
follows the same or stronger allometric pattern. Increasing
facet areas could potentially generate best-fit spheres with
increasing volumes, leading to Type I error.
We performed additional analyses to account for allometric
increases in facet area. A ratio was calculated using the cube
root of sphere volume to the square root of facet area. The
ratio was log-transformed and regressed against
log-transformed body mass. With a ratio, isometric scaling has
a slope of 0; positive and negative allometric relationships
have slopes >0 and <0 respectively. We utilized PGLS and
ordinary least squares regressions. OLS reports a more
conservative slope than RMA, so it is less likely to incorrectly
detect positive allometry.
Regressions were performed on the same groups, with an
additional group comprised of all primates except lorisids.
Lorisids have very small articular surface areas for their body
mass21, leading to high volume/area ratios compared to other
primates. Summary statistics for these regressions are
presented in Table 2. Regressions of the lateral tibial and ectal
facet ratios are shown in Figure 3.
• Phylogenetic autocorrelation remains significant for most
comparisons. Combining the two variables into a ratio
generates a stronger phylogenetic signal than considering
sphere volume (above) or facet area21 separately.
• Correlation coefficients are significant for six regressions: the
lateral tibial facet ratio exhibits positive allometry among
primates, all primates except lorisids, haplorhines, and
anthropoids. The navicular facet exhibits isometry among
haplorhines and anthropoids.
• For all other regressions, including the ectal facet in each
group, isometry cannot be rejected.
ACKNOWLEDGMENTS
We would like to thank Jimmy Thostenson at the SMIF lab at Duke University , and the staff at the AMNH mammalogy department and microscopy lab for access to the
specimens and CT-scanning. We would like to acknowledge a Leakey Grant to Biren Patel and a Wenner-Gren grant to Caley Orr, who provided access to Gorilla and
Pongo specimens. Finally, we would like to thank Anne Su for access to several catarrhine specimens. This research was supported by BCS 1317525 (formerly BCS
1125507), an American Association of Physical Anthropologists Professional Development Grant in 2009 to D. Boyer.
REFERENCES
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1989. Folia Primatol 53:125-141; 5) Larson SG, Schmitt D, Lemelin P, Hamrick MW. 2001. J Zool Lond 255:353-365; 6) Vilensky JA, Gankiwicz E, Townsend DW. 1988. Amer J Phys Anthropol
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EE. 1988. Int J Primatol 9:281-345; 11) Hamrick MW. 1996a. J Morph 230:113-127; 12) Hamrick MW. 1996b. Amer J Phys Anthropol 100:585-604; 13) Visualization Sciences Group. 2009. Avizo
6.0. Burlington, MA: Mercury Computer Systems; 14) MacConnaill MA. 1973. Irish J Med Sci 142:19-26; 15) Smith RJ, Jungers WL. 1997. J Hum Evol 32:523-559; 16) Hammer O, Harper DAT,
Ryan PD. 2001. Paleontol Electronica 4:1-9; 17) Orme CDL, Freckleton RP, Thomas GH, Petzoldt T, Fritz SA. 2012. caper R package 0.5; 18) Arnold C, Matthews LJ, Nunn CL. 2010. Evol An-
thropol 19:114-118; 19) Warton DI, Wright IJ, Falster DS, Westoby M. 2006. Biol Rev 81:259-291; 20) Smith RJ. 2009. Amer J Phys Anthropol 140:476-486; 21) Yapuncich GS, Boyer DM. 2014.
J Anat 224:150-172; 22) Szalay FS. 1984. Evol Biol 18:215-258; 23) Boyer DM, Patel BA, Larson SG, Stern JT. 2007. J Hum Evol 53:119-134; 24) MacConnaill MA. 1953. J Bone Joint Surgery
35:290-297; 25) Markze MW, Tocheri MW, Steinberg B, Femiani JD, Reece SP, Linscheid RL, Orr CM, Marzke RF. 2010. Amer J Phys Anthropol 141:38-51; 26) Dunn RH, Tocheri MW, Orr CM,
Jungers WL. 2014. Amer J Phys Anthropol 153:526-541.
