week 3

• Biological Scaling


  The study of the relationship between the size of organisms and their form and physiology
• Topics in Biological Scaling

  • Scale of life and size of organisms
  • Scaling analysis
  • Effects of Size- Movement
  • Effects of Size-Transport
  • Effects of Size- Support
  • Effects of size: Muscle force
  • Size limitations: Surface tension vs. gravity
  • Allometry
• The size differences among organisms are extreme, varying over at least 7 orders of magnitude in body length and more than 10^21 in mass
• Because of their different size, a whale and a bacterium live in a different physical world; and their body shape and physiology differ accordingly
• The size of an organism is perhaps the single most important determinant of its form and physiology
• Isometry (Geometric similarity)


  Two objects or organisms are isometric if they have identical relative dimensions, i.e. the same shape, although they may be of different sizes
• Any area is proportional to any length squared (L^2)
• Any volume or mass is proportional to any length cubed (L^3)
• Any area is proportional to any volume^(2/3) or mass^(2/3), i.e. Surface area to volume ratio (SA/V) = 2/3
• Cell sizes


  • Radius 1 μm, Surface area 12.57 μm^2, Volume 4.19 μm^3
  • Radius 2 μm, Surface area 50.03 μm^2, Volume 33.51 μm^3
  • Radius 3 μm, Surface area 113.1 μm^2, Volume 113.1 μm^3
• Small animals are relatively stronger than large animals due to the scaling of muscle force with body size
• Small insects and spiders can walk on water due to surface tension forces, but this becomes less effective as they get larger
• Allometry


  The study of the relationship of body size to shape, i.e. deviations from isometric scaling
• Larger organisms compensate for their smaller surface-to-volume ratio by increasing the surface area of key structures like respiratory surfaces, gut, and circulatory system