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First published online May 1, 2009
Journal of Experimental Biology 212, 1442-1448 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.025544
A comparative study of the mechanical properties of Mytilid byssal threads
1 Committee on Evolutionary Biology, the University of Chicago, Chicago, IL
60637, USA
2 Department of Organismal Biology and Anatomy, the University of Chicago,
Chicago, IL 60637, USA
* Author for correspondence (e-mail: trpearce{at}uchicago.edu)
Accepted 6 February 2009
| Summary |
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Key words: mussel, byssus, byssal threads, Mytilidae, biomechanics, material properties
| INTRODUCTION |
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|
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Early endobyssate (infaunal or semi-infaunal species with byssal
attachment) and epibyssate (epifaunal species with byssal attachment) bivalves
appear to have evolved successively from burrowing taxa, although some
endobyssate groups may be secondary soft-bottom dwellers
(Stanley, 1972
;
Seilacher, 1984
). Evolutionary
trends have often involved the disappearance of byssate groups. In the
Paleozoic, endobyssate taxa declined, and the Mesozoic saw a reduction in
exposed byssate suspension feeders
(Stanley, 1972
;
Stanley, 1977
;
Skelton et al., 1990
). These
trends away from byssate forms may have been driven by increased predation
pressure, which can push groups toward greater mobility or purely infaunal
life habits (Vermeij, 1983
;
Aberhan et al., 2006
;
Harper, 2006
).
This evolutionary history provides a rich background for comparisons of
life habits and byssal properties among the modern Bivalvia. There are few
extant endobyssate taxa, whereas most epifaunal bivalves are byssally
attached. Several orders within the Pteriomorphia contain both epibyssate and
endobyssate taxa, but among these the Mytiloida stand out for two reasons.
First, the mytiloid byssus always takes the form of numerous threads. Among
the Arcoida, in contrast, the byssus of semi-infaunal and infaunal species
consists of a small number of threads, and the byssus of epifaunal species
takes the form of a sheet or plug (Oliver
and Holmes, 2006
). Second, the mytiloid byssus is collagenous,
which distinguishes it from the byssal threads of pinnids, anomiids and
dreissenids (Jackson et al.,
1953
; Pujol et al.,
1970
; Mascolo and Waite,
1986
; Anderson and Waite,
1998
).
There have been several comparative studies of mytilid byssal thread
properties. Mytilus californianus Conrad threads are stiffer and more
extensible than those of Mytilus trossulus Gould and Mytilus
galloprovincialis Lamarck, which may be a factor in the dominance of
M. californianus on wave-swept shores
(Bell and Gosline, 1996
;
Bell and Gosline, 1997
;
Carrington and Gosline, 2004
).
Recently, a comparison of the thread properties of endobyssate and epibyssate
mytilids found no significant differences between species
(Brazee and Carrington, 2006
).
This seems to indicate that thread material properties are not tailored to a
specific flow regime or environment, and it could be argued on that basis that
the number and size of byssal threads are more important than the threads'
inherent material properties.
However, previous comparative studies suffer from a number of
methodological problems. Because of the high variance in measured properties
among different threads of the same species, a large sample size is often
needed to obtain statistical power. More importantly, although it is known
that the length and area of byssal threads, due to their high extensibility,
change substantially during measurement of tensile properties, previous
researchers have consistently reported material property values that assume
negligible changes in length and area
(Smeathers and Vincent, 1979
;
Price, 1981
;
Bell and Gosline, 1996
;
Vaccaro and Waite, 2001
;
Lucas et al., 2002
;
Carrington and Gosline, 2004
;
Brazee and Carrington, 2006
;
Moeser and Carrington, 2006
;
Harrington and Waite, 2007
).
This assumption is violated to different degrees, depending on the
extensibility of the sample in question. Thus, if thread extensibility varies
significantly between species, and/or exceeds 10%, comparisons of material
property values that rely on the assumption of negligible changes in area or
length during testing can be misleading. Finally, a number of biologically
interesting variables, e.g. toughness (energy absorbed before failure), have
never been measured.
