Sunday, February 16, 2014

Scaling

Scaling means relating an organism's body size to an entity of process. It is usually done with power functions. Body size is important because it affects a variety of aspects:


  1. Metabolisms
  2. Growth and shape
  3. Survival
  4. Impact of predation and competition
  5. Population density and growth
  6. Territory area
  7. Food acquisition
  8. Species diversity
  9. Reproduction
Some key aspects to consider:
  1. There are general scaling rules that apply across organisms
  2. Scaling relationships can be inter-related producing counterintuitive insights.

Power functions

Y= Yom^b
log(Y) = log(Yo)+ b*log(m)

m=mass
b= predictive of slope.

Log transformations allow a better appreciation of the slope of the function.
b = 1.0 means it is isometric, which indicates that the process/pattern to mass ratio is 1:1. (This is rare)
b ≠ 1.0 means it is allometric
b = 0 means there is a scale invariance

Scaling can also be geometric, this means shape doesn't change with body size:
b = 1/3 means the scaling process is in relation to length
b = 2/3 means the scaling process is in relation to area

Types of scaling:
  1. Within organisms
    • Tree cross-sectional area
      • Geometric scaling with area M^0.66
      • M^0.75 gives a greater slope. Extra scaling gives tree an advantage against buckling and fractures in high flow forces
    • Mammalian heart rate
      • M^-0.25
      • Number of heart beats per lifetime does not vary with body size
  2. Among individuals
    • Standard metabolic rate
      • Energy expenditure at rest; Kleiber's rule (1932)
      • MR = M^0.75
  3. Scaling at population-community levels
    • Scaling of body mass and population density of mammalian herbivores
    • (Population density)(Metabolic rate) = M^0 = scale invariance
    • Energetic Equivalence Rule (EER) =  population energy flux of individuals is invariant with body size
      • Species of different body sizes use approximately equal amounts of energy
      • Plants: Population density related to mass; M^-0.75
      • Metabolic resource use in plants; M^0.75
      • EER applies to marine and terrestrial plants
Types of size-density relationships
  1. Global size-density relations
  2. Local size-density relations
    • All population data taken from a single region

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