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Biol. Lett.
doi:10.1098/rsbl.2011.0674
Published online
Palaeontology
Opinion piece
Models in palaeontological
functional analysis
Models are a principal tool of modern science. By
definition, and in practice, models are not literal
representations of reality but provide simplifications or substitutes of the events, scenarios or
behaviours that are being studied or predicted.
All models make assumptions, and palaeontological models in particular require additional
assumptions to study unobservable events in deep
time. In the case of functional analysis, the
degree of missing data associated with reconstructing musculoskeletal anatomy and neuronal control
in extinct organisms has, in the eyes of some
scientists, rendered detailed functional analysis of
fossils intractable. Such a prognosis may indeed
be realized if palaeontologists attempt to recreate
elaborate biomechanical models based on missing
data and loosely justified assumptions. Yet multiple
enabling methodologies and techniques now exist:
tools for bracketing boundaries of reality; more
rigorous consideration of soft tissues and missing
data and methods drawing on physical principles
that all organisms must adhere to. As with many
aspects of science, the utility of such biomechanical
models depends on the questions they seek to
address, and the accuracy and validity of the
models themselves.
Keywords: palaeobiology; biomechanics; function;
feeding; locomotion
1. INTRODUCTION
Biological systems are invariably complex, consisting
of multiple interdependent parameters with nonlinear
relationships. Such systems can be prohibitively difficult to replicate completely for experimental or
analytical purposes, so creating a simplified model
allows the system to be investigated more easily. By
their nature, models can also deal with uncertainty in
the parameters of a system. This is especially important to palaeontologists, who are often missing
important data (figure 1). A key advantage of modelling in palaeobiology is the ability to construct
models focusing on specific aspects of a system, holding constant or simplifying parameters which are
unknown or not of interest, and permitting sensitivity
analyses of how certain variables affect the outcome
of the model. Figure 2 outlines examples of different
model types of utility to palaeontology.
2. APPLYING MODELS IN PALAEONTOLOGY
(a) Validation
Models are simplifications of reality, so it is important
to have a strong understanding of the modelling
One contribution to a Special Feature on ‘Models in palaeontology’.
Received 1 July 2011
Accepted 3 August 2011
parameters. In palaeontology, a great deal of data
may be incomplete (such as muscles, material properties and neurological data). These issues can cause
major errors in functional analyses performed using
fossil data [5], particularly, where palaeobiologists are
attempting to perform similar mechanical analyses to
biologists [6].
Analysis of the sensitivity and the validity of models
is therefore crucial. Approaches such as calculating
moment arms of muscles [7], bending and torsion
resistance in bone [8] and the use of experimental
techniques such as wind tunnels [9] rely on the fact
that all organisms respond to similar physical principles, and such approaches have been used
successfully for many years to deduce extant organismal function. It is well known how output
parameters from these models, such as mechanical
advantage and coefficients of lift and drag, relate to
organismal performance. For computational models
such as finite-element analysis (FEA) and computational fluid dynamics (CFD), sensitivity analysis
involves modifying parameters in the model to see
how they influence results. Models can be validated
using experimental data; comparing performance in
extant taxa with a best-fit computational model. FE
skull models created with a paucity of input data can
generally reproduce patterns and orientations of bone
strain but tend to poorly estimate absolute numerical
values [10,11], yet those with more precise input
data become more accurate [12]. Unless the input parameters are confidently known, palaeontological FE
models are likely to be most useful for comparing
relative rather than absolute performance.
(b) What questions can we address with models
in palaeontology?
Palaeontological models can address questions of varying complexity at numerous hierarchical levels [6]. The
majority of studies focus on specimen-specific questions, in part owing to the time required to construct
some computational models. These studies address
‘classic’ functional questions: how hard could an
animal bite [13], how fast could it run [14] or
even how crinoids were able to support themselves in
the water column [15]. A fruitful line of enquiry is
comparative analyses of form– function, such as analysing changes in posture across therapsid groups
[16] and three-dimensional dynamic projections of
locomotion in extinct vertebrates [17]. By virtually
manipulating geometry in computer-based FE
models, researchers may make morphological changes
whose effects on model performance can be evaluated
[18]. This can involve the simple addition or removal
of features such as sutures or fenestrae in a skull [19]
or altering the morphology to mimic that of closely
related groups [20]. It is also possible to create idealized models which can be modified one parameter at
a time to explore morphospace [21]. Some workers
have used FEA to pare down a generic block of
material into a skull shape based solely on optimization
for dealing with functional stresses [22]. Similarly,
other workers have created theoretical morphospaces
encompassing all possible morphologies of a system,
then used biomechanical theory to eliminate untenable
forms until a range of possible functions remains [23].
