„You can drop a mouse down a thousand-yard mine shaft; and ...ffffffff-f77d-1dab... · Size matters „You can drop a mouse down a thousand-yard mine shaft; and, on arriving at

Size matters

„You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom,

it gets a slight shock and walks away, provided the ground is fairly soft.

A rat is killed, a man is broken, a horse splashes. (J.B.S. Haldane, 1928: On being the right size)

Allometric principles and metabolic allometry

Marcus Clauss Clinic for Zoo Animals, Exotic Pets and Wildlife, Vetsuisse Faculty, University of

Zurich, Switzerland Wildlife Digestive Physiology Course Vienna 2013

42 D. Adams: Hitchhiker‘s Guide to the Galaxy

0.75 Max Kleiber (1932)

0

2

4

6

8

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14

16

500 1000 1500 2000 2500

Mass (kg)

Co

nsu

mp

tio

n (

l/1

00

km

)

Data from ADAC (2007)

y = 0.0059x - 0.2554

R2 = 0.9616

0

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4

6

8

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14

16

500 1000 1500 2000 2500

Mass (kg)

Co

nsu

mp

tio

n (

l/1

00

km

)


y = 0.0063x0.99

R2 = 0.9622

0

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4

6

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16

500 1000 1500 2000 2500

Mass (kg)

Co

nsu

mp

tio

n (

l/1

00

km

)


Kleiber (1932)

0

5000

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15000

20000

25000

30000

35000

40000

0 200 400 600 800

Body mass (kg)

Basal m

eta

bo

lic r

ate

(kJ/

d)

Kleiber (1932)

0

5000

10000

15000

20000

25000

30000

35000

40000

0 200 400 600 800

Body mass (kg)

Basal m

eta

bo

lic r

ate

(kJ/

d)

Kleiber (1932)

0

5000

10000

15000

20000

25000

30000

35000

40000

0 200 400 600 800

Body mass (kg)

Basal m

eta

bo

lic r

ate

(kJ/

d)

Kleiber (1932)

0

5000

10000

15000

20000

25000

30000

35000

40000

0 200 400 600 800

Body mass (kg)

Basal m

eta

bo

lic r

ate

(kJ/

d)

Kleiber (1932)

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5000

10000

15000

20000

25000

30000

35000

40000

0 200 400 600 800

Body mass (kg)

Basal m

eta

bo

lic r

ate

(kJ/

d)

Kleiber (1932)

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15000

20000

25000

30000

35000

40000

0 200 400 600 800

Body mass (kg)

Basal m

eta

bo

lic r

ate

(kJ/

d)

Kleiber (1932)

y = 308x0.74

R2 = 0.999

0

5000

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15000

20000

25000

30000

35000

40000

0 200 400 600 800

Body mass (kg)

Basal m

eta

bo

lic r

ate

(kJ/

d)

Kleiber (1932)

y = 308x0.74

R2 = 0.999

1

10

100

1000

10000

100000

0.1 1 10 100 1000

Body mass (kg)

Basal m

eta

bo

lic r

ate

(kJ/

d)

Allometry

Target parameter = a * body massb

Z = a * BMb

Allometry


Z = a * BMb

BM

Z

b = 1

Allometry


Z = a * BMb

BM

Z

b > 1

Allometry


Z = a * BMb

BM

Z

b < 1

Allometry


log (Z) = log(a) + b log(BM)

BM (log)

Z (

log

)

b < 1

Liver (kg) = 0.033 BW0.87

Brain (kg) = 0.011 BW0.76

Blood (kg) = 0.069 BW1.02

Muscle (kg) = 0.450 BW1.00

Skeleton (kg) = 0.061 BW1.09

Integument (kg) = 0.134 BW0.92

Gut contents (kg) = 0.093 BW1.08

(Parra 1978, Calder 1983)

Organ allometry

Basal metabolic rate

  Energy production   in resting  awake  at thermoneutrality   „post-absorptive (not digesting)

Rubner s Surface Law (1883)

  The basal metabolism of an animal is determined by its energy losses to the environment.

  These losses are determined by the contact surface to the environment - i.e. the body surface.

 With increasing body mass the ratio of surface to volume decreases.













6:1 24:8=3:1


  The volume of a geometric body increases with mass3/3 = mass1.

  The surface of a geometric body increases with mass2/3 = mass0.67.

  The length of a geometric body increases with mass1/3 = mass0.33.

 Basal metabolic rate should scale to mass0.67.


  If every cell of an elephant produced the same heat as a mouse cell, the elephant would be well done within a day.

  If every cell of a mouse produced the same heat as an elephant cell, the mouse would need a 20 cm-thick fur to maintain a constant body temperature.