In this comparative study of four mytilid species, we have sought to avoid
these methodological problems to the greatest extent possible. We employ
`logarithmic' strain, which assumes neither constant length nor constant
volume. In calculating stress values, we rely on the assumption that thread
volume remains constant during the testing procedure. Although there may be
inaccuracies in our results (in proportion to any changes in sample volume),
the constant volume assumption is more conservative than the constant area
assumption. Our revised methodology allows a more powerful test of whether
significant differences exist between the properties of the byssal threads of
mytilid species with different life habits living in different environments.
These new and likely more accurate measurements for mytilid threads provide a
clear baseline for future comparisons with the threads of species outside the
Mytilidae [see accompanying paper (Pearce
and LaBarbera, 2009
)].
| MATERIALS AND METHODS |
|---|
|
|
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We measured the shell length of all M. edulis, M. modiolus, G. demissa and M. californianus specimens using digital calipers. Unfortunately, thread size could not be reliably correlated with individual shell length because of animal movement within the tanks. Shell length of the P. canaliculus specimens was measured onsite in New Zealand.
The animals were kept on glass plates at the bottom of each tank. To harvest threads, we transferred one of the plates and any attached animals (continuously submerged) to a smaller tray, which could be lifted out of the tank. We then snipped each thread with iris scissors at the proximal end, and separated the distal plaques from the glass plate using a razor blade. To allow collection of threads without dissection, and to ensure comparability with non-mytilid threads (which do not have the two distinct regions in the thread typical of mytilids), we collected only the distal region of each thread for testing. All samples were stored in salt water (31–32 p.p.t.) at 5°C until testing.
Thread mechanical properties were measured using a custom-built tensile
tester. The apparatus consisted of a lower grip at the bottom of a Plexiglas
tank and an upper grip that could be displaced by turning a crank on a
dovetail slider (Velmex, Bloomfield, NY, USA; Model A6027K1M-S6). The upper
grip was attached to a 10 lb (
45 N full scale) force transducer
(OmegaDyne®, Sunbury, OH, USA; Model LC703-10). The four strain gauges in
the transducer were set up as a full Wheatstone bridge supplied with a
constant 5 V excitation; the excitation and amplification of the voltage
output of the bridge circuit were performed by a bridge amplifier (Vishay®
Micro-Measurements, Shelton, CT, USA; Model 2120A). We calibrated the voltage
output of the amplifier to determine a voltage-to-force conversion factor. A
linear variable differential transformer (Pickering Controls, Plainview, NY,
USA; Model 7308-X2-A0) powered by a constant 5V DC from an external power
supply converted the displacement of the upper grip into a voltage, which
could then be converted back into a displacement value following calibration.
The voltage was digitized using a GW Instruments (Somerville, MA, USA) Model
100B analog-to-digital converter.
We limited each testing run to 10–15 byssal thread samples to minimize drying during preparation. Between one and six byssal threads from each individual were tested, with a total sample of about 20–25 threads per species. To ensure proper gripping, we sandwiched each end of each thread between two small squares of 100% rag paper using a drop of cyanoacrylate adhesive (Loctite® `Gel Control' super glue; Henkel Consumer Adhesives, Inc., Avon, OH, USA) to maximize adhesion. Before testing, we measured the length of each byssal thread sample with digital calipers.
Prior to each test, we secured one end of the thread in the upper grip of the tester and the other end in the lower grip at the base of the tank; the entire thread was immersed in sea water for the duration of the test. The tank was filled with sea water from the 5°C tank (salinity 31–32 p.p.t.) during all tests but the tank was maintained at room temperature. Once the thread was secured, we initiated data capture in the application instruNet World Mac (GW Instruments) and displaced the upper grip at approximately 0.5 mm s–1 until thread failure. At the outset of the test, the samples were slack; the beginning of the tensile test was taken to be the point at which there was a non-negligible force on the sample.
Following testing, we inspected the broken ends of each byssal thread under a dissecting microscope to assess the failure mode (e.g. smooth break, fraying, etc.) and checked to ensure that all of the samples came from the smooth-surfaced distal thread region. We took digital photographs (Nikon D100 camera back) of each broken end through the dissecting microscope at approximately x100, and measured thread diameter using ImageJ (NIH). Initially we measured the minimum thread diameter before testing, but discovered that the samples invariably broke at a different (and wider) location, presumably a cryptic weak point in the structure. Thus the diameter at failure was used in all calculations of strain to ensure consistency, although this undoubtedly results in underestimation of the inherent strength of byssal thread material.