This journal is q 2011 The Royal Society
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P. S. L. Anderson et al.
Opinion piece. Function in palaeontology
soft tissue
fluid
properties
ine
loa
eng
material
properties
ds
recon
kinematic
structural
fracture
fluid
form–structure
Figure 1. All palaeobiological models require some amount of input data. The flow chart above illustrates the relationship
between models (blue rectangles) and input parameters (red ovals). The input parameters can include aspects of the biological
organism and/or the medium the organism is interacting with. Form/structure includes body size and overall body shape
for fluid analyses. Other parameters, such as material properties or soft tissue are usually unknown, but can be assumed or
reconstructed (recon; green hexagon).
(a)
(b)
PC2pos
PC1neg
(c)
PC2neg PC1pos
(d)
(e)
max dorsal
mean
max ventral
Figure 2. Examples of models useful to palaeobiologists. (a) Structural models focus on how physical structures react to applied
loads, e.g. beam theory of jaws and limbs or more sophisticated computer-based finite-element models (here incorporated with
geometric morphometrics [1]). (b) Kinematic models focus on the movement dynamics of a biological system and involve the
transfer of force and speed through connected structures such as the feeding system of extinct fishes [2] (red lines represent
muscle lines of action). (c) Models whose primary purpose is the reconstruction of organisms from fossil data (e.g. estimation
of body mass in dinosaurs [3]). (d) Fluid models focus on how biological organisms interact with fluids, either external or
internal. These include experiments on physical models in flow tanks/wind tunnels as well as computer-based flow analyses
(C. Palmer 2011, unpublished data). (e) New techniques permit geometries to be morphed from one shape to another [4].
Parts (c) and (e) adapted from John Wiley and Sons Ltd.
These virtual modelling approaches permit user control over input variables, which can be advantageous
over traditional comparative analyses that must focus
solely on taxonomic variation.
Biol. Lett.
A more recent development uses models to derive functionally relevant measures that can be applied as data
points in large-scale palaeontological analyses. Some
recent examples include extinction selectivity across the
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Opinion piece. Function in palaeontology P. S. L. Anderson et al.
Cretaceous–Tertiary boundary (K–T) [24], functional
disparity of placoderm faunas [25], jaw diversity in the
earliest radiation of gnathostomes [26], bite force evolution in theropods [27] and morphofunctional evolution
of crocodilians [28]. In all these studies, the data are
simple biomechanical metrics but future advances will
incorporate biomechanical data from more complex
models (FEA and CFD). Here, we can study the evolution of functional diversity on a temporal scale, within
sister groups or across clades.
3. OPPORTUNITIES FOR THE FUTURE
Increases in computing capability are streamlining the
construction of palaeontological models, allowing scientists to analyse large amounts of three-dimensional
digital data in relatively short amounts of time. This presents the opportunity for larger scale comparative studies
based on sophisticated techniques like FEA or CFD and
opens the door to comparative functional analyses.
It is becoming possible to combine functional models
with other techniques to answer new questions. Geometric morphometrics can be combined with FEA,
where shape variation is analysed for variation in mechanical behaviour [1,4]. In this way, existing and hypothetical
morphologies can be assessed for their structural performance. FE models can also be linked to multibody dynamic
analyses to incorporate kinematics and muscular loads
[29]. CFD [30] has been used very little in palaeontology
yet has the potential to inform on the performance of
extinct animals in aerial and aquatic habitats as well as respiratory anatomy or pneumatization. Similarly, fracture
models [31] have not been extensively used, yet they can
aid a great deal in understanding dental evolution and
development. Phylogenetic methods offer the potential
to assess historical constraint on form–function relationships, reconstruct ancestral function and to assess
temporal and evolutionary trends in functional behaviour.
Many of the new techniques employed in palaeontological functional analysis are shifting emphasis away (i)
from a qualitative assessment of function by analogy
with morphology, and (ii) from a paradigm-based
approach [32] in which function is predicted by the
best-fit match to a selection of model systems. The
new techniques focus on quantitative analysis: models
are testable and repeatable, numerical results are generated and sensitivity analysis of parameters can be
performed. Yet aside from the perennial problem of missing data, the ‘black-box’ nature of some techniques can
be misleading and seductive as it can produce visually
impressive results with little understanding of model process or input parameters. To use this new breed of
methodologies, it is important for researchers to define
and stay focused on particular questions or hypotheses,
and to recognize the sophistication of model required
to address palaeontological questions in the full.
