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The full size range (extant) Mycoplasma < 0.1 pg < g Average bacterium0.1 ng g Large amoeba0.1 mg g Bee100 mg 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

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

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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

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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)

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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

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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 = So b = -0.25

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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

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Dinosaurs disappear here (except for lineage leading to birds). = 65 mya Mammals diversified in the Cretaceous, between 144 and 65 mya Artist rendition of early mammal Why did dinosaurs go extinct?

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From Jerison 1969 Fish and Reptiles Mammals and Birds Primates

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From Jerison 1969 Reptiles Mammals

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But wait a second… What if dinosaurs were endothermic? Dinosaur trackways reveal that dinosaurs may have been able to travel up to 27 mph… Some large dinosaurs had erect posture and a vertical distance between the heart and head to require a high blood pressure, like the giraffe. Where do we draw the line between ectothermic dinosaurs and endothermic ancestors to birds? Dinosaur bone is more similar to mammalian or avian (bird) bone in cross section than it is to typical ectothermic "reptilian" bone

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Big antlers on Irish Elk—10 – 12 feet across! Two outstanding questions: Why the enormous antlers? Did the large antlers contribute to its extinction?

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Megaloceros giganteus Stood 2.1 m tall Went extinct 10,600 years ago Found across Eurasia

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

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But, not the last word on Irish Elk? *New study by Moen et al 1999: what about nutrient requirements? *Irish elk antlers weighing 40 kg at the end of velvet shedding would have contained 2.1 kg nitrogen, 7.6 kg calcium and 3.8 kg phosphorus. *to grow 40 kg antlers in 150 days, need: 60 g calcium, 30 g phosphorous daily for 60 days *In the model, 6% of calcium, 10% of phosphorous taken from skeleton because dietary intake of minerals insufficient to meet requirements of antler mineralization *climate change!!!

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