The stress (force per unit area) and strain (displacement per unit length)
for each test were plotted in Microsoft® Excel® to produce a
stress–strain curve. Because strains were always in excess of 50%, it
was clear that byssal thread cross-sectional area and length changed
significantly during the test. Thus instead of `engineering' strain
(
E=
L/L0, where L
is length and subscript 0 indicates initial) we used `true' or `logarithmic'
strain [
T=ln(L/L0)], which does
not assume constant length or constant volume. Stress is always calculated
assuming a certain value for Poisson's ratio (
), which is defined in this
case as the negative of the ratio of tranverse to axial strain. The
instantaneous diameter of the thread is given by
d=d0exp(–
T). There are
two possible approaches. (1) `Engineering' stress (
E)
assumes constant area:
=0, thus d=d0 and
E=F/A0 (where F is
force and A is cross-sectional area). (2) `True' stress
(
T) assumes constant volume:
=0.5, and
T=
Eexp(
T). We
conservatively assumed constant volume rather than constant area (see
Discussion). A number of different mechanical properties can be determined
from the stress–strain curve. In almost all cases, there was a sharp
drop in stiffness at a characteristic stress level – the yield stress.
The slope of the stress–strain curve represents the stiffness of the
material; thread stiffness was determined both for the initial loading of the
thread and at thread failure. We also measured extensibility, or strain at
failure, and strength, or maximum stress – the latter was equivalent to
the failure stress in all but two cases. Finally, by fitting a polynomial to
the curve and integrating over the total strain, the area under the
stress–strain curve was determined; this area is the energy absorbed per
unit volume, or the toughness of the material.
A small percentage of the byssal thread stress–strain curves for each species differed dramatically from the characteristic shape of the curve for that species. In almost all cases, the discrepancy appeared to result from splitting and fraying of the thread prior to failure; we did not include the data from these samples in the analysis.
We analyzed the data using StatView 5.0 (SAS Institute, Cary, NC, USA). First, we conducted an ANOVA on the threads of each individual, followed by an ANOVA of all threads of each species, split by individual. Because no significant differences were detected, we then pooled the individuals within each species and ran an overall ANOVA, split by species. We performed post-hoc Scheffe tests to determine the specific differences detected by the ANOVA. We also ran a Kruskal–Wallis test (a non-parametric version of a standard ANOVA), as a normal distribution of the data could not be assumed. To compare `engineering' stress and strain values with `true' stress and strain values, we ran paired t-tests as well as the non-parametric equivalent, paired sign tests.
| RESULTS |
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Shell lengths of all species fell into a similar size range, 60–70 mm on average. Despite this, thread diameters for the three epifaunal species, M. californianus, M. edulis and P. canaliculus, were 3–4 times greater than those for the two semi-infaunal species, M. modiolus and G. demissa – a statistically significant difference (Table 1; P<0.0001). M. californianus threads failed at forces 60% greater than those required to break M. edulis threads (Table 1; P<0.0001), which appears to conflict with the fact that they do not differ significantly in diameter or inherent material strength (Tables 1 and 3). This conflict disappears, however, when only those threads for which force and strength data were measured are included in the analysis; in this restricted data set, M. californianus threads were more than 25% thicker than M. edulis threads (ANOVA, Scheffe test: P=0.0014), explaining their higher breaking force values.
|
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Using the `engineering' definition of strain, the failure strain exceeded 75% for all threads. Because this value far exceeds the range (5–10%) where the assumptions underlying the `engineering' approximation hold, `true' strain values were also calculated (see Materials and methods). Stress values were calculated using both the `engineering' and `true' approaches, assuming constant area and constant volume, respectively. Table 2 illustrates the discrepancy between the calculated values of stress and strain using the two definitions of each variable.
|
Values for byssal thread strength (maximum stress) calculated using the `true' stress approach were almost twice the values calculated using the `engineering' definition. True values for thread extensibility (strain at failure), by contrast, were around 30% lower than those calculated using the `engineering' definition (Table 2). These large discrepancies arise from the high strains that byssal threads can undergo before failure – the greater the strain, the greater the discrepancy.
