Size matters. (J.B.S. Haldane, 1928: On being the right size)

Transcription

1 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)

2 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

3 42 D. Adams: Hitchhiker s Guide to the Galaxy

4 0.75 Max Kleiber (1932)

5 16 Consumption (l/100km) Mass (kg) Data from ADAC (2007)

6 Consumption (l/100km) y = x R 2 = Mass (kg) Data from ADAC (2007)

7 Consumption (l/100km) y = x 0.99 R 2 = Mass (kg) Data from ADAC (2007)

8 Kleiber (1932) Basal metabolic rate (kj/d) Body mass (kg)

9 Kleiber (1932) Basal metabolic rate (kj/d) Body mass (kg)

10 Kleiber (1932) Basal metabolic rate (kj/d) Body mass (kg)

11 Kleiber (1932) Basal metabolic rate (kj/d) Body mass (kg)

12 Kleiber (1932) Basal metabolic rate (kj/d) Body mass (kg)

13 Kleiber (1932) Basal metabolic rate (kj/d) Body mass (kg)

14 Kleiber (1932) Basal metabolic rate (kj/d) y = 308x 0.74 R 2 = Body mass (kg)

15 Kleiber (1932) Basal metabolic rate (kj/d) y = 308x 0.74 R 2 = Body mass (kg)

16 Allometry Target parameter = a * body mass b Z = a * BM b

17 Allometry Target parameter = a * body mass b Z = a * BM b b = 1 Z BM

18 Allometry Target parameter = a * body mass b Z = a * BM b b > 1 Z BM

19 Allometry Target parameter = a * body mass b Z = a * BM b b < 1 Z BM

20 Allometry Target parameter = a * body mass b log (Z) = log(a) + b log(bm) b < 1 Z (log) BM (log)

21 Organ allometry Liver (kg) = BW 0.87 Brain (kg) = BW 0.76 Blood (kg) = BW 1.02 Muscle (kg) = BW 1.00 Skeleton (kg) = BW 1.09 Integument (kg) = BW 0.92 Gut contents (kg) = BW 1.08 (Parra 1978, Calder 1983)

22 Basal metabolic rate Energy production in resting awake at thermoneutrality post-absorptive (not digesting)

23 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.

24 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.

25 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.

26 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

27 Rubner s Surface Law (1883) The volume of a geometric body increases with mass 3/3 = mass 1. The surface of a geometric body increases with mass 2/3 = mass The length of a geometric body increases with mass 1/3 = mass Basal metabolic rate should scale to mass 0.67.

28 Rubner s Surface Law (1883) 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 cmthick fur to maintain a constant body temperature.

29 0.67

30 Kleiber (1932) 0.74

31 Kleiber (1932) 0.74

32 Brody (1945): Mouse-to-Elephant-Curve 0.73

33 Brody (1945): Mouse-to-Elephant-Curve 0.73

34 Calculation of BMR (kj/d) in vertebrates

35 Calculation of BMR (kj/d) in vertebrates mammals: 293 BM 0.75 Basal metabolic rate (kj/d) Body mass (kg)

36 Calculation of BMR (kj/d) in vertebrates mammals: 293 BM 0.75 birds: 335 BM 0.67 Basal metabolic rate (kj/d) Body mass (kg)

37 Calculation of BMR (kj/d) in vertebrates mammals: 293 BM 0.75 birds: 335 BM 0.67 reptiles (30 C): 28 BM 0.77 Basal metabolic rate (kj/d) Body mass (kg)

38 Calculation of BMR (kj/d) in vertebrates mammals: 293 BM 0.75 birds: 335 BM 0.67 reptiles (30 C): 28 BM 0.77 Basal metabolic rate (kj/d) Body mass (kg)

39 0.67 or 0.75?

40 0.67 or 0.75? Brody: 0.73 Kleiber: 0.74

41 Why 0.75?

42 Why 0.75?

43 Why 0.75? The widespread use and acceptance of Kleiber s exponent can probably be attributed to a remarkably tight regression fit (r 2 =0.999; n=13). To put this r 2 in perspective, we randomly selected 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 regressions, only four had an r 2 greater than and none an r 2 greater than The strength of Kleiber s exponent therefore seems to stem from an exceedingly fortuitous selection of data. (White & Seymour 2003)

44 0.67 or 0.75?

45 0.67 or 0.75?

46 0.67 or 0.75?

47 Savage, West et al. (2004): 626 Species! Basal metabolic rate (kj/d) y = x R 2 = Body mass (kg) Data from Savage et al. (2004)

48 Savage, West et al. (2004): Body mass- binning! Basal metabolic rate (kj/d) y = x R 2 = Body mass (kg) Data from Savage et al. (2004)

49 White & Seymour (2003): 626 Species! Basal metabolic rate (kj/d) y = x R 2 = Body mass (kg) Data from Savage et al. (2004)

50 White & Seymour (2003): exclude large animals! Basal metabolic rate (kj/d) y = x R 2 = y = x R 2 = Body mass (kg) Data from Savage et al. (2004)

51 Basal metabolic rate Energy production in resting awake at thermoneutrality post-absorptive (not digesting)

52 White & Seymour (2003): exclude large animals! 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)

53 White & Seymour (2003): exclude large animals! 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) t Elephant = t Mouse (KM Elephant 0.25 / KM Mouse 0.25 ) t Mouse = 3 hours t Elephant = 53 hours

54 White & Seymour (2003): exclude large animals! 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) t Elephant = t Mouse (KM Elephant 0.25 / KM Mouse 0.25 ) t Mouse = 3 hours t Elephant = 53 hours