CONCLUSIONS
In the primate talus, the curvature of the lateral tibial facet decreases allometrically, while curvature of the ectal
and navicular facets scale isometrically (more accurately, isometric scaling cannot be rejected). As the lateral
tibial facet is a convex facet, decreasing curvature should reduce joint mobility. These data confirm the
hypothesis that animals reduce limb excursion angles as they become larger1,2,3, at least for interspecific
comparisons of the talocrural joint.
The most important future direction of this work will focus on application of more sophisticated ways for estimating
surface curvature, including quadratic function fitting25,26, and recording additional parameters that may confound
the degree to which sphere volume reflects curvature (such as the facet perimeter/area ratio). These parameters
will also influence the ability of the joint to resist displacement under multidirectional loading. Additionally, more
work correlating articular surface curvature with joint excursion angles5,6,7,8 is needed. Comparisons must also be
made to non-primates, which generally have lower hindlimb excursion angles than primates5 and should therefore
have convex facets with reduced curvature for a given body mass. Finally, this analysis could be applied to fossil
taxa in order to better understand their positional behaviors.
4 5 6 7 8 9 10 11 12
ln(Body Mass)
-0.24
-0.16
-0.08
0.00
0.08
0.16
0.24
0.32
0.40
LTF volume1/3
LTF area1/2
ln( )
No lorisids
p<0.0001
All primates
p<0.001
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
4 5 6 7 8 9 10 11 12
ln(Body Mass)
ln( )
Ectal volume1/3
Ectal facet area1/2
Catarrhines
Platyrrhines
Tarsiers
Lemuroids
Lorisids
Galagids
No lorisids
p=0.6730
All primates
p=0.8261
Table 2. Summary
statistics for sphere
volume/facet area
ratios to body mass
regressions. Bold text
indicates significant
p-value.
Fig. 3. Regressions of
facet area/sphere volume
ratio to body mass for
lateral tibial and ectal
facets. Solid line indicates
“all primates but lorisids”,
dashed line indicates “all
primates”. Shaded regions
show confidence intervals.
Fig. 2. All-primate regressions of sphere volume to body mass for
lateral tibial, ectal, and navicular facets. Confidence intervals are
indicated by shaded regions.
ln(Body Mass)
3 4 5 6 7 8 9 10 11 12 13
ln(Lateral Tibial Facet Volume)
1
2
3
4
5
6
7
8
9
10
11
12
PGLS
lnLTF Volume=1.14(lnBM)-2.45
r2 = 0.95
p<0.0001
Catarrhines
Platyrrhines
Tarsiers
Lemuroids
Lorisids
Galagids
ln(Body Mass)
3 4 5 6 7 8 9 10 11 12 13
ln(Ectal Facet Volume)
1
2
3
4
5
6
7
8
9
10
11
12
PGLS
lnEctalVolume=1.08(lnBM)-2.16
r2 = 0.84
p<0.0001
ln(Body Mass)
3 4 5 6 7 8 9 10 11 12 13
ln(Navicular Facet Volume)
1
2
3
4
5
6
7
8
9
10
11
12
RMA
lnNavicular Volume=1.06(lnBM)-3.09
r2 = 0.96
p<0.0001
RESULTS
Scaling of “best fit spheres”
All-primate regressions are presented in Figure 2. Summary statistics are presented in Table 1.
• Among all groups, the best-fit sphere of the lateral tibial facet scales with positive allometry,
indicating that curvature is decreasing as body mass increases.
• The best-fit sphere of the navicular facet scales with positive allometry in haplorhines and
anthropoids, but isometrically among primates, strepsirrhines, and prosimians.
• The best-fit sphere for the ectal facet scales isometrically in all groups.
Table 1. Summary statistics for sphere volume to body mass regressions.
METHODS AND MATERIALS
Facet curvature measurements
• All measurements were taken on specimens microCT-scanned at the American Museum of
Natural History, Duke University, or Stony Brook University. Scans were reconstructed using
Avizo 6.013.
• One concave (ectal) and two convex (lateral tibial and navicular) ovoid facets (sensu
MacConnaill14) were cropped from tali of 222 individuals from 71 primate species (Fig. 1A).