We thank Paul Barrett and Andrew Smith for the
opportunity to contribute to this special feature in Biology
Letters on Models in Palaeontology and three referees for
helpful comments.
Philip S. L. Anderson, Jen A. Bright, Pamela G. Gill,
Colin Palmer and Emily J. Rayfield*
Biol. Lett.
3
School of Earth Sciences, University of Bristol, Wills
Memorial Building, Queens Road, Bristol BS8 1RJ, UK
*[email protected]
1 Pierce, S. E., Angielczyk, K. D. & Rayfield, E. J. 2008
Patterns of morphospace occupation and mechanical performance in extant crocodilian skulls: a combined
geometric morphometric and finite element modelling
approach. J. Morph. 269, 840 –864. (doi:10.1002/jmor.
10627)
2 Anderson, P. S. L. & Westneat, M. W. 2007 Feeding
mechanics and bite force modelling of the skull of
Dunkleosteus terrelli, an ancient apex predator. Biol. Lett.
3, 76–79. (doi:10.1098/rsbl.2006.0569)
3 Allen, V., Paxton, H. & Hutchinson, J. R. 2009 Variation
of center of mass estimates for extant sauropsids and its
importance for reconstructing inertial properties of
extinct archosaurs. Anat. Rec. 292, 1442– 1461. (doi:10.
1002/ar.20973)
4 O’Higgins, P., Cobb, S. N., Fitton, L. C., Groning, F.,
Phillips, R., Liu, J. & Fagan, M. J. 2011 Combining geometric morphometrics and functional simulations: an
emerging toolkit for virtual functional analyses. J. Anat.
218, 3 –15. (doi:10.1111/j.1469-7580.2010.01301.x)
5 Lauder, G. V. 1995 On the inference of function from
structure. In Functional morphology in vertebrate paleontology (ed. J. J. Thomason), pp. 1 –18. Cambridge, MA:
Cambridge University Press.
6 Plotnick, R. E. & Baumiller, T. K. 2000 Invention by
evolution: functional analysis in paleobiology. Paleobiology
26, 305 –323. (doi:10.1666/0094-8373(2000)26[305:
IBEFAI]2.0.CO;2)
7 Hutchinson, J. R., Anderson, F. C., Blemker, S. S. &
Delp, S. L. 2005 Analysis of hindlimb muscle moment
arms in Tyrannosaurus rex using three-dimensional
musculoskeletal computer model: implications for
stance, gait and speed. Paleobiology 31, 676 –701.
8 Therrien, F. 2005 Feeding behaviour and bite force
of sabretoothed predators. Zoo. J. Linn. Soc. 145,
393 –426. (doi:10.1111/j.1096-3642.2005.00194.x)
9 Palmer, C. 2011 Flight in slow motion: aerodynamics of
the pterosaur wing. Proc. R. Soc. B 278, 1881 –1885.
(doi:10.1098/rspb.2010.2179)
10 Bright, J. A. & Rayfield, E. J. In press. Sensitivity and ex
vivo validation of finite element models of the domestic
pig cranium. J. Anat. (doi:10.1111/j.14690-7580.2011.
01408.x)
11 Rayfield, E. J. 2007 Finite element analysis and understanding the biomechanics and evolution of living and
fossil organisms. Ann. Rev. Earth Planet. Sci. 35, 541 –
576. (doi:10.1146/annurev.earth.35.031306.140104)
12 Strait, D. S., Wang, Q., Dechow, P. C., Ross, C. F.,
Richmond, B. G., Spencer, M. A. & Patel, B. A. 2005
Modeling elastic properties in finite element analysis: how
much precision is needed to produce an accurate model?
Anat. Rec. 238A, 275–287. (doi:10.1002/ar.a.20172)
13 Wroe, S. et al. 2008 Three-dimensional computer analysis of white shark jaw mechanics: how hard can a great
white bite? J. Zool. 276, 336– 342. (doi:10.1111/j.14697998.2008.00494.x)
14 Hutchinson, J. R. & Garcia, M. 2002 Tyrannosaurus was
not a fast runner. Nature 415, 1018–1021. (doi:10.1038/
4151018a)
15 Donovan, S. K., Kallmeyer, J. W. & Veltkamp, C. J. 1995
Functional morphologies of the columns of Upper Ordovician Xenocrinus and Dendrocrinus. Lethaia 28, 309–315.
