Diversity of Limb-Bone Safety Factors for Locomotion in Terrestrial

Integrative and Comparative Biology
Integrative and Comparative Biology, volume 54, number 6, pp. 1058–1071
doi:10.1093/icb/icu032
Society for Integrative and Comparative Biology
SYMPOSIUM
Diversity of Limb-Bone Safety Factors for Locomotion in Terrestrial
Vertebrates: Evolution and Mixed Chains
Richard W. Blob,1,* Nora R. Espinoza,* Michael T. Butcher,† Andrew H. Lee,‡
Angela R. D’Amico,* Faraz Baig§ and K. Megan Sheffieldô
*Department of Biological Sciences, Clemson University, Clemson, SC, USA; †Department of Biological Sciences,
Youngstown State University, Youngstown, OH, USA; ‡Department of Anatomy, Midwestern University, Glendale, AZ,
USA; §Department of Bioengineering, Clemson University, Clemson, SC, USA; ôClemson Libraries, Clemson University,
Clemson, SC, USA
From the symposium ‘‘Terrestrial Locomotion: Where Do We Stand, Where Are We Going?’’ presented at the annual
meeting of the Society for Integrative and Comparative Biology, January 3–7, 2014 at Austin, Texas.
1
E-mail: [email protected]
Synopsis During locomotion over land, vertebrates’ limb bones are exposed to loads. Like most biological structures,
limb bones have a capacity to withstand greater loads than they usually experience, termed a safety factor (SF). How
diverse are limb-bone SFs, and what factors correlate with such variation? We have examined these questions from two
perspectives. First, we evaluated locomotor SF for the femur in diverse lineages, including salamanders, frogs, turtles,
lizards, crocodilians, and marsupials (opossums). Comparisons with values for hind-limb elements in running birds and
eutherian mammals indicate phylogenetic diversity in limb-bone SF. A high SF (7) is primitive for tetrapods, but low
magnitudes of load and elevated strength of bones contribute to different degrees across lineages; moreover, birds and
eutherians appear to have evolved lower SFs independently. Second, we tested the hypothesis that SFs would be similar
across limb bones within a taxon by comparing data from the humerus and femur of alligators. Both in bending and in
torsion, we found a higher SF for the humerus than for the femur. Such a ‘‘mixed chain’’ of different SFs across elements
has been predicted if bones have differing variabilities in load, different costs to maintain, or high SF values in general.
Although variability in load is similar for the humerus and femur, a high SF may be less costly for the humerus because it
is smaller than the femur. The high SFs of alligators also might facilitate differences in SF among their limb bones.
Beyond these specific findings, however, a more general implication of our results is that evaluations of the diversity of
limb-bone SFs can provide important perspective to direct future research. In particular, more complete understanding of
variation in SF could provide insight into factors that promoted the evolutionary radiation of terrestrial locomotor
function in vertebrates.
Introduction
The invasion of land presented animals with numerous functional challenges related to the different
physical properties of aquatic and terrestrial habitats
(Clack 2002; Coates et al. 2008; Ashley-Ross et al.
2013). Among the foremost of these were issues of
body-support and locomotion (Kawano and Blob
2013; Pierce et al. 2013). Once out of water, animals
require a structural framework that can resist the
newly significant effects of gravity, as well as allow
effective transmission of force to the substrate to
enable propulsion. In most terrestrial vertebrates,
this framework is provided by the bones of the appendicular skeleton. A variety of actinopterygian fish
species have evolved the ability to traverse over land
using combinations of fins that are supported primarily by flexible bony rays (Pace and Gibb 2009,
2014; Gibb et al. 2013; Kawano and Blob 2013).
However, a much more diverse terrestrial radiation
emerged among the tetrapods, in which the appendages were constructed around stiff limb bones connected by mobile joints. Although limb bones
initially evolved among tetrapod ancestors in an
aquatic environment (Shubin et al. 2006; Coates
Advanced Access publication May 7, 2014
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Evolution of limb-bone safety factors
et al. 2008; Clack 2009), the combination of stiffness
and flexibility that these elements convey to appendages likely facilitated the proliferation of tetrapods
across terrestrial habitats (Kawano and Blob 2013).
Since their initial evolution, the limb bones of
terrestrial tetrapods have diversified considerably, exhibiting a wide variety of shapes, proportions, and
mechanical properties (Alexander 1983; Currey 1984,
2002; Blob 2000; Erickson et al. 2002; Garcia and da
Silva 2006; Wilson et al. 2009). Phenotypic diversification of structures commonly results from variation
in natural selection on their functional performance
(Wainwright and Reilly 1994; Herrel et al. 2006);
thus, a key to understanding how such structural
and functional diversity emerged in limb bones is
to identify how it relates to differences in the functional demands to which limb bones are exposed.
Because the main demands placed on bones are to
resist and transfer mechanical loads (Currey 1984,
2002), and the activity typically viewed as imposing
the most severe and frequent loads on the limb
bones of terrestrial vertebrates is locomotion
(Biewener 1990, 1993), comparisons of terrestrial locomotor loading across taxa should provide critical
insight for understanding the diversity of limb bones.
Such comparisons are challenging, however, because
the significance of a given load depends on its context. Loads of the same magnitude or regime could
carry very different consequences for bones of different sizes, or for bones having different material
resilience.
One way of accounting for such differences in
comparisons of limb-bone loading across species
(or their skeletal elements) is to consider how closely
bones approach their maximum load capacity. In
other words, do limb bones differ in the amount
of extra protection they have against failure? In engineered structures, such margins of extra protection
are commonly called safety factors (SFs). The consideration of SF in a biological context was pioneered
by Alexander (1981, 1997, 1998), and has since been
advanced for a wide range of organismal structures
and measurements of performance (e.g., Rubin and
Lanyon 1982; Biewener 1983, 1993; Currey 1984,
2002; Diamond and Hammond 1992; Corning and
Biewener 1998; Diamond 1998). In its most basic
expression, SF can be regarded as the ratio of the
load that causes a structure to fail, compared with
the usual load that the structure experiences
(Alexander 1981). How such loads are evaluated
may depend on several factors (Blob and Biewener
1999; Skedros et al. 2003; Kokshenev 2007; Butcher
and Blob 2008; Vogel 2013), but even with such potential challenges, the concept of SF can provide a
1059
useful context for broad comparisons of functional
diversity and capacity of biological structures.