• For each facet, a “sphere of best fit” was matched to the articular surface using Geomagic
Studio. For facets with similar areas, flatter surfaces have “spheres of best fit” with greater
volumes, while tightly curved facets are best matched by spheres with lower volumes (Fig. 1B).
Chlorocebus aethiops (n=2)
Macaca nigra (1)
Macaca nemestrina (4)
Macaca fascicularis (5)
Nasalis larvatus (4)
Trachypithecus cristatus (3)
Trachypithecus obscurus (1)
Presbytis melalophus (2)
Hylobates lar (6)
Symphalangus syndactylus (2)
Gorilla gorilla gorilla (4)
Pan troglodytes troglodytes (5)
Pan troglodytes verus (1)
Pongo abelii (2)
Pongo pygmaeus (3)
Alouatta caraya (10)
Alouatta seniculus (1)
Ateles belzebuth (2)
Ateles georoyi (3)
Lagothrix lagotricha (1)
Aotus azarai boliviensis (4)
Aotus infulatus (1)
Aotus nancymaae (1)
Aotus trivirgatus (2)
Callimico goeldii (2)
Callithrix pygmaea (3)
Callithrix penicillata (2)
Leontopithecus rosalia (1)
Saguinus midas (3)
Saguinus niger (1)
Saguinus oedipus (1)
Saguinus mystax (2)
Cebus apella (10)
Saimiri boliviensis (5)
Saimiri sciureus (2)
Cacajao calvus (3)
Chiropotes satanas (3)
Pithecia pithecia (2)
Callicebus donacophilus (3)
Callicebus moloch (4)
Tarsius bancanus (2)
Tarsius syrichta (2)
Tarsius spectrum (3)
Microcebus griseorufus (10)
Cheirogaleus major (1)
Cheirogaleus medius (2)
Lepilemur leucopus (4)
Lepilemur mustelinus (1)
Indri indri (2)
Avahi laniger (1)
Propithecus verreauxi (7)
Propithecus diadema (1)
Eulemur fulvus albifrons (5)
Eulemur fulvus fulvus (1)
Eulemur fulvus collaris (3)
Eulemur mongoz (2)
Hapalemur griseus griseus (4)
Lemur catta (3)
Varecia variegata variegata (3)
Daubentonia madagascariensis (1)
Arctocebus calabarensis (3)
Perodicticus potto (9)
Loris tardigradus (4)
Nycticebus coucang (1)
Nycticebus menagensis (1)
Nycticebus javanicus (1)
Euoticus elegantulus (2)
Galago moholi (2)
Galago senegalensis (7)
Otolemur crassicaudatus (8)
Galagoides demido (5)
9.0 mya
Lateral Tibial
Facet
Ectal Facet
Navicular
Facet
Galagoides
AMNH 241121
Pongo
NMNH 142169
Fig. 1. A) Included specimens and phylogenetic tree used for
phylogenetic generalized least squares regressions. B) Tali
of small and large-bodied primates with best fit spheres
matched to articular surfaces. Facets are oriented oblique to
the viewing plane, thus tali are not in standard anatomical
orientation.
A B
RMA and PGLS Regressions
• Extant primate body masses were collected from published sources15. Male values were used
for all specimens that lacked a sex (n=29, 13% of total sample), a potential source of bias.
• The volume of the “sphere of best fit” was log-transformed and regressed against log-body
mass using reduced major axis (RMA) and phylogenetic least squares (PGLS) methods. RMA
regressions were calculated in PAST16, while the R package caper17 was used for PGLS. The
phylogenetic tree (Fig. 1A) was downloaded from 10kTrees18.
• For RMA regressions, individuals from species that exhibit less than 25% sexual dimorphism
were averaged into species means. If dimorphism exceeded 25%, specimens were averaged by
sex. Species means were used for PGLS regressions. Separate regressions were performed for
primates, strepsirrhines, haplorhines, prosimians, and anthropoids.
• Although there is considerable debate surrounding regression methods19, we favor PGLS
whenever phylogeny contributes significant information (ie. maximum likelihood λ does not equal
zero). When λ does not significantly differ from zero, RMA regressions are more appropriate19,20.