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Mycoplasma weighs < 0.1 pg 10 -13 g. What’s the worlds largest known living organism?. Largest Living Animal?. Blue whale = 100 tons 10 8 g. 10 10 g. Largest Organism : sequoia at 4,000 tons. Smallest?. Historically: Largest Mammal:
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Mycoplasma weighs < 0.1 pg 10 -13 g What’s the worlds largest knownliving organism? Largest Living Animal? Blue whale = 100 tons 108 g 1010 g Largest Organism: sequoia at 4,000 tons Smallest?
Historically:Largest Mammal: Baluchitherium, a relative of the modern rhinoceros, ~30 tons Currently: the elephant, at about 5 tons. 106 g 107 g What about the largest terrestrial animals? Historically: Largest dinosaur: Seismosaurus, topping out at about 80 tons. 107g
The full size range (extant) Mycoplasma < 0.1 pg < 10 -13 g Average bacterium 0.1 ng 10 -10 g Large amoeba 0.1 mg 10 -4 g Bee 100 mg 10 -1 g Hamster 100 g 10 2 g Human 100 kg 10 5 g Elephant 5,000 kg (5 tons) 5 x 10 6 g Blue Whale 100 tons 10 8 g Sequoia 5000 tons 10 10 g
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
Must be WIDER as well NO 1. Dimensions Can you just make the wall taller? Side view ofbrick wall Does this happen in animals?
% of body mass that is skeleton elephant 1. Dimensions Sorex(shrew) 3.8% Human 18.8% 27%
steel hydrostatic support/exoskeleton bone support 2. Materials used brick
Unicellular organism 0.1 mm = 5 sec 1 mm = Diffusion 10 cm = 3. Design Long bridge Short bridge Tensile support, steel Compressive support, stone Oxygen Delivery—design changes with size Diffusion Problem!: Time to diffuse is proportional to the square of the distance 500 sec ~ 27 days
Unicellular organism Vertebrate Insect • bulk flow delivery • hemoglobin increases oxygen in blood Diffusion through air via tracheal system Diffusion Long bridge Short bridge 3. Design Tensile support, steel Compressive support, stone Oxygen Delivery—design changes with size
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…
A “power” function Physiological parameter of interest Body Mass (M) Scaling Relationships Y = a Xb
A “power” function Physiological parameter of interest Body Mass (M) Scaling Relationships Y = aMb a = proportionality constant b = scaling exponent (describes strength and direction of the effect of mass on Y)
Physiological parameter of interest Body Mass (M) Scaling Relationships Y = a Mb If it scaled in constant proportion… …then b would = 1 This would be an ‘isometric’ relationship But, this is not usually the case …for example:
elephant Scaling of Skeletal mass to body mass Sorex(shrew) Y = 0.061X1.090 Human
8. BODY SIZE affects MR • “Whole animal” O2 consumption • “Mass-specific” O2 consumption
How does whole animal O2 consumption scale with body size? Whole animal O2 consumption (mlO2/hr) Body Mass (M) Y = a Mb • O2 consumption increases with body mass in a regular way • but not in constant proportion b = 0.75
b = 0.75 slope = 0.75 E = a Mb Body mass Log E Y-intercept slope log Body mass log E = log a + b log M Physiologists often use log-log plots • allow for huge range of body sizes • generate a straight line • slope of line = b O2 consumption (E)
How does mass-specific O2 consumption scale with body size? Mass-specific MR (02 consumption per gram of tissue) Log O2/g*hr log Body mass Y = a Mb So b = -0.25 Take log: Slope = -0.25
b: describes relationship of X to Y as Y gets bigger If b = 0 If 0 < b < 1 If b = 1 b = 0.75 No relationship e.g. [hemoglobin] e.g. whole animal metabolic rate Isometric relationship e.g., blood volume in mammals -constant fraction of body mass If b < 0 If b > 1 b = -0.25 e.g., mass specific metabolic rate e.g., bone thickness
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 = aXb • 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?
Take the log of both sides Log(SA) = Log(6 V2/3) = Log(6) + 2/3 * Log(V) The actual equation for surface area as a function of volume is SA = 6 V2/3
Take log of both sides to get: Log(y) = Log(a) • b Log(x) The key coefficient—the scaling exponent Real organisms usually are not isometric. Rather, certain proportionschange in a regular fashion. Such non-isometric scaling is calledallometric scaling. An amazing number of biological variables can be described bythe allometric equation: y = a • xb
Slope = 1.08 Ex. Skeleton mass of mammals rises faster thanbody mass. Large mammalshave disproportionately largeskeletons. Log y Log x What the scaling exponent, b, means. Slope = 1 Ex. The cost of applesrises ‘isometrically’ with the mass bought. Log y Log x
Slope = 0.75 Ex. Metabolic raterises with body mass, butless than proportionately. Log y Log x Slope = 0 Ex. Hematocrit inmammals is independentof body mass. Log y Log x Slope = -0.25 Ex. Heart rate in mammalsdecreases with body mass. Log y Log x
b = 1 b = 0.75 b = 0.6 b = 1 b = 0.75 b = 0.6
= 65 mya Mammals diversifiedin the Cretaceous,between 144 and 65 mya Dinosaurs disappear here(except for lineage leadingto birds). Artist rendition of early mammal
Fish and Reptiles Mammals and Birds Primates From Jerison 1969
Reptiles Mammals From Jerison 1969
2. Anatosaurus 1. Allosaurus 5. Diplodocus 3. Brachiosaurus 6. Iguanodon 4. Camptosaurus 7. protoceratops 8. Stegasaurus 10. Tyrannosaurus 9. Triceratops
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
Example 1: A pressing question: were dinosaurs stupid? Mammals diversifiedin the Cretaceous,between 144 and 65 mya = 65 mya Dinosaurs disappear here(except for lineage leadingto birds). Using allometry.
Brain cast offossil dinosaur From Jerison 1969
Megaloceros giganteus Stood 2.1 m tall Went extinct 10,600 years ago Found across Eurasia
Most of dots represent extant species of deer Irish elk Two species of moose Maximum length of antler Antler length = 0.064 * Shoulder height1.68 Height of shoulder Gould 1974
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: 7.6 kg calcium, 3.8 kg phosphorous (60 g calcium and 30 g phosphorous per day) • *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!!!
Example 2: Big antlers on Irish Elk—10 – 12 feet across! This species went extinct in Ireland about 10,000 years ago. Two outstandingquestions: Why the enormous antlers? And why did they go extinct?
Most of dots represent extant species of deer Irish elk Two species of moose Maximum length of antler Antler length = 0.064 * Shoulder height1.68 Height of shoulder From Gould 1974
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. Rutting moose