Autumn.wmf (12088 bytes)Introduction to Organismal Biology (BIOL221) - Dr. S.G. Saupe; Biology Department, College of St. Benedict/St. John's University, Collegeville, MN 56321;;

An Introduction to Form & Function

I.  General

II. Correlation between form/function occurs at all levels of the biological hierarchy

III.  Biological form & function is an evolutionary compromise = trade-offs

IV.  Biological form & function is a product of evolution

V.  Surface-to-volume ratios - important determinant of biological form & function 
Surface-to-volume ratios, abbreviated S/V, are very important in biology.  Surface area (SA), which is expressed in squared units (e.g., mm2, �m2), is the amount of an object that is directly exposed to the environment.  For a cell, it would represent the area of the plasma membrane and for a person it would represent the amount of skin.  Volume is a rough measure of the size of a structure and the amount of space it occupies.  Volume is expressed by cubic units (e.g., mm3, cm3 = milliliters).  The surface-to-volume ratio (S/V) refers to the amount of surface a structure has relative to its size; or stated in a slightly more gruesome manner, S/V ratio is the amount of "skin" compared to the amount of "guts."  To calculate the S/V ratio, simply divide the surface area by the volume. 

    The reason that surface-to-volume ratios are important is because a cell or organism continuously exchanges materials, such as food, waste, water, and heat, with its environment.  Depending on the circumstances, it may be advantageous to have a small S/V while at other times a large S/V is an advantage.  Thus, optimizing S/V ratios has been a driving force in the evolution of all organisms.  Since S/V is a function of both size and shape, these have also been under strong evolutionary pressure.   

A.  Definitions

B.  Consider a cube
         1.  Complete the following calculations 

  Small Cube Large Cube
Length of a side (millimeters) 1 3
surface area (mm2)    
volume (mm3)    
surface/volume ratio    
overall size increase in cube  
overall increase in surface area  
overall increase in volume  

            2.  Some conclusions:

  • As the cube gets larger, the surface area (increases, decreases)

  • As the cube gets larger, the volume (increases, decreases)

  • As the cube gets larger, the s/v ratio (increases, decreases)

  • As the cube gets larger, the surface area increases by the (square, cube) of the linear dimensional increase. 

  • As the cube gets larger, the volume increases by the (square, cube) of the linear dimensional increase

C.  Why are S/V ratios important?

  1. Organisms open systems, must exchange materials with environment

  2. Exchange (diffusion, etc.) occurs via SA

  3. SA must be appropriate for volume & need

VI.  Practical Implications of Surface/volume ratios - Driving force in evolution of shape

A.  Overall plant and animal shapes - a consequence of motility
    Did you ever wonder why animals can move around but plants cannot? The answer is simple - to obtain food. Recall that animals are heterotrophic and must obtain organic compounds (food) from their environment. Since their food is scattered around in the environment, it was necessary to move to get it. In contrast, plants never had an evolutionary pressure for "motility" since their essential nutrients (water, ions and carbon dioxide) are "omnipotent". To support this idea consider some non-motile animals like coral, hydras, and sea fans. They all live in aquatic environments which enables them to "feed like a plant" - their food is essentially brought to them via water currents. Thus, they never had any pressure for motility - and interestingly, they have very similar lifestyles/forms as plants.

    As a consequence - plants have evolved to be a cluster of filaments and flattened boxes whereas the body plan of an animal is like a square.  The reason - for a given volume, a square has less surface area than a comparable-sized filament or flattened box.   Animals evolved to have a minimal s/v which reduces frictional resistance and is easier to move around.  That's why bike racers strive for aerodynamic designs, etc.  In contrast, the evolutionary pressure on plants has been to maximize their s/v ratio to efficiently absorb nutrients from their environment.

B.  Gut shape & length are a function of s/v ratios

C.  Leaf shape - xerophyte vs. mesophyte

D.  Respiratory surface (lungs vs. gills) is a function of s/v ratios

VI.  Practical Implications of Surface/volume ratios - Impact on organismal size

A. Size and structural organization
    To get larger an organism can either: (a) increase the size of its cells; or (b) increase the number of its cells. Recall from lab last semester and our cell unit that cells are small, about 100 μm in diameter.  Why?  Cells must remain small in order to efficiently  function. Thus, our take-home-lesson is that bigger organisms have more cells than smaller ones. Or, stated another way, an increase in size is accompanied by an increase in the number of cells in the organism.  Thus, elephants have more cells than a shrew.  In evolutionary terms, getting larger permitted (and required) an increase in complexity (specialization) of organisms.

    Again recall that increasing the size of an object decreases it s/v ratio. Thus, among the changes in form that accompany an increase in size are mechanisms to increase s/v ratios. Some examples: (1) lungs increase surface area for gas absorption; (2) guts are long and thin tubes for increased surface area; (3) the brain is convoluted to get rid of excess heat (an overheated brain is not a pretty sight); (4) one way that Neanderthals differ from modern humans in that their skulls had bony projections into their nasal cavity. These apparently functioned to increase the surface area to allow for more rapid warming of air before it reached the lungs (Discover March 1997).

