Transcript Slide 1

What’s the worlds largest known
living organism?
Largest Living Animal?
Blue whale = 100 tons
108 g
1010 g
Largest Organism:
sequoia at 4,000 tons
Smallest?
Mycoplasma weighs < 0.1 pg
10 -13 g
What about the largest terrestrial animals?
Currently: the elephant, at about 5 tons.
106 g
Historically: Largest dinosaur:
Seismosaurus, topping out at about
80 tons.
108 g
Historically: Largest Mammal:
Baluchitherium, a relative of the
modern rhinoceros, ~30 tons
107 g
The full size range (extant)
< 0.1 pg
< 10 -13 g
Average bacterium
0.1 ng
10 -10 g
Large amoeba
0.1 mg
10 -4 g
Bee
100 mg
10 -1 g
Hamster
100 g
10 2 g
Human
100 kg
10 5 g
Mycoplasma
Elephant
Blue Whale
Sequoia
5,000 kg (5 tons)
100 tons
5000 tons
5 x 10 6 g
10 8 g
10 10 g
Scaling: structural and functional consequences of change in
size among otherwise similar organisms.
Three basic ways that organisms can change with size:
1. Dimensions
2. Materials used
3. Design
1. Dimensions
Side view of
brick wall
Can you just make
the wall taller?
Does this happen in animals?
Must be WIDER as well
1. Dimensions
% of body mass
that is skeleton
Sorex
(shrew)
3.8%
Human
18.8%
elephant
27%
2. Materials used
brick
hydrostatic support/exoskeleton
steel
bone support
3. Design
Long bridge
Short bridge
Tensile support, steel
Compressive support, stone
Oxygen Delivery—design changes with size
Unicellular organism
0.1 mm = 5 sec
Diffusion Problem!:
Time to diffuse is proportional
to the square of the distance
1 mm = 500 sec
Diffusion
10 cm =~ 55 days
Long bridge
Short bridge
3. Design
Compressive support, stone
Tensile support, steel
Oxygen Delivery—design changes with size
Unicellular organism
Insect
Vertebrate
• bulk flow delivery
Diffusion through air via
tracheal system
Diffusion
• hemoglobin
increases oxygen
in blood
Scaling: structural and functional consequences of change in
size among otherwise similar organisms.
Three basic ways that organisms can change with size:
1. Dimensions
2. Materials used
3. Design
Let’s look at this graphically…
Scaling Relationships
Physiological parameter
of interest
Y = a Xb
A “power” function
Body Mass (M)
Scaling Relationships
Physiological parameter
of interest
Y = a Mb
A “power” function
a = proportionality constant
b = scaling exponent (describes strength
and direction of the effect of mass on Y)
Body Mass (M)
Scaling Relationships
Physiological parameter of
interest
Y = a Mb
If it scaled in constant proportion…
…then b would = 1
This would be an ‘isometric’ relationship
But, this is not usually the case
…for example:
Body Mass (M)
8. BODY SIZE affects MR
 “Whole animal” O2
consumption
 “Mass-specific” O2
consumption
How does whole animal O2 consumption
scale with body size?
Whole animal O2
consumption (mlO2/hr)
Y=a
Mb
• O2 consumption increases with body
mass in a regular way
• but not in constant proportion
b = 0.75
Body Mass (M)
• allow for huge range of body sizes
•generate a straight line
•slope of line = b
b = 0.75
Body mass
Log E
O2 consumption (E)
Physiologists often use log-log plots
log Body mass
Y-intercept
E = a Mb
slope
log E = log a + b log M
How does mass-specific O2 consumption
scale with body size?
(02 consumption per
gram of tissue)
Mass-specific MR
Y = a Mb
Log O2/g*hr
Take log:
So b = -0.25
Slope = -0.25
log Body mass
b:
describes relationship of X to Y as Y gets bigger
If b = 0
If 0 < b < 1
If b = 1
b = 0.75
No relationship
e.g. [hemoglobin]
Isometric relationship
e.g., blood volume in mammals
-constant fraction of body mass
If b > 1
e.g. whole animal metabolic
rate
If b < 0
b = -0.25
e.g., bone thickness
e.g., mass specific
metabolic rate
Scaling Summary
• organisms cover 21 orders of magnitude in size
• Processes can scale by changing:
– Dimension
– Materials
– design
• Scaling relationships tend to fit a power function
– Y = aXb
– a = proportionality constant
– B = scaling exponent (!!!Very informative!!!)
• Two examples:
– Whole animal metabolic rate
– Mass-specific metabolic rate
• How does changing b describe X:Y relationship?