For vertebrates’ limb bones, analyses by Biewener
(1982, 1983, 1990, 1991, 1993) provided the earliest
broad comparative framework for considering how
loading and SF might vary across species. These
comparisons focused primarily on eutherian mammals (particularly ungulates) and on ground-dwelling birds, and identified two general patterns: (1)
bending was the primary loading regime for most
limb bones in these taxa and (2) SF for limb bones
in these species generally ranged between 2 and 4.
The dramatic differences in body-plan between species like horses and chickens suggested the possibility
that these patterns might be similar across all vertebrates. However, despite many differences, eutherians
and ground birds also share important characteristics
that are not typical of other lineages, including an
endothermic metabolism with high rates of remodeling and repair of bone (de Ricqlès 1975; Lanyon
et al. 1982; Burr et al. 1985; de Ricqlès et al. 1991),
and generally parasagittal limb kinematics (Biewener
et al. 1983, 1988; Gatesy 1999; Reilly 2000) that
could predispose limb bones of these taxa to bending
loads (Bertram and Biewener 1988). Other vertebrate
lineages, such as amphibians, turtles, crocodilians,
and squamates, are ectothermic and might exhibit
lower capacities for remodeling and repair of bone
(Owerkowicz and Crompton 1997); moreover, they
use postures in which the limbs move outside of
parasagittal planes (Walker 1971; Brinkman 1981;
Gatesy 1991; Ashley-Ross 1994; Marsh 1994; Reilly
and DeLancey 1997; Blob et al. 2008), placing the
limbs at a different orientation to locomotor forces
and impacting skeletal loading regimes (Blob and
Biewener 1999, 2001). With such differences across
vertebrate lineages, it might be expected that the patterns of limb-bone loading and SF found in eutherians and birds are not typical of all vertebrates, and
that these lineages instead independently converged
on such patterns through evolution (Blob and
Biewener 1999, 2001; Sheffield et al. 2011). Recent
studies have considerably expanded the diversity of
lineages from which bone loading and SF data have
been collected for terrestrial locomotion (Butcher
and Blob 2008; Butcher et al. 2008, 2011; Sheffield
and Blob 2011; Gosnell et al. 2011), but comparisons
of these data in an explicitly phylogenetic context
remain limited (Sheffield et al. 2011).
Because the limbs are composed of multiple skeletal elements, and many vertebrates use quadrupedal
locomotion that imposes loads both on forelimbs
and hind limbs, there is a potential for intraspecific
variation in limb-bone SF as well as for interspecific
1060
variation. Drawing an analogy between the bones
that make up the limbs and the links of a chain,
intraspecific variation in limb-bone SF might be
expected to be limited (Alexander 1997, 1998). If
the ‘‘chain’’ of bones from which the limbs are constructed would always fail at its weakest link, and
such failure might put the survival of the whole
animal at risk, then little selective advantage would
be expected for some limb bones to have greater SFs
than others, because the energy to make and maintain that extra protection would not prevent overall
failure of the individual. Such expectations provide
an intuitive null hypothesis, but Alexander (1997,
1998) proposed three exceptions for which different
SFs might be advantageous across the elements of
limbs (or, at least, not disadvantageous), forming
what he described as a ‘‘mixed chain’’. These conditions included: (1) elements that are more costly to
move or maintain might have lower SFs; (2) elements that have more variable loads than the rest
of the skeleton might have higher SFs that could
protect against occasional high loading peaks; and
(3) when SFs are high for all the elements of the
skeleton, there might be more opportunity for variation in SF across different elements. Computational
models supported the potential of these conditions
to facilitate a ‘‘mixed chain’’ of SFs across limb
bones (Alexander 1997, 1998). In addition, limited
empirical data comparing frequencies of fractures in
the limb bones of racehorses (Currey 2002), as well
as differences in SF between the femur and tibia for
iguanas and alligators (Blob and Biewener 1999), indicate the presence of lower SFs in distal elements of
limbs for these taxa. However, systematic comparisons of intraskeletal variation in SF have not formally
evaluated correlations with all three conditions
outlined by Alexander (1997, 1998).
In this article, we evaluate the functional diversity
of limb bones used for terrestrial locomotion across
and within tetrapod species, using SF as a framework
for our perspective. First, we perform a phylogenetic
comparison of limb bone SF across vertebrate
lineages, providing insight into the evolutionary diversification of this trait and evaluating how factors
such as variations in loading, and differences in the
mechanical properties of bone, contribute to that
diversity. Second, we compare new SF data for the
humerus of alligators to previous data for the femur
(Blob and Biewener 1999) to test for a ‘‘mixed
chain’’ of SFs in this species, and to ascertain
which of Alexander’s (1997, 1998) proposed conditions might facilitate its presence. Through these
analyses, we can consider how diversity in features
such as limb-bone SF may have contributed to the
R. W. Blob et al.
radiation of the structure and function of limbs that
evolved after vertebrates moved onto land.
Materials and methods
Calculations of SF
To standardize our comparisons, we sought a
common format for evaluating SFs across different
taxa and limb bones. Recalling Alexander’s (1981)
conception of SF as the ratio of ‘‘failure load’’ to
‘‘ordinary load’’, we established the following standards for these terms, with the goal of maximizing
our ability to draw on published data that appropriately reflected significant parameters for the survival
of species in our comparisons. First, ‘‘failure load’’
was considered to be the point of yield (i.e., the
point at which the bone has been damaged by plastic
deformation), rather than fracture (Currey 1990;
Biewener 1993). Second, to the extent possible, we
standardized comparisons of failure and ordinary
loads in terms of strains, rather than stresses.