B. Metabolism as a function of size
    The metabolic rate of an animal refers to the amount of energy an animal uses in a given period of time. It can be measured by monitoring, among things: (a) amount of oxygen consumed (or carbon dioxide produced) by the animal in a respirometer; or (b) heat lost by an animal in a calorimeter . These studies show that there is an inverse correlation between animal size and metabolism. Or, more simply stated, larger animals have a lower rate of metabolism than smaller ones. Why?

    At least for endotherms, the answer may rely on s/v ratios. Recall that small objects have a larger s/v than larger objects of the same size. Thus, a smaller animal will loose heat more for its size than a larger one (remember Goldilocks? block vs. cube ice?). Thus, it is necessary to metabolize faster to make up for the heat that is lost through the surface.

C.  What determines the lower size limit for an animal?
   Obviously, the smallest animal possible can be no smaller than a single cell. However, let�s consider mammals, and more specifically small humans like the Lilliputians in Gulliver's Travels. Can such small humans exist? To answer this question let�s consider intelligence. As we mentioned above, a smaller animal has fewer cells than a larger one. Thus, a Lilliputian would have a brain made of many fewer cells than Gulliver�s or our own. At a certain point there would be too few cells to allow for human-like intelligence. Further, Lilliputian vision wouldn�t be too good either. As the eye gets smaller the number of rods/cones also declines decreasing visual acuity. This explains why cute little mice have such large eyes compared to their body size. But, why do elephants have such small eyes in comparison to size? As the eye gets larger it will let in more light. At a certain point, so much light will enter that it "blinds" the individual.

    Oops honey, I shrunk my brain.

D. What determines the upper size limit for an animal?  Support
    No matter what size, an animal must support its body. In water this is less of a problem than on land because of the buoyancy of water. Thus, it�s no surprise that most of the earth�s largest animals are aquatic or semi-aquatic (i.e, whales, hippos, brontosaurus).

    Terrestrial animals must support their bodies and fight the force of gravity. One function of leg bones is support. Mechanical engineers know that the height/mass of material that can be supported is a function of the cross sectional area of the support. Thus, the greater the support area, the greater the height/mass that can be supported. Hence, elephants have fatter bones than shrews.

    However, once again recall our discussion of s/v ratios - we concluded that as an object gets larger, its surface area increases as the square of the linear dimension whereas the volume increases as the cube. Thus, volume increases more rapidly than surface area. Consider a typical adult female (5 foot tall and 110 pounds). Let's compare her to a 50 foot tall Brobdingnagian from Gulliver�s Travels.  Since the Brobdingnagian is 10x taller than a typical female, then the Brobdingnagian's mass is 103 times, or 1000x, greater.  Thus, although Jonathan Swift doesn�t tell us, a Brobdingnagian would weigh over 50 tons (110 pounds x 1000 = 110,000 pounds). Since the cross sectional area increases by the square, we expect the area of the femur to be only 102 or 100x larger.  Thus, the femur of these giants will have to support 10x more weight than a typical female - which, a bone can�t do. Oops honey, our enlarged kid has broken bones!

    In short, it is impossible to have normal human proportions carry such a heavy mass. But, then how do some animals get large? (1) shorten the length of the leg bones (think hippos and elephants), (2) smaller head (less mass to support), (3) shorter and fatter neck (compare gazelle, horse, elephant); (4) live in water for support (see above); (5) adapt their posture - a more upright position allows a greater weight to be supported.

E. Constraints on animal size

1. Animals have a mechanical design.
    In other words, they are constructed like a machine, made of numerous, different parts that function together. The parts are highly integrated. Parts cannot be added or removed without reducing the efficiency of the operation of the whole. This makes for a more streamlined body design for motility.

    In contrast, plants have an architectural design. In other words, the plant body is constructed like a building. Essentially a plant is a modular unit made of a limited number of parts, each of which is relatively independent from the others but are united into a single structure. Thus, just like a building is made of rooms, the leaves, stems and roots of a plant are analogous to the rooms in a building. Each room is somewhat independent, yet they all function together to make an integrated whole. You can seal off a room in a building, or remove a leaf or fruit, with little harm to the overall integrity of the structure. This is critical for plants to be able to add or remove parts (leaves, stems, flowers, fruits) as necessary.

    As a result of body design, animals are limited by size and cannot change shape, in contrast to plants. These abilities are important to non-motile organisms like plants to be able to colonize and exploit new areas for resources, but are disadvantageous to an animal because they will make motility more difficult and less predictable.

2. Animals exhibit determinate growth.
    This is the process by which an organism or part reaches a certain size and then stops growing. In contrast plants exhibit indeterminate growth and continue to grow and get larger throughout its life cycle. Again, it�s no surprise that animals are limited by size but plants are not.

F.  Allometric changes (�different measures�)
Increases not proportional to change in size; change occurs at slower or faster rate (slope of line not 1.0)  e.g., BMR � slope = �; bone size increase; cat vs. dog heart; human head growth

G.  Additional changes associated with getting big (Bonner, 2006):

| Top| SGS Home | CSB/SJU Home | Biology Dept | Biol221 Home | Disclaimer |

Last updated: January 06, 2009        � Copyright by SG Saupe