ZOOL 30010 Functional Morphology

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ZOOL 30010 - Functional Morphology Lectures
Tuesday 10.00-10.50 Thursday
10.00-10.50 Practicals Thursday 15.00-17.00
(start week 24th) Assessment exam (60), pracs
(30), comp (10) Gareth Dyke Room
103A gareth.dyke_at_ucd.ie Lecture slides
http//www.ucd.ie/zoology/lecturenotes/index.html
Course Text Pough et al. (1999) Vertebrate
Life Recommended Reading (for various chunks) -
I will provide references and handouts Young
(1984) The Life of Vertebrates Hildebrand (1985)
Functional Vertebrate Morphology, Harvard Uni.
Press.
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Other locations for cancellous bone short
bone, like carpals, tarsals and vertebral centra
are thin capsules of compact bone filled with
cancellous bone trabeculae can have obvious
orientation (e.g., human centra - arranged
longitudinally) this corresponds to the
direction in which they are loaded in
compression can also occur as a sandwich
between two other sheets of bone skull roof,
scapula stiffen and keep plates of bone
apart also function to resist shear no
clear orientation of trabeculae cf. plastic
foam packing areas where muscles attach to
bone are often formed as raised ridges often
filled with cancellous bone line of action
(pull) of a muscle often has a constant
relationship with bone so trabeculae beneath
insertion will have particular orientation
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Measuring loads in structures engineers to do
measure stresses in structures directly use
strain caused by stresses to indirectly measure
stress strain gauge stresses can be deduced
given the Youngs Modulus of a material E
stress/strain hence, stress strain.E remember
that force applied to a structure (whether
compressive or tensile is expressed as force/area
- this is referred to as stress because stress
is proportional to stress, stress/strain
constant this is referred to as Youngs Modulus
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More examples - the internal structure of some
vertebrate long bones
Apatosaurus
horse
pelican
compromising load bearing with lifestyle
reflected in internal structure of cancellous bone
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skeletons as engineering structures
skeletons as columns and beams stresses in
beams I-beams, box beams and tubes why are
tubes stonger than rods? buckling (Euler
Buckling) Poissons Ratio and effect on bone
strength how bones are loaded - graviportal
vs. cursorial animals cancellous bone
stress trajectories and bone structure
trabecular bone at articular surfaces other
locations for cancellous bone in skeletons
measuring loads in structures
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What happens when things get bigger? Scaling and
allometry scaling is a fundamental technique
in functional morphology terrestrial animals
rely on their legs and flying animals on their
wings in order to support the weight of their
bodies (especially during movement) we will
discuss flight in later lectures contrast
this with fishes and other aquatic animals that
operate in a medium where they are able to rely
on bouyancy how do the muscles and skeletons
of non-aquatic vertebrates perform in order to
support function?
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Body support in vertebrates any general
discussion of body support in vertebrates must
take into account differences in overall body
size Pigmy shrews (Sorex minutus) have a body
mass around 3 g African elephants (Loxodontia
africana) are about a million times heavier,
with masses in the area of 3 tons imagine if a
shrew were enlarged to 100 times its linear
dimensions but without any change of shape -
the shrew would be 100 times longer, 100 times
wider and 100 times higher, but its body volume
would be increased by a factor of 1 million
(1003) if the densities of the parts of the
shrew remained unchanged then it would be as
heavy as the elephant but the areas (and hence
the strengths) of the bones and muscles would
be increased only by 10,000 (1002). how would
the shrew be able to stand?
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To put this another way . .. how are
elephants possible?
. what about sauropod dinosaurs?