Although strain-based comparisons complicated our
incorporation of data from salamanders (see below),
it allowed us to include new data from anurans, and
provided a complementary perspective to previous
stress-based comparisons of diversity of SF offered
by Sheffield et al. (2011). Third, we considered
values reported as ‘‘mean peak loads’’ to represent
‘‘ordinary’’ loads, where ‘‘mean peak loads’’ reflect
the average load under standard locomotor activities
requiring high levels of exertion. Such values indicate
different behaviors in different taxa (e.g., turtles
versus horses), but represent an effort to make comparisons that are meaningful within the context of
functional capacities for limb bones. Finally, for interspecific comparisons, our analyses focused both
on ‘‘failure’’ and ‘‘ordinary’’ loads in bending,
again maximizing our ability to compare across diverse taxa. For intraspecific comparisons of elements
in alligators, however, we compared data both for
bending and for shear (i.e., torsional loading).
Assembly of data on bone loading, mechanical
properties, and SF
Phylogenetic comparisons
To obtain a broad sample of tetrapod lineages for
phylogenetic comparisons, we compiled published
data on loading during terrestrial locomotion,
mechanical properties (typically yield strains, see
above), and SF for skeletal elements from the hind
limb. Data for eutherian mammals and birds were
extracted from the analysis by Biewener (1993),
which provided 10 values of peak strains from elements of the hind limbs (from four eutherian and
1061
Evolution of limb-bone safety factors
two avian species), and an estimate of 7000 microstrain (m") as the average yield strain of bone (Reilly
and Burstein 1975; Currey 1984). Data for other
lineages were primarily from our own published
studies, and focused on values for the femur in particular because other elements were typically too
small for attaching strain gauges. Data included
mean in vivo peak strains, mechanical properties of
bones, and calculations of SF for American alligators
(Alligator mississippiensis) (Blob and Biewener 1999),
green iguana lizards (Iguana iguana) (Blob and
Biewener 1999), Argentine black and white tegu lizards (Tupinambis merianae) (Sheffield et al. 2011),
river cooter turtles (Pseudemys concinna) (Butcher
et al. 2008), and marsupial Virginia opossums
(Didelphis virginiana) (Butcher et al. 2011).
To include information from amphibians in our
analysis, we added a stress-based estimate of femoral
SF from tiger salamanders (Ambystoma tigrinum)
(Sheffield and Blob 2011) to our dataset, along
with a value of yield strain for this species derived
from a different study (Erickson et al. 2002). We also
compiled previously unpublished data from in vivo
recordings of femoral strains for two anuran species:
the bullfrog (Lithobates catesbeiana: N ¼ 9, body mass
215–444 g) and cane toad (Chaunus marinus: N ¼ 3,
body mass 147–174 g). Animals were purchased from
commercial suppliers, housed in large plastic enclosures, and daily provided with clean, aged water, and
crickets for food.
Procedures for collection and analysis of in vivo
strains for frogs followed those previously published
for the femur for other taxa (Butcher et al. 2008,
2011; Sheffield et al. 2011), with the following additional clarifications. First, anesthesia of frogs was induced via immersion in a buffered solution of
tricane methanesulfonate (MS-222, 2 g/l), and was
maintained during surgical implantation of gauges
by covering the skin (except the surgical limb) with
gauze soaked in MS-222 (0.5 g/l). Second, effort was
made to implant three gauges on the midshaft of
each femur, with single-element gauges at all locations except the dorsal surface of some of the largest
bullfrogs, to which a rosette gauge was attached.
Lead wires from these gauges emerged through a
small incision at the hip and were soldered into a
microconnector plug. The wires were protected by
wrapping them into a cable using self-adhesive bandage, and the cable was stabilized by wrapping it in a
belt of self-adhesive bandage around the belly of the
frog. Third, after 24 h of recovery, strains were recorded at 2500 Hz from single, forward jumps in
trackway arenas, with several minutes of rest between
jumps. Finally, at the conclusion of recordings, frogs
were euthanized in buffered MS-222 (4 g/l), and the
limb bones with implanted gauges were extracted to
verify the position of gauges and allow sectioning for
analyses of planar strains to evaluate how much peak
strains may have exceeded recordings of strains
(Biewener and Dial 1995; Lieberman et al. 2004;
Butcher et al. 2008, 2011). Mean values of peak
strain for each species were compared with published
data on the mechanical properties of their femora
(Wilson et al. 2009) to evaluate SF.
Intraspecific comparisons
To assess potential differences in SF across elements
of limb bones within a species, previously published
data from the alligator femur (Blob and Biewener
1999) were compared with new recordings of strains
collected from the humerus, along with new mechanical property data both for the humerus and femur.
To conduct new strain recordings, four animals were
obtained from the Rockefeller Wildlife Refuge that
were similar in size (body mass 1.7–2.0 kg, total
length 0.81–0.89 m) to animals from which previous
femoral strain recordings had been collected.
Animals were fed chicken hearts, gizzards, and frankfurters, and were housed in large artificial ponds
maintained in a greenhouse under conditions of natural summer light and temperature.
