Selection for mechanical advantage underlies multiple cranial optima in New world leaf-nosed
bats, Dumont, Elizabeth, Samadevam, Krishna, Grosse, Ian R, Warsi, Omar M, Baird, Brandon,
Davalos, Liliana M
SUPPLEMENTARY METHODS
Model Construction and Validation
The first step in building the CAD model was to create a 3D sterolithography (STL)
model of Carollia perspicillata from micro computed tomography (μCT) scans of a cranium. An
stl model is a 3-D geometry model defined by one or more tessellated surfaces. A tessellated
surface can be envisioned as a sheet composed of flat triangles that fit together along their edges
and together replicate the surface of a solid structure. Each triangle is defined by three vertices
and a unit normal. If properly constructed, the stl of a solid structure forms one or more
watertight volumes or manifolds. We selected points on the outside surface of the C.
perspicillata STL model, imported their 3D coordinates into SolidWorks, and connected them
with sheet-like surfaces to represent bone. The 3D coordinates served as control points that
regulated the shape of the morphable cranium via their mathematical relationship to relative
palate length and width (Samavedam 2011, and below). It was not possible to match relative
palate length in the models to relative palate length as measured from specimens exactly, but the
distributions of species in the morphospaces are very similar (Supplementary Figure S4).
We took advantage of integration between computer-aided design CAD (SolidWorks,
Dassault Systems Solid Works Corporation, Waltham, Massachusetts) and finite element (FE)
software (ANSYS WorkBench 13.0, ANSYS Inc., Canonsburg, PA) to create FE models
automatically. The CAD-based surface models were transformed into FE models by meshing
them with triangular quadratic surface elements (called shell finite elements and specifically
Shell181 in ANSYS) with an element size of 0.3 mm.
Supplementary Methods
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Selection for mechanical advantage underlies multiple cranial optima in New world leaf-nosed
bats, Dumont, Elizabeth, Samadevam, Krishna, Grosse, Ian R, Warsi, Omar M, Baird, Brandon,
Davalos, Liliana M
In contrast to the triangles in an stl model, an FE model composed of triangular shell
elements consists of a set of triangles that form a 3-D surface that does not define a watertight
volume. The surface ‘meshed’ by shell finite elements is typically the mid-plane surface--the
surface midway between two opposing surfaces that define the watertight volume. Each shell
finite element is assigned a constant thickness value or a thickness function that defines how the
element thickness varies within the model. Quadratic triangular shell elements are defined by 6
nodes: three vertices and three nodes that lie on the element’s three edges. The edges of
quadratic shell elements may be curvilinear and the element need not be planar, i.e. lie in a single
plane.
A convergence study with respect to total strain energy found that smaller element sizes
resulted in <1 % change in the total strain energy, indicating that a 0.3 mm element size was
appropriate. A validation study using three species confirmed that the FE models composed of
surface elements performed well in comparison to FE models composed of solid elements (see
below).
Relative palate length
In phyllostomids, the location of the caudal edge of the palate varies relative to the last
molar tooth. To simplify building of the surface model in SolidWorks, we fixed the posterior end
of the palate according to its location in C. perspicillata. We then measured the distance between
the upper first molar and canine (M-C length) from STLs of 24 morphologically diverse
phyllostomid species. We calculated a “pseudo” palate length for each of the 24 species by
multiplying their M-C lengths by the ratio of M-C length and palate length in C. perspicillata.
The formula is used to this end is:
Supplementary Methods
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Selection for mechanical advantage underlies multiple cranial optima in New world leaf-nosed
bats, Dumont, Elizabeth, Samadevam, Krishna, Grosse, Ian R, Warsi, Omar M, Baird, Brandon,
Davalos, Liliana M
 Palate Length Carollia 
 Pseudo Palate Length i  
  M-C Length i
 M-C Length Carollia 
where i designates each species. There was a strong correlation between pseudo-palate length
and true palate length (R² = 0.869 P-value < 0.001, N = 24). Therefore, we took the mean of
palate length for each of the 85 species used to construct the morphospace, and used the
regression equation (pseudo-palate length = 0.8874(measured palate length) + 1.2069) to predict
pseudo-palate length for each one. As we did for measurements of palate length taken directly
from crania, we normalized pseudopalate length for each species by dividing it by the maximum
width of the cranium posterior to the external auditory meatus. The distribution of species in the
morphospaces defined by relative palate length and relative pseudopalate length are very similar
(Supplementary Figure S4).
Bone thickness
Bone thickness varies throughout the cranium within and among species, and we
incorporated this variation into our models. We divided the models into a brain case region (the
cranium posterior to and including the cribriform plate and glenoid fossa) and a rostrum. Based
on comparisons between volumes and stresses in surface and solid FE models from three
morphologically distinct species (Carollia perspicillata, Centurio senex, and Glossophaga
soricina), we assigned the braincase a uniform thickness of 0.21 mm. There was a negative linear
relationship between palate length and rostrum thickness in solid models of three species,
rostrum thickness = -0.1592*palate length/posterior skull width + 0.4199). We used that
relationship to assign rostrum thicknesses to models based on the length of their palates.
