Scaling Flashcards
What is isometry
When 2 variables scale proportionately
What is allometry
When 2 variables don’t scale proportionately ( non-equal scaling)
What is the equation for allometry
Y = aM^b
Draw the different allometric curves
(slide 16)
How does surface area scale
M^(2/3)
How does length scale
M^(1/3)
Why is the surface area to volume ratio important
SA allows exchange of gas and nutrients, heat and waste
it is the interface between the environment and animal
How do we prevent a decrease in SA/volume ratio
increase in 1 dimmension. have small alveoli increase independently
How does surface area per unit mass scale with mass
M^2/3 / M^1 = M^ -1/3
What is stress
force/ area = pressure
How does a skeleton work
- needs to bear weight of animal
2. stiff support system
What happens if the skeletal mass scales isometrically
mass is proportional to weight, weight = SA*length. M^1 = M^2/3 * M ^1/3. but then stress = M^1 / M^ 2/3 = M^ 1/3. so the stress the skeletal system has to take on increases, stress may cause breakage
What happens to the skeletal mass if the stress on teh skeleton is constant
stress = force (=weight) / area. so area of skeleton = M^1 and so M^1 * M ^1/3, so skeletal mass scales M ^4/3.
What is the solution to keeping a constant stress when the skeletal mass would increase by M^4/3
- have a different gait to lower impact on bone
2. adopt upright posture to keep skeletons under compressive stress
How does metabolic rate scale with mass based on Rubner
M^2/3 because it followed surface area ( losing of heat)