Procedures for the collection and analysis of
strains from the alligator humerus followed previously published methods (Butcher et al. 2008, 2011;
Sheffield et al. 2011), with the following additional
clarifications. First, initial sedation and analgesia
were provided by intramuscular injections of butorphenol (1 mg/kg), ketamine (30 mg/kg), carprofen
(2 mg/kg), and detomidine (0.2 mg/kg). Alligators
were then intubated and maintained at a surgical
plane of anesthesia by administration of isoflurane
(initially 3–4% at O2 supply of 1 l/min, reduced to
0.5–1% after 20–30 min and further reduced to 0%
after attachment of gauges). Second, gauges were implanted onto the midshaft surface of the humerus,
between reflections of the brachialis and humeroradialis muscles (Meers 2003), via a ventral incision on
the arm. Lead wires from implanted gauges emerged
through a small incision at the shoulder, and were
soldered into a microconnector plug. The wires were
protected by wrapping them in a cable using selfadhesive bandage, and the cable stabilized by wrapping it in a belt of self-adhesive bandage wrapped
around the chest of the alligator. Third, after 48 h
of recovery, strains (recorded at 2500 Hz) were collected over the next 1–2 days during bouts of locomotion on a treadmill. Bouts of 30 s duration were
conducted at 0.3–0.4 m/s (comparable to previous
1062
recordings from the femur) (Blob and Biewener
1999), with several minutes of rest between bouts.
Finally, at the conclusion of recordings, alligators
were euthanized by an overdose of sodium pentobarbital solution (Beuthanasia, 120 mg/kg intraperitoneal injection), and animals were frozen for later
extraction of limb bones to conduct analyses of
planar strains and tests of mechanical properties.
Although a value of yield strain in bending
(6495 m") had been published previously for the alligator femur (Blob and Biewener 1999), to calculate
SF for the humerus and femur during both bending
and torsion, additional data on mechanical properties were required. Available specimens of humerus
and femur were extracted from animals frozen after
use both in current and earlier studies of femoral
strains (Blob and Biewener 1999). Bending and torsional tests were conducted on thawed specimens,
using the methods and the Instron materials-testing
machines used for frogs (Wilson et al. 2009).
Reconstruction of the evolution of SF for
tetrapod femora
To evaluate how SFs for bones of the tetrapod hind
limb have changed through evolution, and which
groups show significant changes from their ancestors,
we mapped values of SF onto a cladogram of tetrapod relationships, and used comparative methods to
reconstruct ancestral states of SF at internal nodes of
the phylogeny. Our analysis used the generalized
least squares (GLSs) approach for continuous characters presented by Martins and Hansen (1997), as
implemented in the COMPARE 4.6 software package
(Martins 2004). In this approach, values and standard errors for the character states of ancestral taxa
are estimated from character-state values for the taxa
under study, a phylogeny of taxonomic relationships,
data on branch-lengths for that phylogeny, and a
model of character-change. This approach can also
incorporate information about the standard errors of
the values of traits for each terminal taxon (Martins
and Lamont 1998). Based on available data, it is difficult to represent, in terms of typical standard
errors, what is known about variation in SF among
members of the taxa we analyzed. However, to acknowledge the presence of uncertainty in those SF
values, for each terminal taxon we applied an estimated standard error of 10% of the SF, basing this
estimate on common magnitudes of standard errors
for measurements of mechanical properties of bones
(Blob and Snelgrove 2006).
Estimates of tetrapod phylogeny and branchlengths for the taxa we considered were taken from
R. W. Blob et al.
the literature (Laurin 2004; Donoghue and Benton
2007; Hugall et al. 2007; Kumazawa 2007; Vidal
and Hedges 2009; Pyron 2011; dos Reis et al.
2012). GLS analyses were run in COMPARE using
the ‘‘Linear’’ option, which uses Brownian motion as
a model of character-change and assumes that divergence between taxa increases linearly with phylogenetic distance. Although objections have been raised
to this model (e.g., Butler and King 2004), our objective was to represent the unpredictability of the
evolution of characters under natural selection,
rather than a genuinely random process (Schluter
et al. 1997; Blob and Snelgrove 2006). Our specific
goal in these analyses was to evaluate whether eutherian mammals, birds, or any other lineage showed SF
values that deviated significantly from those of their
ancestors. Toward this goal, we compared whether
the magnitude of evolutionary change in SF along
any branch of the phylogeny exceeded a factor calculated as 1.96 (average standard error of the two
taxa marking the branch). Such lineages could be
considered to show a magnitude of change greater
than a rough 95% confidence interval of expected
change for that lineage (Martins and Lamont 1998;
Martins 2004).
Our analysis of ancestral states for the SF for limb
bones should be approached with a measure of caution. First, critical evaluations of methods for reconstructing ancestral character states have noted a
variety
of
limitations
to
such
analyses
(Cunningham et al. 1998; Cunningham 1999; Losos
1999; Omland 1999; Polly 2001; Webster and Purvis
2002). These include the potential for the standard
errors of reconstructed states to become quite large,
limiting the potential for identifying significant
change through evolution (Schluter et al. 1997;
Martins 1999; Moran 2004). This particular limitation actually helps to make our consideration of evolutionary change in SF conservative, as only the most
robust changes should be identified as significant.
Another potential issue is that SF is itself a ratio of
two variables, each of which might evolve independently. To address this issue, we report values for
both variables that contribute to calculations of SF
for each taxon, allowing qualitative appraisal of potentially distinct evolutionary paths for the loading
and mechanical properties of limb bones. However,
because these values are reported as a mix of both
tensile and compressive values in the original studies
from which they were derived (and actually as stresses, rather than strains, for salamanders) (Sheffield
and Blob 2011), it is difficult to formally reconstruct
ancestral values for these traits without a variety of
further assumptions. In addition to these general
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Evolution of limb-bone safety factors
issues, the details of our reconstruction of phylogenetic relationships, as well as its branch-lengths,
might also be called into question (e.g., the historically contentious placement of turtles) (Chiari et al.
2012; Shaffer et al. 2013). Although a variety of such
considerations could be adjusted and explored further, for our present analysis we have focused on
identifying at least one strongly supported phylogenetic context, and examine the perspective it can give
for evaluating the evolution of SF for limb bones
during terrestrial locomotion.