Supplementary Methods
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Selection for mechanical advantage underlies multiple cranial optima in New world leaf-nosed
bats, Dumont, Elizabeth, Samadevam, Krishna, Grosse, Ian R, Warsi, Omar M, Baird, Brandon,
Davalos, Liliana M
Qualitative validation
To evaluate the shape of our CAD-based models, we compared them to STL models of
Carollia perspicillata, Centurio senex, and Glossophaga soricina. Carollia perspicillata is
located near the center of our morphospace, Centurio senex is an exceptionally short and widefaced bat that feeds on canopy fruits, and Glossophaga soricina has a long and narrow rostrum
that reflects its nectarivorous diet. We scaled the solid model isometrically so that the posterior
width of the cranium matched that of the corresponding STL model. We overlayed the surface
models onto their corresponding STL models in Geomagic Studio (Three D Systems, Rock Hill,
SC) to visually compare them, and found that the CAD-based models appeared to reasonably
approximate the true shapes of their corresponding crania (Supplementary Figure S5).
Quantitative comparisons
We compared our CAD-based finite element models composed of shell elements to solid
finite element models constructed from STL models for the three species. The underlying
mechanics of surface finite element models are based on bending and membrane theories that are
appropriate for thin structures. Solid finite-element models can be used to model thin structures
with bending and in-plane loads but require significant more elements to achieve the same level
of accuracy as surface finite element models.
We compared the volumes of shell element and solid finite element model for each of the
three species. In a shell finite element model, the geometry of each element defines a surface,
and a thickness value is assigned to each element. The sum of the product of the area of each
element and its thickness represents the volume of the shell finite element model. For solid finite
element models, the geometry of each finite element defines a volume, and the sum of all the
element volumes provides the volume of the structure. The total volumes of the shell and solid
Supplementary Methods
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Selection for mechanical advantage underlies multiple cranial optima in New world leaf-nosed
bats, Dumont, Elizabeth, Samadevam, Krishna, Grosse, Ian R, Warsi, Omar M, Baird, Brandon,
Davalos, Liliana M
finite element models were similar for the three test cases (C. senex, C. perspicillata, G.
soricina), with the volumes of the shell element models within 11 percent of the volumes for the
corresponding solid element models Supplementary Table S4. The differences among the three
species in the volumes of their solid and surface models were no more than 3.1 percent. We
believe that this is within the volumetric accuracy of the process for creating solid models from
CT scans, and therefore caution the reader against inferring interspecies trends.
The differences among species in the areas of their solid and surface models were more
substantial (up to 19 percent, Supplementary Table S4). The direction of differences among
species is associated with their relative palate lengths. Centurio has the shortest palate and lowest
areas; Glossophaga has the longest palate and highest areas.
We also performed finite element analysis and compared the results for mechanical
advantage and von Mises stress within each pair of shell and solid finite element models.
Supplementary Table S5 shows that the mechanical advantage determined from surface model
results of C. senex, C. perspicillata and G. soricina are within two percent of the mechanical
advantage determined from the corresponding solid models. The 98% von Mises stress predicted
in the snout region by the shell models of C. senex and G. soricina surface model fell within 17%
of those predicted by the solid element models. The percent error was higher for C. perspicillata,
but for both types of models C. perspicillata exhibited substantially lower stresses compared to
both C. senex and G. soricina.
Phylogenetic analyses
Genetic sampling
DNA sequence data were collected from two introns; thy or thyrotropin beta chain, stat5a
or signal transducer and activator of 5A; one 3’-untranslated region (UTR); plcb4 or
Supplementary Methods
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Selection for mechanical advantage underlies multiple cranial optima in New world leaf-nosed
bats, Dumont, Elizabeth, Samadevam, Krishna, Grosse, Ian R, Warsi, Omar M, Baird, Brandon,
Davalos, Liliana M
phospholipase C beta 4; three autosomal exons; bdnf or brain-derived neurotrophic factor, ttn6 or
titin 6, rag2 or recombination-activating protein 2; and the X-chromosome exon atp7a or
ATPase-7A. A small number of new complete sequences were sequenced from the
mitochondrial locus cytochrome b or cytb. Published sequences from the mitochondrial genes
cox1 or cytochrome oxidase I, cytb, and the ribosomal RNAs 12S, tRNAval and 16S (mtr) were
also included to maximize sampling of species for which we had engineering data (Baker et al.
