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PROBLEMS OF SIZE AND SCALE. Why Size is So Important. We know that a whale. requires more energy (food, calories) per day than a mouse. Metabolic Rate vs. Body Size Scaling. But how much more?. written by Jonathan Swift in 1726. Gulliver in Lilliput - Lilliputian King is faced

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problems of size and scale

PROBLEMS OF SIZE AND SCALE

Why Size is So Important

slide3

We know

that a whale

requires more energy (food, calories) per day

than a mouse.

Metabolic Rate vs. Body Size

Scaling

But how much more?

slide4

written by Jonathan Swift

in 1726

Gulliver in Lilliput -

Lilliputian King is faced

with a physiological problem -

How much to feed Gulliver?

King calculated 1728 Lilliputian portions.

slide5

The story begins with

early research on LSD

using cats.

If we’re not careful, we can run afoul

of assumptions - to wit

LSD and the Elephant

It was discovered that a dose of 0.1 mg of

LSD in a 2.6 kg cat caused aggressive behavior.

It was subsequently decided that this might be

a good model for studying musth in bull elephants.

slide6

Musth is a condition of violent

and uncontrollable rage.

The elephant weighed 7722 kg.

The “investigators” scaled up the dose by weight:

(7722 kg /2.6 kg) = 2970

2970 X 0.1 mg = 297 mg

(approximately 1500 X the human dose for a “trip”)

slide7

Following injection, the elephant:

      • began trumpeting & running around
      • stopped
      • swayed
      • collapsed
      • convulsed
      • defecated, and
      • died

The scientists concluded that elephants

are particularly sensitive to LSD.

Not so! Assumptions were incorrect!

slide8

VO2 (or Em) = aMb

log VO2 = log(aMb)

log VO2 = log(a) + b log(M)

which has the form y = a + bx,

where b is the slope of the line

There is an exponentialrelation between

metabolic rate and mass:

on a log-log plot

this equation becomes a straight line:

slide9

Em

(kcal • d-1)

log VO2 = log(a) + b log(M)

10000

1000

100

10

slope = b

~0.75

0.1 1.0 10 100 1000

Body Mass (kg)

slide11

VO2 / M

(l O2 • h-1) / (kg)

aM b

VO2/M = = a M b-1 = aM -0.25

M

What about the weight-specific metabolic rate?

slide13

mouse elephant

Em

(kcal • d-1)

Em’

(kcal•kg-1•d-1)

slope = -0.25

10000

1000

100

10

slope = 0.75

0.1 1.0 10 100 1000

Body Mass (kg)