Results
Phylogenetic comparisons
In vivo strains from the femora of frogs
Recorded femoral strains from both species of frogs
indicate predominantly tensile axial loads on the
dorsal and anterior surfaces that grade into compressive loads toward the anteroventral aspect of the
cortex (Table 1). The presence of both tensile and
compressive strains around the cortex of these elements indicates that bending is a significant loading
regime in the femur of both species (e.g., Biewener
et al. 1983; Blob and Biewener 1999). Rosette recordings from the dorsal surface of bullfrogs show principal strains that approach 1.7 greater magnitudes
than axial strains; moreover, the angle of principal
tensile strains to the long axis of the femur (t) averages 44.6 20.28, approaching the 458 expected for
pure torsion (Table 1). The large standard deviation
for this variable indicates that individual jumps
probably do not ever actually experience pure torsion, a result corroborated by the values of axial
strain also recorded from the rosette gauges
(Table 1). However, a predominance of high t
values above and below 458, along with values of
shear strains that closely match those of principal
strains (Table 1), indicates that torsion may be at
least similar in importance to bending as a loading
regime for the limb bones of jumping frogs.
Entry of the average axial strains recorded from
each location into analyses of planar strains that account for the positions of gauges (Biewener and Dial
1995; Blob and Biewener 1999; Lieberman et al. 2004)
indicate values of peak tensile and compressive axial
strains of þ488 m" and 1260 m" for bullfrogs, and
þ342 m" and 1401 m" for cane toads. The presence
of higher magnitudes of compression versus tension
on the cortex indicates that axial compression (likely
from the support of body weight) is superimposed on
bending and torsion in both species. Peak loads for
toads are comparable (possibly even slightly higher)
than those for bullfrogs, a potential surprise given the
explosive jumps typical of bullfrogs, relative to the
seemingly less dramatic hopping behaviors typical of
toads (Marsh 1994; Wilson et al. 2009). Because estimates of peak compressive loads in bending were
much higher than those for peak tensile loads in
both species, these estimates of peak compressive
loads were compared with measurements of mechanical properties for the femora of both species (Wilson
et al. 2009) to calculate SF values for phylogenetic
analyses. After correcting originally reported tensile
mechanical properties to account for bone typically
being 25% weaker in tension than in compression
(Currey 1984; Biewener 1993), femoral SF in bending
was calculated as 7.7 for L. catesbeiana and 8.5 for
C. marinus (Fig. 1).
Reconstruction of ancestral values and patterns of
evolutionary change in limb-bone SF for terrestrial
locomotion in tetrapods
The phylogenetic distribution of SFs for bones of the
hind limb in bending during terrestrial locomotion,
along with magnitudes of peak load and mechanical
properties, is illustrated in Fig. 1. All three of these
parameters show considerable variation across tetrapod lineages. Eutherian mammals and birds have the
Table 1 Recorded axial strains ("axial) measured from the femur of bullfrogs (Lithobates catesbeiana) and cane toads (Chaunus marinus)
during terrestrial locomotion, with principal tensile ("t), principal compressive ("c), and shear strains for bullfrogs
Species
Gauge location
"axial (m")
"t (m")
"c (m")
t (8)
Shear (m")
L. catesbeiana
Dorsal
Anterior
Anteroventral
282 264 (144, 9)
229 142 (98, 6)
371 234 (145, 9)
470 316 (64, 5)
393 783 (64, 5)
44.6 20.2 (58, 5)
475 6112 (64, 5)
C. marinus
Dorsal
Anterior
Anteroventral
198 184 (175, 3)
208 100 (111, 3)
181 184 (121, 2)
Notes: Values are means SD across all individuals; the numbers of jumps analyzed and individuals tested, respectively, are listed in parentheses
after each mean. Angles of principal tensile strains to the long axis of the bone (t) are also reported (positive angles indicate inward/medial
rotation).
1064
R. W. Blob et al.
Fig. 1 Evolution of SF for hind-limb bones in bending during terrestrial locomotion, evaluated across tetrapod diversity. Values of SF,
failure (Yield), and usual load (Load) for taxa from which data are available are reported in the three right-hand columns. SF values are
reported with SE ¼ 10% mean SF, reported to two decimal places to avoid rounding error (Blob and Snelgrove 2006). SFs for
terminal taxa were used to calculate GLS reconstructions of SF values (1 SE) for ancestral nodes of tetrapod phylogeny (Martins
2004). Branch-lengths (with citations) and the significance of evolutionary change along branches are reported in Table 2. Data on SF,
yield, and load were derived from the following sources: salamanders—Sheffield and Blob (2011); frogs—present study, Wilson et al.
(2009); Didelphis virginiana—Butcher et al. (2011); eutherians—Biewener (1993); Iguana iguana—Blob and Biewener (1999); Tupinambis
merianae—Sheffield et al. (2011); turtles—Butcher et al. (2008); crocodilians—Blob and Biewener (1999); and birds—Biewener (1993).
a
To supplement stress-based yield and load data for salamanders, a published yield strain from Erickson et al. (2002) is also reported;
this reference also provided the original value for tensile bending strain in opossum femora, converted to the compressive value
reported here by Butcher et al. (2011).
**Branches with absolute values of changes in SF that are greater than the rough confidence interval of expected change for the branch
(Table 2) (Martins 2004).
*Other branches with changes in absolute magnitude of SF of 42 that are considered in the text.
lowest SFs, whereas salamanders and iguanas have
the highest. However, taxa that might be regarded
as having higher values of SF can achieve them in
different ways. For example, in alligators, SF is high
primarily because of low loads; in opossums, SF is
high primarily because yield strains are high; and in
iguanas, SF is high both because loads are low and
yield strains are high (Fig. 1).
Reconstructions of ancestral state lead to an estimate of 6.8 2.4 for the ancestral value of SF for
tetrapods (Fig. 1). Across tetrapod phylogeny, only
four branches show an absolute change in SF of 42,
in each case between a node and a branch-tip represented by a terminal taxon. These include decreases
in SF of 42 for the branches leading to eutherian
mammals and to birds, and increases in SF of 42
1065
Evolution of limb-bone safety factors
for the branches leading to salamanders and iguanas.