2003; Clare et al. 2007; Clare et al. 2011). Primers and PCR conditions are described in detail in
Dávalos et al. (Accepted). Briefly, we used Qiagen Taq to amplify target loci with previously
published and new primers (Eick et al. 2005; Teeling et al. 2005; Murphy and O'Brien 2007).
Resulting PCR products were cleaned using Agencourt AMPure XP magnetic beads (Beckman
Coulter, Inc.) following the manufacturer’s protocol, cycle-sequenced using BigDye Terminator
3.1 (Applied BioSystems, Inc.) chemistry, and sequenced in two directions using Applied
Biosystems 3730 sequencers. New sequences generated for this study as well as GenBank
records for published sequences are listed in Supplementary Table S1.
Maximum likelihood analyses
Maximum likelihood (ML) inference and the modified Bayesian Information Criterion
(BIC) were used to select the best approach to partitioning the data and optimal models of
sequence evolution for each of the partitions as implemented in the python script PartitionFinder
v1.0.1 (Lanfear et al. 2012). Since the goal of phylogenetic analyses was to obtain a series of
dated phylogenies, only the subset of models of DNA evolution implemented in Beast v.1.7.5
(Drummond et al. 2012) was considered. To avoid dependencies between estimates of the
approximate distribution of rate heterogeneity among sites (gamma), and the proportion of
invariant sites (Gu et al. 1995), only models with no rate heterogeneity, invariant sites or gamma-
Supplementary Methods
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Selection for mechanical advantage underlies multiple cranial optima in New world leaf-nosed
bats, Dumont, Elizabeth, Samadevam, Krishna, Grosse, Ian R, Warsi, Omar M, Baird, Brandon,
Davalos, Liliana M
distributed heterogeneity were considered when searching for the best-fit model of sequence
evolution.
Each protein-coding locus in the alignment was partitioned into its 3 codon positions
resulting in 18 different (6 loci x 3 codon positions) partitions, in addition to each of the introns
and the mitochondrial ribosomal rRNA partition (3 introns + 1 mtrRNA), for a total of 22
possible partitions. To reduce computational time, the greedy algorithm was used to search for
the optimal partitioning scheme.
The optimal partitioning scheme (Supplementary Table S2) was then used in 100 rapid
bootstrap pseudoreplicates followed by a thorough maximum likelihood search in RAxML
v7.4.6 (Stamatakis 2006; Stamatakis et al. 2008). A time-calibrated estimate of the ML
phylogeny was then obtained using the penalized likelihood “r8s” algorithm (Sanderson 2003) as
implemented in the chronopl routine in the Ape v. 3.0-7 R package (Paradis et al. 2004). A
smoothing parameter of 0.5, and three node calibrations corresponding to the constraints
described in detail in the “Relaxed molecular clock phylogenies” section below were used to
obtain a chronogram.
Relaxed molecular clock phylogenies
Three nodes were used to calibrate relaxed molecular clock analyses using Beast. To
constrain calibration points, Beast allows the user to specify bounded prior distributions. Each
calibration node was constrained using a normal distribution and then constrained to a minimum
and maximum age. The oldest calibration node was the divergence between ingroup
phyllostomids and one mormoopid outgroup, calibrated to a normal distribution centered on 33
My BP with a standard deviation (sd) of 3 and constrained to a minimum of age of 30.8 My BP
corresponding to the Whitneyan layer in which an undescribed mormoopid fossil was found
Supplementary Methods
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Selection for mechanical advantage underlies multiple cranial optima in New world leaf-nosed
bats, Dumont, Elizabeth, Samadevam, Krishna, Grosse, Ian R, Warsi, Omar M, Baird, Brandon,
Davalos, Liliana M
(Czaplewski and Morgan 2012). Two additional nodes were also calibrated for divergences
between Platalina and its sister taxa, and Vampyrum and its sister taxon (Dávalos et al.
Accepted). The prior on both divergences was calibrated using normal distributions centered on
12.2 My BP and sd of 3 with a minimum age of 11.8 My BP, corresponding to the Miocene La
Venta fossils (Czaplewski et al. 2003). The optimal partitioning scheme and models of DNA
evolution were used in three independent Markov chain Monte Carlo (MCMC) chains of 10
million generations sampled every 1000 generations in CIPRES (Miller et al. 2010). A Yule
pure-speciation model was used to infer branching events in the phylogeny.
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Selection for mechanical advantage underlies multiple cranial optima in New world leaf-nosed
bats, Dumont, Elizabeth, Samadevam, Krishna, Grosse, Ian R, Warsi, Omar M, Baird, Brandon,
Davalos, Liliana M
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Selection for mechanical advantage underlies multiple cranial optima in New world leaf-nosed
bats, Dumont, Elizabeth, Samadevam, Krishna, Grosse, Ian R, Warsi, Omar M, Baird, Brandon,
Davalos, Liliana M
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