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The answer is simple . that is that elephants
are not simply scaled up shrews some linear
proportions are more than 100 times those of a
shrew, while others are less imagine scaled
photographs differences in stance - elephants
are graviportal - they stand with their legs
straight and are not very agile these
differences are referred to as scale effects
those that can be related to differences in body
size or proportions the rest of this lecture
is about scaling problems associated with body
support, and the compromises that have to be made
as size increases
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This dates back to Galileo
Galileo begins his book "Two New Sciences" with
the striking observation that if two ships, one
large and one small, have identical proportions
and are constructed of the same materials, so
that one is purely a scaled up version of the
other in every respect, nevertheless the larger
one will require proportionately more
scaffolding and support on launching to prevent
its breaking apart under its own weight. He goes
on to point out that similar considerations apply
to animals, the larger ones being more
vulnerable to stress from their own weight (page
4)
born Pisa, Italy in 1564
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Theories of scaling generally produce
equations in the form y axb where x and
y are dimensions of other quantitative properties
of animals of different sizes and where a and b
are constants this relationship was already
hinted at in discussions of 1003 and 1002 and
the scaling of the shrew scientists who have
made measurements on related animals of
different sizes have most often found that
results are described accurately by equations
such as d 5.2m0.36 where d is
femur diameter (in mm) of mammals of different
masses (m) this is an allometric
equation
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Allometric scaling equations one of the
properties of an allometric equation is that it
will give a straight line when plotted on
logarithmic coordinates you can show that this
must be the case y axb log y
log (axb) log a b log x hence a graph of log
y against log x will produce a straight line of
slope b but remember (and the math is not
important to the concept) the equations
present summaries of relationships we can
always find relationships that dont fit this
simple relationship (e.g., wing areas of auks
and puffins) equations are biologically
useless - these provide us with starting points
for experiments, analyses only
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Scaling is a mathematical trick . . it is
actually a numerical formulation of similarity,
which is a real biological concept biological
similarity - consider birds and insects
damselfly
hummingbird
birds and insects are very different, but
similar because they are constrained by
physical forces, and the properties of these
forces
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Constraining similarity MATERIAL similarity -
better than humans can produce - materials
used in the same way - constrained by physical
forces ENVIRONMENTAL PROPERTIES - all
flying animals in same medium - low density
how heavy? - viscous medium how much
friction? PHYLOGENY - all birds have a common
ancestor - their morphologies will reflect
this - evolution is limited by this
PHYSIOLOGY - all birds have same muscles, same
properties - efficient flight depends on
energy supply - similarities in the way that
food is gathered
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The Berlin Archaeopteryx
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Consensus phylogeny of the origin of birds and
the evolution of flight adaptations
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a Archaeopteryx 1.16b chicken Gallus gallus
1.09c carrion crow Corvus corone 0.86d swift
Apus apus 0.48e crane Grus grus 0.90f
albatross Diomedea sp. 1.02
Wing skeletons and flight morphology in birds
(from Böker 1927, 1935)
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Worked example of scaling relationship
deriving a similarity equation this one common
to many text books consider two cows, that have
the same shape
(measured this one!)
KL
L
all dimensions constant multiples assume
linear dimension ratio K
there are some questions we cant ask - how fast
did they move? but we can predict things like
area (A) and volume (V) this is geometric
similarity
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And heres the sums .. area A K2 volume
V K3 if the big cow is twice the size of the
small allow for x2 size x depth each unit
volume in the little will be 8 times volume in
big hence if we double the linear size between
the cows, we must x8 the volume therefore, we
can derive V ? L3 we know that mass
volume x density (assume that density is
uniform) V ? M ? L3
L ? M1/3 hence A ? M2/3
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What does it mean? just like the first
equation I showed you y
axb A ? M2/3 (i.e., the
relationship between area A and mass M) is a
similarity equation this time derived from two
simple assumptions of shape and density you
will see this relationship in the practical
variables of size scale mass 2/3 vs. areas
(lengths) 1/3 - gradients on graphs
experimental data will tell us whether animals
actually conform to these simple
relationships if not then why? one
assumption, as the case in albatross and bird
wing shape why?
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Unpredictable wing shape in some birds
tropicbird
wandering albatrosses
most gliding/soaring birds have wide, rounded
wings albatrosses have long pointed wings
related to amount of time spent in the air
dealing with high wind speed, southern ocean
this shape not predicted by simple scaling
relationships
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Usually a very predictable relationship
Arm wing skeletons in birdshummingbird (top)
with very low BI, and pelican (bottom) with BI
1(from Steinbacher 1960)
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Some points about scaling equations units
must be constant units must match across ?,
hence this constant of proportionality has
units i.e, A M2/3 would be
incorrect (units dont match) always given in
SI units most fundamental of which are mass,
length and time (MLT) these must balance in any
equation when they balance out, you have a
dimensionless equation e.g., aspect ratio in
birds wing shape measure tell us what
should be constant regardless of size
calculator for tommorrow - gradients of graphs
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Lecture 4 - scaling and allometry body
support in vertebrates theories of scaling
allometric scaling equations constraining
similarity worked example scaling cows
unpredictable shapes bird wings conventions
of scaling equations