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What’s the worlds largest knownliving organism?
Smallest?
Blue whale = 100 tons108 g
Mycoplasma weighs < 0.1 pg10 -13 g
Largest Organism: sequoia at 4,000 tons
1010 g
Largest Living Animal?
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)
Mycoplasma < 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
Elephant 5,000 kg (5 tons) 5 x 10 6 g
Blue Whale 100 tons 10 8 g
Sequoia 5000 tons 10 10 g
Scaling: structural and functional consequences of change insize among otherwise similar organisms.
Three basic ways that organisms can change with size:
1. Dimensions2. Materials used
3. Design
1. Dimensions
Side view ofbrick wall
Does this happen in animals?
Can you just make the wall taller?
Must be WIDER as well
% of body mass that is skeleton
3.8%Sorex(shrew)
18.8%
27%elephant
1. Dimensions
Human
2. Materials used
brick steel
hydrostatic support/exoskeleton bone support
Compressive support, stone
3. DesignShort bridge Long bridge
Tensile support, steel
Oxygen Delivery—design changes with size
Unicellular organism
Diffusion
Diffusion Problem!: Time to diffuse is proportional to the square of the distance
0.1 mm = 5 sec
1 mm =
10 cm =
500 sec
~ 55 days
Compressive support, stone
3. Design Short bridge Long bridge
Tensile support, steel
Oxygen Delivery—design changes with size
Unicellular organism
Diffusion
Insect
Diffusion through air via tracheal system
Vertebrate
• bulk flow delivery
• hemoglobin increases oxygen in blood
Scaling: structural and functional consequences of change insize among otherwise similar organisms.
Three basic ways that organisms can change with size:
1. Dimensions2. Materials used
3. Design
Let’s look at this graphically…
Scaling Relationships
Y = a Xb A “power” function
Body Mass (M)
Ph
ysi
olo
gic
al
para
mete
r of
inte
rest
Scaling Relationships
Y = a Mb A “power” function
Body Mass (M)
Ph
ysi
olo
gic
al
para
mete
r of
inte
rest
a = proportionality constant
b = scaling exponent (describes strength and direction of the effect of mass on Y)
Y = a Mb
Body Mass (M)
Ph
ysi
olo
gic
al p
ara
mete
r of
inte
rest
If it scaled in constant proportion…
…then b would = 1
But, this is not usually the case…for example:
This would be an ‘isometric’ relationship
Scaling Relationships
8. BODY SIZE affects MR
“Whole animal” O2 consumption
“Mass-specific” O2 consumption
How does whole animal O2 consumption scale with body size?
Y = a Mb
b = 0.75
• O2 consumption increases with body mass in a regular way
• but not in constant proportion
Body Mass (M)
Wh
ole
anim
al O
2
con
sum
pti
on
(m
lO2
/hr)
Physiologists often use log-log plots
log Body mass
Log
E
log E = log a + b log ME = a Mb
O2 c
on
sum
pti
on
(E)
Body mass
b = 0.75
• allow for huge range of body sizes • generate a straight line• slope of line = b
slopeY-intercept
slope = 0.75
Mass-specific MR
How does mass-specific O2 consumption scale with body size?
(02 consumption per gram of tissue)
Y = a Mb
Take log:
log Body mass
Log O
2/g
*hr
Slope = -0.25
So b = -0.25
b: describes relationship of X to Y as Y gets bigger
If b = 0 If b = 1 If 0 < b < 1
If b > 1 If b < 0
Isometric relationshipe.g., blood volume in mammals-constant fraction of body mass
No relationshipe.g. [hemoglobin]
e.g. whole animal metabolicrate
b = 0.75
e.g., bone thickness e.g., mass specificmetabolic rate
b = -0.25
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?
The actual equation for surface area as a function of volume is
SA = 6 V2/3
0 0.2 0.4 0.6 0.8 1 1.20
1
2
3
4
5
6
7
Volume
Su
rfac
e ar
ea
Take the log of both sides
Log(SA) = Log(6 V2/3)
= Log(6) + 2/3 * Log(V)
-4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0-2
-1.5
-1
-0.5
0
0.5
1
f(x) = 0.670000000000001 x + 0.778151250383644
Log(Volume)
Lo
g(S
urf
ace
area
)
Real organisms usually are not isometric. Rather, certain proportionschange in a regular fashion. Such non-isometric scaling is calledallometric scaling.
An amazing number of biological variables can be described bythe 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.
Log x
Log
y
Slope = 1Ex. The cost of applesrises ‘isometrically’ with the mass bought.
Log x
Log
y
Slope = 1.08Ex. Skeleton mass of mammals rises faster thanbody mass. Large mammalshave disproportionately largeskeletons.
Log x
Log
y
Slope = 0.75Ex. Metabolic raterises with body mass, butless than proportionately.
Log x
Log
y
Slope = 0Ex. Hematocrit inmammals is independentof body mass.
Log x
Log
y
Slope = -0.25Ex. Heart rate in mammalsdecreases with body mass.
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Log x
Lo
g y
0 20 40 60 80 100 1200
20
40
60
80
100
120
XY
b = 1
b = 0.6
b = 0.75
b = 1
b = 0.6
b = 0.75
Dinosaurs disappear here(except for lineage leadingto birds).
= 65 mya
Mammals diversifiedin the Cretaceous,between 144 and 65 mya
Artist rendition of early mammal
From Jerison 1969
Fish and Reptiles
Mammals and BirdsPrimates
From Jerison 1969
Reptiles
Mammals
1. Allosaurus
5. Diplodocus
3. Brachiosaurus
2. Anatosaurus
9. Triceratops10. Tyrannosaurus
8. Stegasaurus7. protoceratops
6. Iguanodon
4. Camptosaurus
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.
Dinosaurs disappear here(except for lineage leadingto birds).
= 65 myaMammals diversifiedin the Cretaceous,between 144 and 65 mya
Example 1: A pressing question: were dinosaurs stupid?
From Jerison 1969
From Jerison 1969
Brain cast offossil dinosaur
Megaloceros giganteus
Stood 2.1 mtall
Went extinct10,600 years
ago
Found acrossEurasia
Gould 1974Height of shoulder
Max
imum
leng
th o
f an
tler
Most of dots represent extant species of deer
Antler length = 0.064 * Shoulder height1.68
Irish elk
Two species of moose
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 kgnitrogen, 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 outstandingquestions: Why the enormous antlers? And why did they go extinct?
From Gould 1974
Height of shoulder
Max
imum
leng
th o
f an
tler
Most of dots represent extant species of deer
Antler length = 0.064 * Shoulder height1.68
Irish elk
Two species of moose
Rutting moose
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.