`True' stress and strain were used to construct the stress–strain
curves for all of the byssal thread samples. The curve for a representative
thread sample from each species is given in
Fig. 1. As previously reported
(Brazee and Carrington, 2006
),
M. modiolus byssal threads exhibit two distinct yield points, one in
the same range as the yield points of the threads of the other species in this
study, and one at a higher stress and strain.
|
Modiolus modiolus byssal threads were significantly stronger than those of G. demissa. Although M. modiolus threads were significantly stiffer than M. edulis threads, they were also significantly less extensible (Table 3). The byssal threads of M. californianus and M. edulis did not differ significantly in any of their material properties, despite M. californianus threads breaking on average at higher forces (Table 1, Table 3). ANOVA revealed significant differences between species for all mechanical properties except toughness, the energy absorbed by the material before failure (Table 3). (For a complete list of property values for all the individual threads tested in this study, see supplementary material Table S1.)
| DISCUSSION |
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|
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Byssal threads produced in aquaria may have different properties to byssal
threads produced in the wild, given that byssal thread chemistry and
mechanical properties can be greatly affected by external conditions
(Moeser and Carrington, 2006
).
Comparisons between the breaking force of laboratory-produced and
field-produced threads have revealed significant differences, although it is
unknown whether these translate into significant differences in inherent
material properties (Bell and Gosline,
1996
). One advantage of testing laboratory-produced threads,
however, is that the different species produce their threads under relatively
similar circumstances – the controlled environments of aquaria. The
results in this study can thus be used as a baseline of comparison for future
studies of field-produced byssal threads.
The results presented in Table 2 indicate that previous studies of byssal thread material properties have overestimated the inherent extensibility of thread material by almost 30%. Although there is an even larger discrepancy between the values for `engineering' and `true' stress – the latter are 75–100% greater than the former – the calculation of `true' strain does not assume constant volume during tensile testing while the calculation of `true' stress does. Hence, in the comparison between `engineering' and `true' stress as measures of the inherent strength of a material, we are faced with two competing assumptions: either (1) the Poisson's ratio is assumed to be zero, i.e. constant area during testing is assumed; or (2) the Poisson's ratio is assumed to be 0.5, i.e. constant volume during testing is assumed (see Materials and methods).
We think `true' stress is a superior measure of the strength of byssal
thread materials because it makes the more conservative assumption. It is
known that thread area is reduced during testing, and that this reduction is
substantial given that byssal threads can be stretched to almost twice their
length prior to failure. However, it is not known whether thread volume
remains constant during testing; the Poisson's ratio (
) of byssal threads
has never been measured. If
=0.00–0.25, `engineering' stress is more
accurate than `true' stress, whereas if
=0.25–0.50, `true' stress is
more accurate. For materials with complex architecture, it is possible to have
>0.5, but although both `engineering' stress and `true' stress become
more inaccurate as
enters this higher range, calculations based on the
strains in our study show that `true' stress is more accurate for
=0.25–0.90 (supplementary material Fig. S1). Moreover, published
data for similar materials suggest that the constant volume assumption may
hold for byssal threads: the Poisson's ratio of rubber is 0.5, and spider silk
fibers do not change in volume during tensile testing
(Vogel, 2003
;
Guinea et al., 2006
).
Employing the proper formulas, it is straightforward to convert `true' stress
into `engineering' stress, and also to breaking force given thread area, and
thus it is straightforward to compare new results with those of previous
researchers. (We have provided complete values for all of these variables for
each individual thread tested in supplementary material Table S1.)
The benefits of using `true' stress and strain are many. The instantaneous
stiffness can be calculated at any point on the stress–strain curve by
taking the first derivative to find the slope at that point, and the inherent
toughness of the material, or the energy absorbed by the material prior to
failure, can be accurately calculated
(Table 3). In comparative
studies both within and outside the Bivalvia the use of `true' stress and
strain is especially important, since the discrepancy between `engineering'
and `true' values is dependent on the inherent extensibility of the material
in question. For example, the methodology of the current study allows accurate
comparison, for the first time, of bivalve byssal thread and the dragline silk
of spiders – the former is more extensible, but not as stiff, strong or
tough as the latter (Swanson et al.,
2006
). Of course, if the Poisson's ratio of byssal thread
materials were to vary greatly between bivalve species, this would also
compromise comparisons; thus, we hope that these ratios will be measured by
future workers.