(doi:10.1111/j.1502-3931.1995.tb01820.x)
16 Blob, R. W. 2001 Evolution of hindlimb posture in nonmammalian therapsids: biomechanical tests of paleontological
Downloaded from http://rsbl.royalsocietypublishing.org/ on June 18, 2017
4
17
18
19
20
21
22
23
24
P. S. L. Anderson et al.
Opinion piece. Function in palaeontology
hypotheses. Paleobiology 27, 14–38. (doi:10.1666/00948373(2001)027,0014:EOHPIN.2.0.CO;2)
Sellers, W. I., Manning, P. L., Lyson, T., Stevens, K. &
Margetts, L. 2009 Virtual palaeontology: gait reconstruction of extinct vertebrates using high performance
computing. Palaeont. Electronic. 12, 26p. (http://palaeoelectronica.org/2009_3/180/index.html).
Rayfield, E. J., Norman, D. B., Horner, C. C., Horner,
J. R., Smith, P. M., Thomason, J. J. & Upchurch, P.
2001 Cranial design and function in a large theropod dinosaur. Nature 409, 1033–1037. (doi:10.1038/35059070)
Rayfield, E. J. & Milner, A. C. 2008 Establishing a framework for archosaur cranial mechanics. Paleobiology 34,
494 –515. (doi:10.1666/07006.1)
Stayton, C. T. 2009 Application of thin-plate spline
transformations to finite element models, or, how to
turn a bog turtle into a spotted turtle to analyze both.
Evolution 63, 1348–1355. (doi:10.1111/j.1558-5646.
2009.00655.x)
Anderson, P. S. L., Gill, P. G. & Rayfield, E. J. 2011
Modeling the effects of cingula structure on strain patterns and potential fracture in tooth enamel. J. Morph.
272, 50–65. (doi:10.1002/jmor.10896)
Witzel, U. & Preuschoft, H. 2005 Finite-element model
construction for the virtual synthesis of the skulls in
vertebrate: case study of Diplodocus. Anat. Rec. A 283,
391 –401. (doi:10.1002/ar.a.20174)
Gatesy, S. M., Baker, M. & Hutchinson, J. R. 2009 Constraint-based exclusion of limb poses for reconstructing
theropod dinosaur locomotion. J. Vert. Paleont. 29,
535 –544. (doi:10.1671/039.029.0213)
Friedman, M. 2009 Ecomorphological selectivity among
marine teleost fishes during the end-Cretaceous
Biol. Lett.
25
26
27
28
29
30
31
32
extinction. Proc. Natl Acad. Sci. USA 106, 5218–5223.
(doi:10.1073/pnas.0808468106)
Anderson, P. S. L. 2009 Biomechanics, functional patterns, and disparity in Late Devonian arthrodires.
Paleobiology 35, 321 –342. (doi:10.1666/0094-8373-35.
3.321)
Anderson, P. S. L., Friedman, M., Brazeau, M. D. &
Rayfield, E. J. In press. Initial radiation of jaws demonstrated stability despite faunal and environmental
change. Nature. (doi:10.1038/nature10207)
Sakamoto, M. 2010 Jaw biomechanics and the evolution
of biting performance in theropod dinosaurs.
Proc. R. Soc. B. 277, 3327– 3333. (doi:10.1098/rspb.
2010.0794)
Pierce, S. E., Angielczyk, K. D. & Rayfield, E. J. 2009
Shape and mechanics in thalattosuchian (Crocodylomorpha) skulls: implications for feeding behavior and niche
partitioning. J. Anat. 215, 555– 576. (doi:10.1111/j.
1469-7580.2009.01137.x)
Curtis, N. 2011 Craniofacial biomechanics: an overview
of recent multibody modelling studies. J. Anat. 218,
16–25. (doi:10.1111/j.1469-7580.2010.01317.x)
Rigby, S. & Tabor, G. 2006 The use of computational
fluid dynamics in reconstructing the hydrodynamic properties of graptolites. GFF 128, 189–194. (doi:10.
1080/11035890601282189)
Anderson, P. S. L. & LaBarbera, M. 2008 Functional
consequences of tooth design: effects of blade shape on
energetics of cutting. J. Exp. Biol. 211, 3619–3626.
(doi:10.1242/jeb.020586)
Rudwick, M. J. S. 1964 The inference of function from
structure in fossils. Br. J. Phil. Sci. 15, 27– 40. (doi:10.
1093/bjps/XV.57.27)