Based on Martins’ (2004) criterion for significance,
that the amount of change along a branch must
exceed a rough 95% confidence interval for the
amount of change expected for that branch, only
the evolutionary changes in SF for birds and salamanders are significant (Table 2). However, the decrease in SF for eutherian mammals is nearly
significant: actual change differs from expected
change by only 0.21, 510% of mean eutherian SF
(compared with a shortfall of 0.82 between actual
and expected change for the branch leading to iguanas). The significant increase in SF on the branch
leading to salamanders should also be regarded
with caution, as the estimate of SF for this taxon
was derived from force-platform analyses (Sheffield
and Blob 2011), which can lead to higher estimates
of SF than obtained by in vivo strain data (Biewener
et al. 1983; Butcher and Blob 2008; Butcher et al.
2008; Schoenfuss et al. 2010). As a result, the primary evolutionary changes in SF for limb bones, in
bending, during terrestrial locomotion, appear to be
evolutionary decreases in birds and, potentially, eutherian mammals.
Intraspecific comparisons
In vivo strains from the humerus of alligators
Recorded strains from the humerus of alligators indicate predominantly tensile axial loads on the anterior
and anteroventral surfaces that grade into compressive
loads toward the ventral aspect of the cortex
Table 2 Comparisons of magnitude of evolutionary change in limb bone SF for bending during terrestrial locomotion along branches of
tetrapod phylogeny, with rough 95% confidence intervals for each branch
Branch
Branch length
(millions of years)
57.2a,b
Rough 95%
confidence interval
for branch
Evolutionary change
in SF along branch
4.19
0.71
b
2.88
2.96c
b
2.02
0.40
Node 3 to Lithobates catesbeiana
b
129.2
2.88
0.24
Node 3 to Chaunus marinus
129.2b
2.95
0.56
Root to node 4 (Amniotes)
a
12.7
2.43
0.16
164.5a,d
3.23
1.88
Root to node 2 (Amphibians)
Node 2 to Salamanders
Node 2 to node 3 (Frogs)
Node 4 to node 5 (Mammals)
292.8
163.6
Node 5 to Didelphis virginiana
d
172.8
2.75
0.31
Node 5 to Eutherians
172.8d
2.50
2.29e
52.8a,f,g,h
1.08
0.06
Node 6 to node 7 (Lepidosaurs)
105.1f,g,h,i
3.95
1.71
Node 7 to Iguana iguana
179.4i
3.29
2.47e
i
3.09
0.47
1.83
0.36
263.9f,g
2.29
1.86
18.9f,g
1.97
0.19
Node 9 to Crocodilians
f,h
245.0
2.62
0.24
Node 9 to Birds
245.0f,h
2.33
2.76c
Node 4 to node 6 (Reptiles)
Node 7 to Tupinambis merianae
Node 6 to node 8 (Turtles þ Archosaurs)
Node 8 to Turtles
Node 8 to node 9 (Archosaurs)
179.4
20.6f,g,h
Notes: Branches are named based on the numbering of nodes in Fig. 1. Rough 95% confidence intervals are calculated as 1.96 (average
standard error of the two taxa marking the branch) (Martins 2004). Magnitudes of evolutionary change are calculated as (descendent node
SFancestral node SF), so that positive values indicate an evolutionary increase in SF through evolution, and negative values indicate an
evolutionary decrease.
a
Laurin (2004).
b
Pyron (2011).
c
Changes with absolute values greater than the corresponding rough confidence interval.
d
Dos Reis et al. (2012).
e
Other changes with an absolute magnitude 42 considered in the text.
f
Hugall et al. (2007).
g
Kumazawa (2007).
h
Donoghue and Benton (2007).
i
Vidal and Hedges (2009).
1066
R. W. Blob et al.
(Table 3). The presence of both tensile and compressive strains around the cortex indicates that bending is
a significant loading regime (e.g., Biewener et al. 1983;
Blob and Biewener 1999). Rosette recordings from the
ventral surface show principal strains that approach
1.7 greater magnitudes than axial strains, with t
averaging 4208 (Table 3). With these considerable
t values, shear strains exceed principal strains
(Table 1), indicating that torsion, as well as bending,
is a significant loading regime for the alligator humerus. Analyses of planar strains (Biewener and Dial
1995; Blob and Biewener 1999; Lieberman et al. 2004)
indicate that peak loads may be as much as 2.83 times
greater than recorded loads, thereby providing a correction factor to apply to recorded loads for calculations of SF.
Comparisons of SF from the humerus and femur
of alligators: testing for the presence of a
mixed chain and proposed correlated conditions
New measurements of yield strains in bending and
torsion for the alligator humerus were compared
with corrected values of tensile bending strain and
shear strain to calculate SF for this bone in both
loading regimes (Table 4). New measurements of
yield strain in torsion for the alligator femur were
also collected, allowing refined comparison of humeral SF values to previously published (Blob and
Biewener 1999) estimates for the femur (Table 4).
These comparisons show the humerus to exceed
the SF of the femur by 42 in both loading regimes:
8.4 versus 6.3 in bending and 7.8 versus 5.0 in torsion (Table 4). These differences are primarily due to
differences in yield strain between these elements, as
the magnitudes of load are nearly identical (Table 4).
