2. What’s the worlds largest known living organism? Smallest? Blue whale = 100 tons 10 8 g Mycoplasma weighs < 0.1 pg 10 -13 g Largest Organism: sequoia at 4,000 tons 10 10 g Largest Living Animal?

3. What about the largest terrestrial animals? Currently: the elephant, at about 5 tons. 10 6 g Historically: Largest dinosaur: Seismosaurus, topping out at about 80 tons. 10 8 g Historically: Largest Mammal: Baluchitherium, a relative of the modern rhinoceros, ~30 tons 10 7 g

4. The full size range (extant) Mycoplasma < 0.1 pg < 10 -13 g Average bacterium0.1 ng 10 -10 g Large amoeba0.1 mg 10 -4 g Bee100 mg 10 -1 g Hamster100 g 10 2 g Human100 kg 10 5 g Elephant 5,000 kg (5 tons)5 x 10 6 g Blue Whale 100 tons 10 8 g Sequoia5000 tons10 10 g

5. Scaling: structural and functional consequences of change in size among otherwise similar organisms. Three basic ways that organisms can change with size: 1. Dimensions 2. Materials used 3. Design

6. 1. Dimensions Side view of brick wall Does this happen in animals? Can you just make the wall taller? Must be WIDER as well

7. % of body mass that is skeleton 3.8% Sorex (shrew) 18.8% 27% elephant 1. Dimensions Human

8. 2. Materials used brick steel hydrostatic support/exoskeletonbone support

9. Compressive support, stone 3. Design Short 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

10. 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

11. Scaling: structural and functional consequences of change in size among otherwise similar organisms. Three basic ways that organisms can change with size: 1. Dimensions 2. Materials used 3. Design Let’s look at this graphically…

12. Scaling Relationships Y = a X b A “power” function Body Mass (M) Physiological parameter of interest

13. Scaling Relationships Y = a M b A “power” function Body Mass (M) Physiological parameter of interest a = proportionality constant b = scaling exponent (describes strength and direction of the effect of mass on Y)

14. Y = a M b Body Mass (M) Physiological parameter of interest 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

15. 8. BODY SIZE affects MR “Whole animal” O 2 consumption “Mass-specific” O 2 consumption

16. How does whole animal O 2 consumption scale with body size? Y = a M b b = 0.75 O 2 consumption increases with body mass in a regular way but not in constant proportion Body Mass (M) Whole animal O2 consumption (mlO2/hr)

17. Physiologists often use log-log plots log Body mass Log E log E = log a + b log M E = a M b O2 consumption (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

18. Mass-specific MR How does mass-specific O 2 consumption scale with body size? (0 2 consumption per gram of tissue) Y = a M b Take log: log Body mass Log O2/g*hr Slope = -0.25 So b = -0.25

19. 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 relationship e.g., blood volume in mammals -constant fraction of body mass No relationship e.g. [hemoglobin] e.g. whole animal metabolic rate b = 0.75 e.g., bone thickness e.g., mass specific metabolic rate b = -0.25

20. 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 = aX b –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?

22. The actual equation for surface area as a function of volume is SA = 6 V 2/3 Take the log of both sides Log(SA) = Log(6 V 2/3 ) = Log(6) + 2/3 * Log(V)

23. Real organisms usually are not isometric. Rather, certain proportions change in a regular fashion. Such non-isometric scaling is called allometric scaling. An amazing number of biological variables can be described by the allometric equation: y = a x b Take log of both sides to get: Log(y) = Log(a) b Log(x) The key coefficient—the scaling exponent

24. What the scaling exponent, b, means. Log x Log y Slope = 1 Ex. The cost of apples rises ‘isometrically’ with the mass bought. Log x Log y Slope = 1.08 Ex. Skeleton mass of mammals rises faster than body mass. Large mammals have disproportionately large skeletons.

25. Log x Log y Slope = 0.75 Ex. Metabolic rate rises with body mass, but less than proportionately. Log x Log y Slope = 0 Ex. Hematocrit in mammals is independent of body mass. Log x Log y Slope = -0.25 Ex. Heart rate in mammals decreases with body mass.

26. b = 1 b = 0.6 b = 0.75 b = 1 b = 0.6 b = 0.75

27. Using allometry. Dinosaurs disappear here (except for lineage leading to birds). = 65 mya Mammals diversified in the Cretaceous, between 144 and 65 mya Example 1: A pressing question: were dinosaurs stupid?

28. From Jerison 1969

29. Brain cast of fossil dinosaur

30. Example 2: Big antlers on Irish Elk—10 – 12 feet across! This species went extinct in Ireland about 10,000 years ago. Two outstanding questions: Why the enormous antlers? And why did they go extinct?

31. From Gould 1974 Height of shoulder Maximum length of antler Most of dots represent extant species of deer Antler length = 0.064 * Shoulder height 1.68 Irish elk Two species of moose

32. 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.