The correlation between life habit and thread diameter found here –
that epifaunal species have thicker threads – was not found in another
recent comparative study (Brazee and
Carrington, 2006
). One likely reason for this discrepancy is that
the M. modiolus and G. demissa specimens used in the earlier
study were larger, and the M. edulis specimens smaller, than those
used here; thus the relationship between life habit and thread size for
mussels of similar shell lengths could not be observed. Although the threads
of semi-infaunal species are thinner than those of epifaunal species, it has
been shown that M. modiolus produces many more threads than M.
edulis, especially for substrate particle sizes from 250 to 2000 mm
(Meadows and Shand, 1989
).
This relationship between life habit and thread number also seems to hold for
M. californianus and G. demissa (T.P. and M.L., personal
observation). Producing a smaller number of larger diameter threads, then, may
be beneficial for mussels with epifaunal life habits, or vice versa
for mussels with semi-infaunal life habits. Thread diameter measurements for
epifaunal Ctenoides mitis Lamarck and semi-infaunal Atrina
rigida Lightfoot support the relationship reported here between life
habit and byssal thread diameter [see accompanying paper
(Pearce and LaBarbera, 2009
)].
Because overall attachment strength is a function not just of material
properties but also of thread size and thread number, future work should
consider measuring the fraction of proteinaceous nitrogen devoted to the
byssal apparatus in different bivalves. This would indicate whether certain
species achieve a greater attachment strength with a similar investment of
resources.
There were no significant differences in material properties between the
threads of the two Mytilus species examined here, despite recent
claims that M. californianus threads are `mechanically superior' to
M. edulis threads (Carrington and
Gosline, 2004
; Harrington and
Waite, 2007
). The evidence for such claims in the literature is
slight. Bell and Gosline combined their M. californianus data with
the M. edulis data of Smeathers and Vincent, purporting to show that
both the distal and proximal regions of M. californianus threads are
significantly more extensible than those of M. edulis threads
(Smeathers and Vincent, 1979
;
Bell and Gosline, 1996
).
However, both studies used the `engineering' definitions of stress and strain
and each used a different strain rate during tensile testing; moreover,
Smeathers and Vincent only provided 10 data points on extensibility for M.
edulis, which is problematic given the high variance in thread properties
within a given species. Citing Bell and Gosline, Harrington and Waite also
claim that M. californianus threads are 2–3 times stiffer than
M. edulis threads – this is a mistake, as no stiffness values
for M. edulis threads were presented in the earlier paper
(Bell and Gosline, 1996
;
Harrington and Waite, 2007
).
Nonetheless, several differences in the sequences of the proteins making up
the distal regions of M. californianus and M. edulis threads
have recently been discovered, and thus more research is needed to determine
whether these molecular differences translate into significant differences in
thread material properties (Harrington and
Waite, 2007
). Mytilus edulis threads do seem to recover
more slowly than M. californianus threads following cyclical loading,
but the functional importance of this difference is unclear
(Carrington and Gosline, 2004
).
While M. californianus may be better adapted to wave-swept shores,
and may have a greater overall attachment strength than M. edulis,
our findings indicate that the latter is likely to be due to differences in
the number or size of threads rather than to any inherent mechanical
superiority of the material in M. californianus threads.
The stress–strain curves presented here are qualitatively similar to
those found in earlier studies. It has been suggested that homogeneous
threads, i.e. those lacking two distinct regions (proximal and distal), have
less complex stress–strain behavior
(Brazee and Carrington, 2006
).
However, there were clear yield points for almost all threads of all species
tested here, despite the fact that samples were taken only from the distal
region. The extraordinary double-yield behavior of M. modiolus
threads was consistently produced when testing only the distal portion of
threads. Although G. demissa threads did not have two clear yield
points, new results for A. rigida threads suggest that double-yield
behavior may be correlated with endobyssate life habits
(Pearce and LaBarbera, 2009
).
It would be interesting to re-examine existing molecular analyses of M.
modiolus and A. rigida threads in light of this unusual yield
pattern, which seems to imply an underlying two-phase molecular structure
(Mascolo and Waite, 1986
;
Rzepecki et al., 1991
).