After establishing the presence of a ‘‘mixed chain’’
of SF between the alligator humerus and femur, we
considered the three conditions that Alexander proposed might be correlated with such a pattern. The
presence of a lower SF in the femur than in the
humerus is consistent with Alexander’s (1997,
1998) first predicted condition, because the femur
is larger than the humerus in alligators (Dodson
1975; Livingston et al. 2009). Thus, the femur
likely requires greater energetic resources than the
humerus in order to be moved and maintained, potentially making a lower femoral SF advantageous. In
contrast, our results do not support Alexander’s
(1997, 1998) second condition, which proposed
that elements with more variable loads might have
higher SF. For both the humerus and femur of alligators, coefficients of variation for the magnitudes of
loads (25–52%) are much greater than typical values
for the limb bones of mammals (8%) (Biewener
1991); however, between the limb bones of alligators,
the humerus has a higher SF than the femur, but
comparable or lower coefficients of variation for
load-magnitudes in both bending and torsion
(Table 5). Finally, our results do appear to support
Alexander’s (1997, 1998) third condition, which proposed that when SFs are high for all the elements of
the skeleton, there might be more opportunity for
variation in SF across different elements. Both the
humerus and the femur have SF45 for all loading
regimes (Table 4). This benchmark SF value may be
lower than the ancestral value for all tetrapods, but is
higher than the values found in taxa for which a
significant evolutionary decrease in SF has been identified, such as birds and, potentially, eutherian mammals (Fig. 1).
Discussion
Whether SFs for any structure are a target of natural
selection has been a topic of considerable debate
(Lowell 1985; Lanyon 1991; Diamond 1998;
Garland 1998; Currey 2002; Vogel 2013).
Nonetheless, differences in SF across taxa or structures carry functional consequences, whether SF was
the direct target of selection or an emergent property
of selection on other traits. As a result, understanding patterns in the diversity of SFs can provide an
instructive perspective for understanding factors that
have shaped the diversity of organismal function. For
vertebrates’ limb bones, observations of phylogenetic
Table 3 Axial ("axial), principal tensile ("t), principal compressive ("c), and shear strains recorded from the humerus of American
alligators (Alligator mississippiensis) during terrestrial locomotion
Gauge location
"axial (m")
"t (m")
"c (m")
t (8)
Shear (m")
Ventral
243 152 (247, 3)
355 90 (149, 2)
416 159 (149, 2)
23 16 (149, 2)
520 261 (149, 2)
Anteroventral
357 85 (98, 1)
Anterior
255 77 (247, 3)
Notes: Values are means SD across all individuals; the numbers of steps analyzed and individuals tested, respectively, are listed in parentheses
after each mean. Angles of principal tensile strains to the long axis of the bone (t) are also reported (positive angles indicate inward/medial
rotation).
1067
Evolution of limb-bone safety factors
Table 4 Comparison of yield strains, calculated peak strains, and
SFs between the humerus and femur of American alligators
(Alligator mississippiensis) during terrestrial locomotion
Table 5 Coefficients of variation (CV) for mean recorded bending
and shear strains from the humerus and femur of American
alligators (Alligator mississippiensis) during terrestrial locomotion
Loading
regime
Bone
Bending
Humerus 8423 3090 (5)
Calculated
peak strain (m")
Bone
Bending
Shear
SF
Humerus
25.4%
50.2%
1005
8.4
Femur
48.9%
51.6%
1027a
6.3a
Humerus 11,455 450 (3)
1472
7.8
Femur
1489a
5.0
Femur
Torsion
Yield strain (m")
6495 (1)a
7509 1386 (4)
Notes: Yield strain values are means SD, with the number of bones
tested in parentheses and tensile values reported for bending.
Calculated peak strains are derived from recorded strains and correct
for results of planar strain analyses (see text). Note that SF is at least
2.1 higher for the humerus in both loading regimes.
a
Values derived from Blob and Biewener (1999).
and intraspecific diversity in SF can provide insight
into factors that have shaped the diversity of locomotor function in tetrapods since this lineage
invaded terrestrial habitats.
Interspecific diversity in the SFs of limb bones for
terrestrial locomotion: what evolutionary
changes are we trying to understand?
Birds and eutherian mammals have lower limb-bone
SFs than do other tetrapod lineages. However, an
important perspective that emerges from our phylogenetic comparisons is that these lineages (allowing
slightly generous criteria for eutherians) also show
the best evidence for significant changes in SF from
their closest ancestors, with both exhibiting decreases
(Fig. 1 and Table 2). This insight helps to focus consideration of the kinds of explanations that should be
sought. Rather than asking why higher SFs have
emerged in amphibians and non-avian reptiles
through evolution, it is more appropriate to ask
why lower SFs have emerged in eutherians and birds.
A variety of factors might have facilitated evolutionary decreases in SF for the limb bones of eutherians and birds (Blob and Biewener 1999, 2001).
First, the high levels of sustained or peak activity
commonly shown by species from both of these lineages might make maintaining or carrying the bone
material needed for high SFs energetically costly
(Lanyon 1991), so that lower SFs were advantageous.
Second, the generally greater capacity for remodeling
and for microdamage repair of bone in endotherms
like mammals and birds, compared with amphibians
and non-avian reptiles (Enlow 1969; de Ricqlès 1975;
Lanyon et al. 1982; Burr et al. 1985; de Ricqlès et al.
1991; Owerkowicz and Crompton 1997), might facilitate the capacity of mammals and birds to operate
successfully with lower margins of safety for limb
Note that, counter to predictions from the Alexander (1997, 1998)
‘‘mixed chain’’ model, CV is either essentially equal between the
bones (shear), or lower in the humerus, the bone with the higher SF
(bending).
bones. In a similar context, a third factor might
relate to the greater predictability of the loads encountered by mammalian and avian limb bones
(Bertram and Biewener 1988; Biewener 1991) compared with other taxa (e.g., Table 5). Predictable
loads might also facilitate the capacity of mammals
and birds to operate successfully with lower SFs (e.g.,
Lowell 1985; Alexander 1997), making it advantageous for potential energetic costs of high SFs to
be reduced.
Such arguments, although appealing, encounter
complications. For example, data from opossums
(Butcher et al. 2011; Gosnell et al. 2011) may not
fit the above scenarios as neatly as data from other
mammals. Although opossums are endotherms and
should have predictable loading and strong capacities
for repair of microdamage, their femora had some of
the highest yield strains of any of the taxa we evaluated (Fig. 1). In addition, although our interspecific
analyses focused on bending loads during terrestrial
locomotion, other loading regimes (e.g., torsion) and
behaviors (e.g., digging) could be significant for the
design of limb bones in amphibians or non-avian
reptiles (Blob and Biewener 1999, 2001; Butcher
and Blob 2008; Sheffield and Blob 2011).
