albatross

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albatross
D. Exulans -- up to 12 kG and 3.6 m wingspan
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Hummingbird
Bee hummingbird Mellisuga helena 0.6 g and 0.06 m
wingspan
Source http//www.birdlife.org/images/sized/450/b
_bee_hummingbird.jpg.jpg
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How do we understand the effects of differences
in size on the structures and processes of
organisms?
In the previous two slides, body mass differed
by 12,000/0.6 2000X This is over 3 orders of
magnitude!
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Scaling

• A technique for determining how two phenotypic
  variables change with respect to each other.

• The variables can be morphological or process.

• Most useful when the variables are considered
  over wide ranges of values.

• Therefore, useful in answering large scale
  questions about biological design.

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Isometric and Allometric Scaling
When two variables have a linear relationship
with respect to each other, we say that they
scale isometrically. With respect to size this
means that they are scale models of each other.
However, if the relationship is non-linear it
means that the two organisms are not exact scale
models of each other with respect to the
variables of interest. We call this allometric
scaling.
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Graphically
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Equations
Generalized power function Y mXa b
Isometric -- if similarity is maintained, a
1 Y mX1.0 b
Allometric -- here a has any value not close to
1.0 Y mXa b
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Double log Plots of Scaling Relationships
log(Y) slope log(X) log (y-intercept) log(Y)
b log(X) log(a)
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Metabolism and Body Size
Isometric log(Q) 1.0log(M) log(a)
Allometric -- many possible versions
differentiated from each other by their value of
the coefficient of log(M).
Lets use one that presupposes that metabolism is
constrained by surface area. Why SA?
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Derivation of a SA Model Where SA is Expressed in
Terms of Mass (volume)0.67
Volume ? L3 or V k1L3 L ? V0.334
or L k1 V0.334 Volume1.0 ?
Mass1.0 or V1.0 k2 M1.0 L ? M0.334
or L k3 M0.334 SA ? L2
or SA k3L2 SA ? (M0.334)2 or
SA k4 M0.67
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Double Log Plots of the Models
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Hemmingsen
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Explanations
Compromise between need to maintain a per unit
tissue metabolic rate and the surface constraint.
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What happens to the metabolism of a unit mass of
tissue with change in size?
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Given the Allometry, How Is it Best To Compare
Animals to See if they Conform to the Allometry?
See how close they come to overall regression
expected
Divide metabolic rate by mass raised to the
expected scaling coefficient for the group --
thus, for most groups, divide by M0.75 or the
known exponent for that group (known to the
extent that different animals have been measured)