Early comparative studies demonstrated that there are significant
differences in mechanical properties between the threads of different
Mytilus species (Bell and Gosline,
1996
). However, it has been suggested more recently that material
properties of mytilid threads tend to be similar across a range of life habits
and environments (Brazee and Carrington,
2006
). The data presented here confirm that there are indeed
significant mechanical differences between the threads of different mytilid
bivalves. One of the most interesting findings is that, although threads of
different species tend to differ in strength, stiffness and extensibility,
ANOVA indicates that they absorb similar amounts of energy prior to failure,
i.e. they are equally tough. One explanation for this observation may be that
species with stronger threads, e.g. M. modiolus, tend to have less
extensible threads, and toughness is a function of both strength and
extensibility. In many engineered materials, there is a trade-off between
strength or stiffness and extensibility – think of ceramics, which are
extremely stiff and strong, but are minimally extensible before failure.
Likewise, although M. edulis threads are significantly more
extensible than M. modiolus threads, the latter are significantly
stiffer. However, this trade-off between stiffness and extensibility does not
divide semi-infaunal from epifaunal species, as might be expected given the
difference in experienced fluid forces. Semi-infaunal G. demissa
threads have mechanical properties similar to those of epifaunal
Mytilus threads, apart from a lower final stiffness. Another
hypothesis for the similar toughness of all threads might simply be that
energy absorption by byssal threads is the most important variable when it
comes to attachment or predator resistance, and the different species simply
achieve this toughness via different combinations of other mechanical
properties.
Despite the fact that semi-infaunal and epifaunal species do not group
along any of the mechanical variables measured here, the two semi-infaunal
species investigated each stand out, albeit for different reasons.
Geukensia demissa threads have a significantly lower stiffness at
failure than the threads of other mytilids; moreover, for all species but
G. demissa, final stiffness was significantly greater than initial
stiffness (paired t-test, P<0.0004; paired sign test,
P<0.0001). The low strength and stiffness of threads produced by
G. demissa may be related to its habitat – it usually lives in
low intertidal peat marshes, and attaches to the stems and roots of grasses
(Stanley, 1970
). The
underground network of roots and threads, together with the peat surrounding
its shell, may enhance overall attachment strength, eliminating any selection
pressure for stronger or stiffer threads. To assess this hypothesis, one could
compare the properties of G. demissa threads with those of the
threads of Modiolus americanus Leach, which also frequently attaches
to stems and roots in seagrass meadows
(Peterson and Heck, 2001
).
This comparison would be especially interesting, as the M. modiolus
threads measured here were significantly stronger than those of G.
demissa.
Most studies of bivalve byssal threads have focused on the effect of
abiotic or biotic ecological variables on the size and number of threads
produced (Meadows and Shand,
1989
; Dolmer and Svane,
1994
; Côté,
1995
; Clarke and McMahon,
1996
; Leonard et al.,
1999
; Cheung et al.,
2006
; Moeser et al.,
2006
). Recently, however, it has been shown that thread material
properties vary with the seasons, indicating that more controlled studies
investigating the influence of ecological factors on thread biomechanics would
produce interesting results (Moeser and
Carrington, 2006
). Given recent data demonstrating significant
variation in thread properties among the Mytilidae, the time is ripe for a
systematic comparative study involving ecological, taxonomic and biomechanical
variables. A first step in this direction would involve measuring the
mechanical properties of byssal threads outside the Mytilidae, to find out
whether they suggest any evolutionary patterns (see
Pearce and LaBarbera,
2009
).
This study has illustrated the fruitfulness of comparative work in byssal thread biomechanics. There are significant differences in strength, stiffness and extensibility between different mytilid species living in different environments. Further research, following the methodology outlined here, has the potential to reveal patterns in the evolutionary history of this biomechanical variation.
| Acknowledgments |
|---|
| Footnotes |
|---|
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T. Pearce and M. LaBarbera Biomechanics of byssal threads outside the Mytilidae: Atrina rigida and Ctenoides mitis J. Exp. Biol., May 15, 2009; 212(10): 1449 - 1454. [Abstract] [Full Text] [PDF] |
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