Introduction to Organismal Biology (BIOL221) - Dr. S.G. Saupe; Biology Department, College of St. Benedict/St. John's University, Collegeville, MN 56321; ssaupe@csbsju.edu; http://www.employees.csbsju.edu/ssaupe/

Surface-to-Volume Ratios

Introduction:  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.   

    We will be doing a lab exercise on surface/volume ratios.  Or, you can check out the exercise that gave rise to this lab exercise.  To test your understanding of s/v, can you answer the following questions?

Calculations/Predictions:

1. Consider the movie, �Honey, I Shrunk the Kids� in which Wayne, a brilliant but klutzy scientist accidentally shrinks his kids to about an inch tall.  If his daughter was initially 4 foot tall and weighed 75 pounds, how much did she presumably weigh after being shrunk to one inch? 

2. Consider the classic Grade B horror movie, �The Attack of the 60 foot Woman.�  How much would this woman weigh?  Assume an �average� woman who is 5 foot tall weighs 110 pounds.

3.  According the Guinness Book of World Records the tallest living human female is 7 feet 7 � inches tall.  Using our assumption that a 5 foot woman weighs 110 pounds, how much do you predict this woman weighs?  __________.  (note:  her actual weight = 462 pounds)

 Other questions:

1. Explain why leaves are broad and flat.
2. Why do elephants have large, flat ears?
3. Explain why roots have "hairs."
4. Explain why the shape of animals is basically "spherical", whereas plants and fungi are "filamentous".
5. Explain why small animals have a higher metabolic rate than large animals.
6. Explain why shrews are voracious feeders.
7. Explain why cats can fall off tall buildings and survive. Why do people splat?
8. Explain the advantages/disadvantages of block vs. cube ice.
9. Describe the scientific inaccuracy in the episode of Goldilocks and the porridge.
10. Explain why lungs, gills and intestines have the shape they do.
11. Medieval churches were often built in the shape of a crucifix. Explain why.
12. The earth is geologically active (has a molten core) but the moon is apparently no longer geologically active. Explain why using S/V ratios.
13. Why are there few small animals in the arctic?
14. Explain how S/V ratios relate to the form of plants that have evolved in mesic, xeric and hydric environments.
15. Explain why the cells of the spongy layer of a plant leaf are irregularly shaped.

Allometric Growth in Humans or Why are babies so cute?
     In this exercise we will compare the growth of the human head to the rest of the body through the course of development.  Examine the images of human growth provided in the public folder.  Use a ruler to measure head length and body length in millimeters.  Calculate the head/body ratio and then plot H/B ratio vs. age (months).  What do you conclude from this graph?