The problem with size and scaling
  1. Scaling-- Study of size related effects

    2.  

  2. Isometric vs. allometric scaling

 

bulletIsometric-- geometrically similar objects
  1. The surface area and vol. related to their linear dimension
  2. Surface area = length2 and vol. = length3
  3. Surface area = vol.2/3, or vol. to the power of 0.67
  4. The surfaces of isometric bodies are always related to their volume by the ratio of 0.67
  5. Smaller bodies have larger surface areas relative to their volumes than larger objects of the same shape
bulletAllometric-- analysis of the change in one body part (e.g. limb diameter), or rate of activity (e.g. metabolism), relative to body mass (weight).
1.  Changes in shape in response to size changes (i.e. does not maintain geometric similarity)

      Range in size of adult vertebrates is enormous, going from a small mouse to an elephant

2.  Mass increases as the cube of the increase in linear dimensions, but the strength of the supporting materials (bones)

       and the muscle to move them increases in proportion to their cross-sectional area, a square function. (LIEM- page 201)

       

III. Differing allometries may emerge when analyzing differences within a species

bulletDuring growth of individual animals
bulletAcross individuals of the same age or developmental stage
bulletAcross a range of ages and stages

IV. Allometric analysis-- impact on environmental physiology

bulletEnergy assimilation, respiration and mortality vary with body mass for each species

 

bulletVariations (observations may not fall on the calculated allometric regression line) may explain interaction between environment

                 and adaptation, for example, diving animals have much larger blood volume than expecte

The reason is-- blood store oxygen during a dive.

bulletStructural and functional relationships-- for example,

the larger a diving mammal, the longer lasting are the dives.

bulletRate of O2 consumption relative to the body size is much higher in the small mammal than in the large mammal

 

bulletO2 consumption is mostly lower for cold-blood than for the warm blooded vertebrates

V.  Smaller animal has a larger body surface relative to the body mass than a large animal

bulletThe surface area of geometrically similar bodies of different size is the square of a linear dimension,

            and the volume is the cube of the linear dimension. Their areas will therefore be related as their volumes raised to the power of 2/3, or 0.67

bulletMany physiological processes are functions of surface area

VI.  Structural and functional variables are scaled in relationship to body size

bullet The size of the heart in a horse and a mouse is approximately 0.6% of body mass (Mb)-- heart weight = 0.006 Mb 1.0
bullet The heart rate, cardiac output, is scaled to pump blood at the rate required to supply O2 needed for metabolic rate
bullet The heart rate of small animal is very high and decrease by body size as indicated by the negative slope of -0.25 of the regression line
bullet Some organs are scaled to body mass (exponent = 1)or metabolic rate (exponent = 0.75)

 

kidney mass = 0.021x Mb0.85

liver mass = 0.082 x Mb0.87