Considerations of diversity in SF that accounted for
such factors might provide different comparisons to
values for mammals and birds.
Nonetheless, beyond such complications and the
specific factors potentially contributing to the evolutionary changes we identified, our phylogenetic analysis of the SF for limb bones leads to a further broad
question. Reconstructions of ancestral states indicate
that limb-bone SF for the earliest tetrapods approached values of nearly 7 (Fig. 1). Since this lineage evolved in an aquatic environment where the
forces imposed by body weight were likely negligible
(Shubin et al. 2014), why do their limb bones have
SFs of this magnitude? It is possible that this ancestral margin of safety evolved incidental to factors
related to support of the body, and may have
emerged as a consequence of factors such as the
1068
need for a bone that was sufficiently large to provide
attachment for locomotor muscles (Butcher et al.
2008). However, the presence of such a margin of
safety may have facilitated the invasion of land, and
potentially contributed to the success of tetrapods
over other lineages with different appendicular constructions (Kawano and Blob 2013).
Perspectives and directions for future research
Our analyses examined the diversity of SFs for limb
bones for tetrapods at both interspecific and intraspecific scales. Beyond the phylogenetic patterns just
discussed, our comparisons also emphasized that the
diversity of SFs seen across tetrapods (and their
skeletal elements) emerges from independent
variation both in the magnitudes of loads and in
the mechanical properties of bones (Fig. 1).
Although the mechanical properties of limb bones
have been described as conservative (Erickson et al.
2002), variation, both across taxa (Fig. 1) (Wilson
et al. 2009) and across skeletal elements (Table 4),
contribute to differences in SF that may have significant functional implications. Moreover, the presence
of multiple combinations of load-magnitudes and
mechanical properties that lead to similar SFs in
limb bones reflects the ‘‘many-to-one’’ mapping of
structure to function that promotes the diversification of organismal design (Alfaro et al. 2005;
Wainwright et al. 2005).
The presence of a ‘‘mixed chain’’ of SFs across
limb bones in alligators, with the femur showing
lower values than the humerus (Table 4), supports
Alexander’s (1997, 1998) hypothesis and two of his
three proposed sets of contributing conditions. Of
the two proposed contributing conditions found to
apply for alligators, the advantages of lower SFs in
the energetically costlier femur suggest a selective
explanation for the ‘‘mixed chain’’. The presence of
lower SFs in the tibia of alligators, compared with
the femur, may further support a selective
explanation for ‘‘mixed chains’’, as the more distal
position of the tibia likely makes it more energetically costly to move and might favor a lower SF for
this bone (Blob and Biewener 1999). However, the
possibility that differences in SF among the humerus,
femur, and tibia in alligators could simply reflect a
greater opportunity for variation among elements
with high SFs (Alexander 1997, 1998) might, instead,
indicate a stochastic explanation. To further test the
potential role of selection in promoting intraspecific
variation in SF, additional comparisons are needed
from other taxa with high SF values, including amphibians and non-avian reptiles (Fig. 1). Identifying
R. W. Blob et al.
instances where ‘‘mixed chains’’ were present, but
more costly elements did not have lower SFs,
would implicate stochastic explanations for differences in SF across elements. Currently, however,
the lack of such instances favors selective
explanations.
Efforts to evaluate the SFs of limb bones for
additional systems could provide important perspective for phylogenetic comparisons, as well as for evaluations of the ‘‘mixed chain’’ hypothesis. The
phylogenetic diversity of estimates of SF for limb
bones is still quite limited, with most lineages characterized by values for only one or two species
(Fig. 1). Expansion of this phylogenetic diversity
would provide a foundation for further creative testing of hypotheses with regard to variation in SF.
For example, could comparisons of a broader range
of taxa test the potential for an optimal level of
excess capacity in limb bones? How do such values
compare to the demands placed on other
components of the locomotor system, such as muscles and tendons? How might such demands combine to proscribe the limits of locomotor function,
and, how might skeletal SFs promote or constrain
the evolution of major functional transitions, such
as the invasion of land (Kawano and Blob 2013),
the evolution of upright posture (Blob 2001), or
the origin of flight (Dial 2003)? Although the
evidence for diversity in the SFs of limb bones is
convincing, we are still in the early stages of understanding its functional and evolutionary
significance.
Acknowledgments
The studies contributing to this article benefited
from help and suggestions from many individuals
over several years, including: B. Aiello, T. Bateman,
M. Butler, S. Cirilo, J. Cummings, J. DesJardins,
K. Diamond, J. Gander, C. Gosnell, S. Gosnell,
T. Hedrick, N. Hudzick, S. Kawano, M. LaBarbera,
T. Maie, C. Mayerl, T. Parker, J. Parrish, M. Pruette,
T. Pruitt, A. Rivera, G. Rivera, J. Roos, R. Rusly,
H. Schoenfuss, J. Scott, S. Shah, A. Sheffield,
K. Shugart, J. Sutton, C. Templeton, B. White, and
V. Young. Special thanks to R. Elsey and T. Perry for
providing alligators for experiments on forelimbs,
and D. Lieberman for providing software for analyses
of planar strains. Finally, R.W.B. extends thanks to
Andy Biewener for providing the foundation for this
work and supporting its efforts since the beginning.
Experimental and animal care procedures were
approved by the Clemson University IACUC
(AUP40005 and AUP50018).
Evolution of limb-bone safety factors
Funding
This work was supported by the US National Science
Foundation (IOS-0517340 to R.W.B.). Support for
participation in this symposium was provided by
the Company of Biologists, and the Society for
Integrative and Comparative Biology (Divisions of
Vertebrate Morphology, Comparative Biomechanics,
Neurobiology, and Animal Behavior).
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