55 Voluntary food intake at the zoo Evans & Miller (1968)

56 Energy expenditure in real life (field metabolic rate) Nagy et al. (1999)

57 Endogenous protein losses Brody (1945)

58 Mineral maintenance requirements Rucker & Storm (2002)

59 Endogenous faecal calcium losses Endogenous faecal Ca losses (mg/d) y = 0.32x 0.75 R 2 = Body mass (g) Data from Kamphues et al. (1986), Shoe et al. (1992), Meyer & Coenen (2002), Clauss et al. (2003, 2005)

60 Endogenous vitamin C synthesis Rucker & Steinberg (2002)

61 Interim result A large number of parameters that have a connection to metabolism scale allometrically to body mass - with an exponent of about (but also above or below this)

62 Good correlation but enormous variance! Basal metabolic rate (kj/d) y = x R 2 = Body mass (kg) Data from Savage et al. (2004)

63 Good correlation but enormous variance! 100 y = x R 2 = Basal metabolic rate (kj/d) Body mass (kg) Data from Savage et al. (2004)

64 Good correlation but enormous variance! rel. BMR (kj/kg 0.75 /d) kj/kg 0.75 / d Body mass (kg) Data from Savage et al. (2004)

65 What determines the relative BMR? Adaptation to climate zone: increase with latitude McNab (2002)

66 What determines the relative BMR? Adaptation to climate zone: increase with latitude Adaptation to habitat: increase in marine mammals McNab (2002)

67 What determines the relative BMR? Adaptation to climate zone: increase with latitude Adaptation to habitat: increase in marine mammals decrease in subterranean mammals McNab (2002)

68 What determines the relative BMR? Adaptation to climate zone: increase with latitude Adaptation to habitat: increase in marine mammals decrease in subterranean mammals Taxonomy: marsupials always lower than eutherians McNab (2005)

69 What determines the relative BMR? Adaptation to climate zone: increase with latitude Adaptation to habitat: increase in marine mammals decrease in subterranean mammals Taxonomy: marsupials always lower than eutherians Adaptation to diet: higher the more digestible the food? (higher in carnivores) McNab (2002)

70 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.

71 The Acid Test and Allometry!?

72 The Acid Test and Allometry Lysergic acid diethylamide: its effects on a male Asiatic elephant West et al. (1962) Science 138: !?

73 The Acid Test and Allometry Lysergic acid diethylamide: its effects on a male Asiatic elephant West et al. (1962) Science 138: What dose of LSD is adequate for an elephant?!?

74 The Acid Test and Allometry Lysergic acid diethylamide: its effects on a male Asiatic elephant West et al. (1962) Science 138: What dose of LSD is adequate for an elephant? Dose cat: 0.15 mg/kg Dose elephant: 0.10 mg/kg!?

75 The Acid Test and Allometry Lysergic acid diethylamide: its effects on a male Asiatic elephant West et al. (1962) Science 138: 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!?

76 The Acid Test and Allometry Lysergic acid diethylamide: its effects on a male Asiatic elephant West et al. (1962) Science 138: 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!?

77 The Acid Test and Allometry Lysergic acid diethylamide: its effects on a male Asiatic elephant West et al. (1962) Science 138: 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 Dose LSD (mg) Body mass (kg)!?

78 The Acid Test and Allometry Lysergic acid diethylamide: its effects on a male Asiatic elephant West et al. (1962) Science 138: What dose of LSD is adequate for an elephant? 350 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 Dose LSD (mg) Body mass (kg)!?

79 The Acid Test and Allometry Lysergic acid diethylamide: its effects on a male Asiatic elephant West et al. (1962) Science 138: What dose of LSD is adequate for an elephant? 350 Dose cat: 0.45 mg/3 kg => 0.2 mg/kg 0.75 Dose man: 7mg/70kg => 0.3 mg/kg 0.75 Dose elephant: ca mg/kg kg => 101 mg total dose Dose LSD (mg) Body mass (kg)!?

80 The Acid Test and Allometry Lysergic acid diethylamide: its effects on a male Asiatic elephant West et al. (1962) Science 138: What dose of LSD is adequate for an elephant? 350 Dose cat: 0.45 mg/3 kg => 0.2 mg/kg 0.75 Dose man: 7mg/70kg => 0.3 mg/kg 0.75 Dose elephant: ca mg/kg kg => 101 mg total dose Dose LSD (mg) Body mass (kg)!?

81 Organ allometry Liver (kg) = BW 0.87 Brain (kg) = BW 0.76 Blood (kg) = BW 1.02 Muscle (kg) = BW 1.00 Skeleton (kg) = BW 1.09 Integument (kg) = BW 0.92 Gut contents (kg) = BW 1.08 (Parra 1978, Calder 1983)

82 Allometry of body composition 160 Proportion of body mass (%) Muscles Fat Gut contents Skin (incl. fur) Skeleton Bood Internal organs Body mass (kg) from Hummel and Clauss (2010)

83 Allometry of body composition 160 Proportion of body mass (%) Muscles Fat Gut contents Skin (incl. fur) Skeleton Blood Internal organs Body mass (kg) from Hummel and Clauss (2010)

84 Allometry of body composition 160 Proportion of body mass (%) Muscles Fat Gut contents Skin (incl. fur) Skeleton Blood Internal organs Body mass (kg) from Hummel and Clauss (2010)

85 Allometry of body composition 160 Proportion of body mass (%) Muscles Fat Gut contents Skin (incl. fur) Skeleton Blood Internal organs Body mass (kg) from Hummel and Clauss (2010)

86 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.

87 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.

88

89

90

91

92 Introduction Diagnostics Surgery Discussion Vielen Dank für Ihre Aufmerksamkeit!