Case 1 How large was Pegasus?
Learning goals:
What is allometry?
o Formulas lecture
Allometry: Relative growth, how do proportions of the body scale with body size?
Describes how the characteristics of living creatures change with size
Isometric growth: All body parts grow at approximately the same rate, and the adult
proportions are not significantly different from those of the juvenile.
Example: arms
Allometric growth: body parts do not grow at the same rate, therefore the
proportions of an adult and juvenile will be significantly different.
Example: the head, brain
Formulas
o Allometric equation: y = a*xb
y is the parameter measured in relation to the size of the organism
x is the measure of size used as the basis for comparison,
often a measure of whole body size
a initial growth index (size of y when x = 1)
b scaling exponent (proportional change in y per unit of x)
o The scaling exponent (b)
Defines the type of scaling relationship
If b = 1 ➝isometry: no differential growth
the relative size of y to x is the same for all values of x
If b < 1 ➝negative allometry:
as x increases, y becomes relatively smaller
If b > 1 ➝positive allometry:
as x increases, y becomes relatively larger
This is true only when we compare like dimensions (mass to mass, length to
length)
o Isometry for different dimensions
Example: Head Length vs. Body Length
Linear dimension (m1) vs. linear dimension (m1)
Isometry: m1/m1, b = 1/1 = 1.0
Example: Head Length vs. Body Mass
Linear Dimension (m1) vs. Cubic Dimension (m3)
Isometry: m1/m3, b = 1/3 = 0.33
Example: Surface Area vs. Body Mass
Square Dimension (m2) vs. Cubic Dimension (m3)
Isometry: m2/m3, b = 2/3 = 0.67
o Log transformation
, y is the parameter measured in relation to the size of the organism
x is the measure of size used as the basis for comparison,
often a measure of whole body size
a initial growth index (size of y when x = 1) (intercept)
b scaling exponent (proportional change in y per unit of x) (slope)
o Limit of allometry
Allometric equations express convenient and valuable generalizations.
However,
there are important limits where they can and can't be used, the following
points should be remembered;
Allometric equations are descriptive; they are not biological laws.
Allometric equations are useful for showing how a variable quantity is
related to body size, all other things being equal (which most certainly
they are not).
Allometric equations are valuable tools because they may reveal
principles and connections that otherwise remain obscure.
Allometric equations are useful as a basis for comparisons and can
reveal deviations from a general pattern. Such deviations may be due
to "noise" or may reveal a significant secondary signal.
Allometric equations are useful for estimating an expected magnitude
for some variable, an organ or a function, for a given body size.
Allometric equations cannot be used for extrapolations beyond the
range of the data on which they are based
What are standard body proportions in animals, look at mammals/birds? (heart, liver,
length of bones, bodyweight, heart rate, blood pressure, etc.)
Weight of organs
The bigger the animal, the smaller the percentage of the organ
- The relative sizes of some highly active organs decreases with increasing
body size:
o In a mouse, the liver is 6% of the body mass
o In an elephant, the liver is about 1.6% of the body mass.
→The kidney, brain and liver decrease in relative size with increasing body
size
- Liver: mitochondria density decreases with increasing body size
→ The heart, lungs and skeletal muscle maintain their relative sizes
unchanged.
- The heart is relatively larger for birds
As heart rate decreases, the life expectancy in mammals increases
o Scaling of CV system
Blood pressure, RBC size, hematocrit → size independent
Frequency, cardiac output → size dependent
Active human 220 bmp, in mouse 750 bmp→ increase in heart
rate very different
Larger animals have a lower metabolic rate, but this cannot be explained by the
decreases in
the relative sizes of the metabolically
most active organs.
Two major theories:
Learning goals:
What is allometry?
o Formulas lecture
Allometry: Relative growth, how do proportions of the body scale with body size?
Describes how the characteristics of living creatures change with size
Isometric growth: All body parts grow at approximately the same rate, and the adult
proportions are not significantly different from those of the juvenile.
Example: arms
Allometric growth: body parts do not grow at the same rate, therefore the
proportions of an adult and juvenile will be significantly different.
Example: the head, brain
Formulas
o Allometric equation: y = a*xb
y is the parameter measured in relation to the size of the organism
x is the measure of size used as the basis for comparison,
often a measure of whole body size
a initial growth index (size of y when x = 1)
b scaling exponent (proportional change in y per unit of x)
o The scaling exponent (b)
Defines the type of scaling relationship
If b = 1 ➝isometry: no differential growth
the relative size of y to x is the same for all values of x
If b < 1 ➝negative allometry:
as x increases, y becomes relatively smaller
If b > 1 ➝positive allometry:
as x increases, y becomes relatively larger
This is true only when we compare like dimensions (mass to mass, length to
length)
o Isometry for different dimensions
Example: Head Length vs. Body Length
Linear dimension (m1) vs. linear dimension (m1)
Isometry: m1/m1, b = 1/1 = 1.0
Example: Head Length vs. Body Mass
Linear Dimension (m1) vs. Cubic Dimension (m3)
Isometry: m1/m3, b = 1/3 = 0.33
Example: Surface Area vs. Body Mass
Square Dimension (m2) vs. Cubic Dimension (m3)
Isometry: m2/m3, b = 2/3 = 0.67
o Log transformation
, y is the parameter measured in relation to the size of the organism
x is the measure of size used as the basis for comparison,
often a measure of whole body size
a initial growth index (size of y when x = 1) (intercept)
b scaling exponent (proportional change in y per unit of x) (slope)
o Limit of allometry
Allometric equations express convenient and valuable generalizations.
However,
there are important limits where they can and can't be used, the following
points should be remembered;
Allometric equations are descriptive; they are not biological laws.
Allometric equations are useful for showing how a variable quantity is
related to body size, all other things being equal (which most certainly
they are not).
Allometric equations are valuable tools because they may reveal
principles and connections that otherwise remain obscure.
Allometric equations are useful as a basis for comparisons and can
reveal deviations from a general pattern. Such deviations may be due
to "noise" or may reveal a significant secondary signal.
Allometric equations are useful for estimating an expected magnitude
for some variable, an organ or a function, for a given body size.
Allometric equations cannot be used for extrapolations beyond the
range of the data on which they are based
What are standard body proportions in animals, look at mammals/birds? (heart, liver,
length of bones, bodyweight, heart rate, blood pressure, etc.)
Weight of organs
The bigger the animal, the smaller the percentage of the organ
- The relative sizes of some highly active organs decreases with increasing
body size:
o In a mouse, the liver is 6% of the body mass
o In an elephant, the liver is about 1.6% of the body mass.
→The kidney, brain and liver decrease in relative size with increasing body
size
- Liver: mitochondria density decreases with increasing body size
→ The heart, lungs and skeletal muscle maintain their relative sizes
unchanged.
- The heart is relatively larger for birds
As heart rate decreases, the life expectancy in mammals increases
o Scaling of CV system
Blood pressure, RBC size, hematocrit → size independent
Frequency, cardiac output → size dependent
Active human 220 bmp, in mouse 750 bmp→ increase in heart
rate very different
Larger animals have a lower metabolic rate, but this cannot be explained by the
decreases in
the relative sizes of the metabolically
most active organs.
Two major theories:
