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Metabolism & Allometry

Explore the relationship between metabolic rate, body mass, and energy conservation in animals. Learn about scaling principles, measurement techniques, and the allometric equations that govern metabolic processes. Understand how size affects metabolic rates and the implications for animal behavior and physiology.

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Metabolism & Allometry

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  1. Metabolism & Allometry log metabolic rate log body mass Jan 11th, 2007

  2. Physics Model of an Animal ·Mass & Energy are conserved ΔMin ΔHin In = Out All loses accounted for h ΔWout ·Is the model testable? ΔMstored ΔHstored Measurements to test theory ΔHout ΔMout ΔQout ·Unifying principles can describe phenomena

  3. Zoologist’s Model of an Animal Fuel + O2 = ΔH + waste Heat of reaction, ΔH = Δm h Δm = mass of food [kg] Fuel + O2 h = enthalpy[J/kg] ‘in’ ‘heat’ ΔH ΔH = energy Waste i.e. flight

  4. How do we measure metabolic rate? Fuel + O2 = ΔH + waste ΔH/Δt= metabolic rate or power Г Mass specific metabolic rate Г/M Hummingbird muscle: mass specific power Г/M ≈ 100 W/kg (highest among vertebrates) Measure O2 , and fuel, intake to estimate energy (ΔH)) required to hover (ΔW) (Chai & Dudley, 1995, Nature)

  5. Measuring Г in other animals (usually at rest) ΔHin

  6. Allometry:how things scale with mass Г M

  7. Range of body sizes: 1021 Blue whale: >108 g Mycoplasma: <10-13 g (Giant sequoias excluded for now)

  8. How big is a blue whale? Brachiosaur Blue whale

  9. How much of a difference is 1021? 1021 Blue whale The sun

  10. Does size matter? Blue whale: >108 g Mycoplasma: <10-13 g

  11. "You can drop a mouse down a thousand-yard mine shaft; and,on arriving at the bottom, it gets a slight shock and walksaway, provided that the ground is fairly soft. A rat is killed,a man is broken, a horse splashes." `On being the right size', by J. B. S. Haldane (1928).

  12. How to study the consequences of size: Scaling slope = α Y log(Y) intercept = a mass log(mass) Y = aMα Length of leg, Y

  13. Allometric equations: Y = aMα Isometric, α = 1(i.e. blood volume) log(Y) log(mass)

  14. Allometric equations: Y = aMα Isometric, α = 1(i.e. blood volume) log(Y) Allometric, α ≠ 1(i.e. metabolic rate) log(mass)

  15. Allometric equations: Y = aMα Allometric, α ≠ 1(i.e. skeletal mass, mammals) Isometric, α = 1(i.e. blood volume) log(Y) Allometric, α ≠ 1(i.e. metabolic rate) log(mass)

  16. Size matters, but why? Sleep scales too, but with brain size, not body size: 14 hrs/day 4 hrs/day

  17. Scaling transcends biology: F/M Fruit fly thorax Diesel engine (Marden, J. H. 2005. J. Exp. Biol.)

  18. What determines the allometry of metabolic rate? • Energy demand of all cells • But is it supply limited? (see West et al., 2005) Гo = M0.75 Y o = M-0.25(mass specific met. rate) M

  19. Smaller animals live fast, but die young • A gram of tissue, on average, expends the same amount of energy before it dies in any animal. Y Life span = M1/4 o= M-1/4 M

  20. Metabolic rates (in W) of mammalian cells • Energy requirements of cells are situation dependent West, G. B. et al. 2005

  21. Resting or basal metabolic rate (BMR) scales: 4M3/4

  22. Metabolic rate is dynamic

  23. Metabolic rate is dynamic Aerobic scope ‘metabolic activity factor’ b Гmax=bГo b b Гmax=b4M0.75 In this example, b ≈ 10

  24. Keep this in mind for the staircase olympics Гrun=bГo b= ? b b Гrun=b4M0.75

  25. Consequences of scaling of Г, an example Blood vol. = M1 Г = 4M3/4 log(Y) o = M-1/4 log(mass) Diving capacity = 1000 m deep, 1 hr long

  26. Allometry of diving capacity O2 storage = M1 Γ = M3/4 Dive duration = M1/4 M1/4 (Schreer and Kovacs, 1997; Croll et al., 2001, Halsey et al., 2006)

  27. Other consequences: migration ΔH = Δm h Г = ΔH/Δt Ruby throated hummingbird Humpback whale Г/M high low Migration Alaska - Mexico Alaska - Mexico Fasting capacity low high

  28. Advice for assignments • State your assumptions and justify them with first principles if possible Lift Lift = Mg M Surface area = 4πr2 Mg

  29. Advice for assignments • Look up data from published resources to include in your physical model or to compare your calculated results. Include a copy of the article with your assignment (no monographs please). Hummingbird muscle: mass specific power Г/M ≈ 100 W/kg (Chai & Dudley, 1995, Nature) • Compare your results and conclusions with other animals, or even man-made machines.

  30. Advice for building physical models • Build a model or theory to predict, then test with data • Start simple, add complexity slowly • Model after machines that we know more about Alexander, R. M. (2005). Models and the scaling of energy costs for locomotion. J. Exp. Biol.208,1645 -1652.

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