0.67

Kleiber (1932)

0.74

Kleiber (1932)

0.74

Brody (1945): Mouse-to-Elephant-Curve

0.73

Brody (1945): Mouse-to-Elephant-Curve

0.73

Calculation of BMR (kJ/d) in vertebrates


 mammals: 293 BM0.75

Body mass (kg)

Basal

meta

bo

lic r

ate

(kJ/

d)


 mammals: 293 BM0.75  birds: 335 BM0.67

Body mass (kg)

Basal

meta

bo

lic r

ate

(kJ/

d)



  reptiles (30°C): 28 BM0.77

Body mass (kg)

Basal

meta

bo

lic r

ate

(kJ/

d)



  reptiles (30°C): 28 BM0.77

Body mass (kg)

Basal

meta

bo

lic r

ate

(kJ/

d)

0.67 0.75 1.00 0.50 0.25 0.00

0.67 or 0.75 ?

0.67 0.75 1.00 0.50 0.25 0.00

0.67 or 0.75 ?

Kleiber: 0.74

Brody: 0.73

Why 0.75 ?

Why 0.75 ?

Why 0.75 ?

„The widespread use and acceptance of Kleiber‘s exponent can probably be attributed to a remarkably tight regression fit (r2=0.999; n=13). To put this r2 in perspective, we randomly selected 250000 groups of 13 species from a list of 391 species compiled by Heusner (including Kleiber s data). Each group had a mass range of 3-4 orders of magnitude. Of the 250000 regressions, only four had an r2 greater than 0.9980 and none an r2 greater than 0.9990. The strength of Kleiber s exponent therefore seems to stem from an exceedingly fortuitous selection of data.

(White & Seymour 2003)

0.67 or 0.75 ?

0.67 or 0.75 ?

0.67 or 0.75 ?

Savage, West et al. (2004): 626 Species!

y = 239.05x0.7098

R2 = 0.9497

1

10

100

1000

10000

100000

1000000

0.001 0.01 0.1 1 10 100 1000 10000

Body mass (kg)

Basal m

eta

bolic r

ate

(kJ/

d)

Data from Savage et al. (2004)

y = 291.19x0.7616

R2 = 0.9955

1

10

100

1000

10000

100000

1000000

0.001 0.01 0.1 1 10 100 1000 10000

Body mass (kg)

Basal m

eta

bolic r

ate

(kJ/

d)

Savage, West et al. (2004): Body mass- binning !


White & Seymour (2003): 626 Species!

y = 239.05x0.7098

R2 = 0.9497

1

10

100

1000

10000

100000

1000000

0.001 0.01 0.1 1 10 100 1000 10000

Body mass (kg)

Basal m

eta

bolic r

ate

(kJ/

d)


White & Seymour (2003): exclude large animals!

y = 239.05x0.7098

R2 = 0.9497

y = 215.88x0.6713

R2 = 0.9196

1

10

100

1000

10000

100000

1000000

0.001 0.01 0.1 1 10 100 1000 10000

Body mass (kg)

Basal m

eta

bolic r

ate

(kJ/

d)


Basal metabolic rate

  Energy production   in resting  awake  at thermoneutrality   „post-absorptive (not digesting)


  Large animals are mainly herbivores   Large animals contain a high proportion of body

mass as gut contents with an active but flora   Large animals are rarely post-absorptive (even if a

cow fasts for a day, it still has digesta in its rumen)





tElephant = tMouse (KMElephant0.25 / KMMouse

0.25)

tMouse = 3 hours tElephant = 53 hours





tElephant = tMouse (KMElephant0.25 / KMMouse

0.25)

tMouse = 3 hours tElephant = 53 hours

Voluntary food intake at the zoo

Evans & Miller (1968)

Energy expenditure in real life (field metabolic rate)

Nagy et al. (1999)

Endogenous protein losses

Brody (1945)

Mineral maintenance requirements

Rucker & Storm (2002)

y = 0.32x0.75

R2 = 0.98

1

10

100

1000

10000

100000

10 100 1000 10000 100000 1000000 10000000

Body mass (g)

En

do

gen

ou

s f

aecal C

a lo

sses (

mg

/d)

Data from Kamphues et al. (1986), Shoe et al. (1992), Meyer & Coenen (2002), Clauss et al. (2003, 2005)

Endogenous faecal calcium losses

Endogenous vitamin C synthesis

Rucker & Steinberg (2002)

Interim result

 A large number of parameters that have a connection to metabolism scale allometrically to body mass

- with an exponent of about 0.67-0.75 (but also above or below this)

y = 239.05x0.7098

R2 = 0.9497

1

10

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1000

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100000

1000000

0.001 0.01 0.1 1 10 100 1000 10000

Body mass (kg)

Basal m

eta

bolic r

ate

(kJ/

d)

Good correlation but enormous variance!



y = 239.05x0.7098

R2 = 0.9497

1

10

100

0.001 0.01 0.1

Body mass (kg)

Basal m

eta

bolic r

ate

(kJ/

d)



0

200

400

600

800

1000

1200

0.001 0.01 0.1 1 10 100 1000 10000

Body mass (kg)

rel. B

MR (

kJ/

kg

0.7

5/d

)

293 kJ/kg0.75/d


What determines the relative BMR?