7
Surface area
6
The actual equation for surface
area as a function of volume is
5
4
3
2
SA = 6 V2/3
1
0
0
0.5
1
1.5
Volume
Take the log of both sides
Log(SA) = Log(6 V2/3)
= Log(6) + 2/3 * Log(V)
Log(Surface area)
1
y = 0.67x + 0.7782
0.5
0
-0.5
-1
-1.5
-2
-5
-4
-3
-2
Log(Volume)
-1
0
Real organisms usually are not isometric. Rather, certain proportions
change in a regular fashion. Such non-isometric scaling is called
allometric scaling.
An amazing number of biological variables can be described by
the allometric equation:
y = a • xb
Take log of both sides to get:
Log(y) = Log(a) • b Log(x)
The key coefficient—the scaling exponent
What the scaling exponent, b, means.
Slope = 1
Log y
Ex. The cost of apples
rises ‘isometrically’ with
the mass bought.
Log x
Log y
Slope = 1.08
Log x
Ex. Skeleton mass of
mammals rises faster than
body mass. Large mammals
have disproportionately large
skeletons.
Slope = 0.75
Log y
Ex. Metabolic rate
rises with body mass, but
less than proportionately.
Log x
Slope = 0
Log y
Ex. Hematocrit in
mammals is independent
of body mass.
Log x
Slope = -0.25
Log y
Ex. Heart rate in mammals
decreases with body mass.
Log x
120
2.5
b=1
2
1
b = 0.75
b = 0.6
0.5
Y
1.5
Log y
b=1
100
0
80
60
40
b = 0.75
-0.5
20
b = 0.6
-1
0
-1.5
-1.5
-1
-0.5
0
0.5
Log x
1
1.5
2
2.5
0
20
40
60
X
80
100
120
= 65 mya
Mammals diversified
in the Cretaceous,
between 144 and 65 mya
Artist rendition of early mammal
Dinosaurs disappear here
(except for lineage leading
to birds).
Fish and Reptiles
Mammals and Birds
Primates
From Jerison 1969
Reptiles
Mammals
From Jerison 1969
2. Anatosaurus
1. Allosaurus
5. Diplodocus
3. Brachiosaurus
6. Iguanodon
4. Camptosaurus
7. protoceratops
8. Stegasaurus
9. Triceratops
10. Tyrannosaurus
But wait a second…
What if dinosaurs were endothermic?
•
Dinosaur trackways reveal that dinosaurs may
have been able to travel up to 27 mph…
•
Some large dinosaurs had erect posture and a
vertical distance between the heart and head to
require a high blood pressure, like the giraffe.
•
Where do we draw the line between ectothermic
dinosaurs and endothermic ancestors to birds?
•
Dinosaur bone is more similar to mammalian or
avian (bird) bone in cross section than it is to
typical ectothermic "reptilian" bone
Using allometry.
Example 1: A pressing question: were dinosaurs stupid?
Mammals diversified
in the Cretaceous,
between 144 and 65 mya
= 65 mya
Dinosaurs disappear here
(except for lineage leading
to birds).
From Jerison 1969
Brain cast of
fossil dinosaur
From Jerison 1969
Megaloceros
giganteus
Stood 2.1 m
tall
Went extinct
10,600 years
ago
Found across
Eurasia
Most of dots represent extant
species of deer
Irish elk
Maximum length of antler
Two species of moose
Antler length = 0.064 * Shoulder height1.68
Height of shoulder
Gould 1974
But, not the last word on Irish Elk?
*New study by Moen et al 1999: what about
nutrient requirements?
*Irish elk antlers weighing 40 kg at the end of
velvet shedding would have contained 2.1 kg
nitrogen, 7.6 kg calcium and 3.8 kg phosphorus.
*to grow 40 kg antlers in 150 days, need: 7.6 kg
calcium, 3.8 kg phosphorous (60 g calcium and
30 g phosphorous per day)
*In the model, 6% of calcium, 10% of
phosphorous taken from skeleton because dietary
intake of minerals insufficient to meet
requirements of antler mineralization
*climate change!!!
Example 2: Big antlers on Irish Elk—10 – 12 feet across!
This species went extinct in Ireland about 10,000 years ago. Two outstanding
questions: Why the enormous antlers? And why did they go extinct?
Most of dots represent extant
species of deer
Irish elk
Maximum length of antler
Two species of moose
Antler length = 0.064 * Shoulder height1.68
Height of shoulder
From Gould 1974
Two classes of explanations
1. The allometric relationship itself ‘explains’ the large antlers of
of Irish elk. Can only be true if strong physiological constraint.
2. Increasingly strong selection for large antlers in larger species.
Rutting moose