 Adaptation to climate zone: increase with latitude

McNab (2002)


 Adaptation to climate zone: increase with latitude  Adaptation to habitat:

  increase in marine mammals

McNab (2002)



  increase in marine mammals  decrease in subterranean mammals

McNab (2002)




  Taxonomy: marsupials always lower than eutherians

McNab (2005)




  Taxonomy: marsupials always lower than eutherians  Adaptation to diet: higher the more digestible the

food? (higher in carnivores)

McNab (2002)

Interim result

  The relative BMR of different animal groups varies with various taxonomic, geographic, anatomical and physiological conditions.

  In order to recognize outliers, a knowledge of the fundamental allometric relationship is necessary.

!?

The Acid Test and Allometry

!?


Lysergic acid diethylamide: its effects on a male Asiatic elephant

West et al. (1962) Science 138: 1100-1103

!?



West et al. (1962) Science 138: 1100-1103 What dose of LSD is adequate for an elephant?

!?



West et al. (1962) Science 138: 1100-1103 What dose of LSD is adequate for an elephant? Dose cat: 0.15 mg/kg Dose elephant: 0.10 mg/kg

!?



West et al. (1962) Science 138: 1100-1103 What dose of LSD is adequate for an elephant? Dose cat: 0.15 mg/kg 3 kg => 0.45 mg total dose Dose elephant: 0.10 mg/kg 2970 kg => 297 mg total dose

!?




!?




0

50

100

150

200

250

300

350

0 500 1000 1500 2000 2500 3000

Body mass (kg)

Do

se L

SD

(m

g)

!?



West et al. (1962) Science 138: 1100-1103 What dose of LSD is adequate for an elephant? Dose cat: 0.15 mg/kg 3 kg => 0.45 mg total dose Dose elephant: 0.10 mg/kg 2970 kg => 297 mg total dose same logic: man 70kg => 7 mg total dose

0

50

100

150

200

250

300

350

0 500 1000 1500 2000 2500 3000

Body mass (kg)

Do

se L

SD

(m

g)

!?



West et al. (1962) Science 138: 1100-1103 What dose of LSD is adequate for an elephant? Dose cat: 0.45 mg/3 kg => 0.2 mg/kg0.75 Dose man: 7mg/70kg => 0.3 mg/kg0.75 Dose elephant: ca. 0.25 mg/kg0.75 2970 kg => 101 mg total dose

0

50

100

150

200

250

300

350

0 500 1000 1500 2000 2500 3000

Body mass (kg)

Do

se L

SD

(m

g)

!?



West et al. (1962) Science 138: 1100-1103 What dose of LSD is adequate for an elephant? Dose cat: 0.45 mg/3 kg => 0.2 mg/kg0.75 Dose man: 7mg/70kg => 0.3 mg/kg0.75 Dose elephant: ca. 0.25 mg/kg0.75 2970 kg => 101 mg total dose

0

50

100

150

200

250

300

350

0 500 1000 1500 2000 2500 3000

Body mass (kg)

Do

se L

SD

(m

g)

Liver (kg) = 0.033 BW0.87

Brain (kg) = 0.011 BW0.76

Blood (kg) = 0.069 BW1.02

Muscle (kg) = 0.450 BW1.00

Skeleton (kg) = 0.061 BW1.09

Integument (kg) = 0.134 BW0.92

Gut contents (kg) = 0.093 BW1.08

(Parra 1978, Calder 1983)

Organ allometry

0

20

40

60

80

100

120

140

160

10 100 1000 10000

Pro

port

ion

of b

ody

mas

s (%

)

Body mass (kg)

Muscles Fat Gut contents Skin (incl. fur) Skeleton Bood Internal organs

Allometry of body composition

from Hummel and Clauss (2010)

0

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Pro

port

ion

of b

ody

mas

s (%

)

Body mass (kg)

Muscles Fat Gut contents Skin (incl. fur) Skeleton Blood Internal organs



0

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Pro

port

ion

of b

ody

mas

s (%

)

Body mass (kg)




0

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Pro

port

ion

of b

ody

mas

s (%

)

Body mass (kg)




Interim results

  The reliability of allometric predictions depends on whether the species in question is within the body size range from which the equation was derived, or beyond it.

Summary

  (Empirical) allometric functions with body mass are abundant in biology.

  The explanation of these functions is mostly under debate (but the debate is interesting!).

  The knowledge of these functions allows the identification of outliers and thus facilitates insight into functional and ecological correlations.

  For the calculation of dosages for species for which no data exists one should use an allometric approach.

  The reliability of allometric predictions depends on whether the species in question is within the body size range from which the equation was derived, or beyond it.

Vielen Dank für Ihre Aufmerksamkeit !

Introduction Diagnostics Surgery Discussion

Documents

„You can drop a mouse down a thousand-yard mine shaft; and ...ffffffff-f77d-1dab... · Size matters „You can drop a mouse down a thousand-yard mine shaft; and, on arriving at