Surface to Volume Ratios

•Big animal •Large surface area •Big rug

•Small animal •Small surface area •Small rug

Surface Area = Length X Width X Number of Sides Volume = Length X Width X Height 1 centimeter cube Surface area = 1 cm X 1 cm X 6 = 6 cm2 Volume = 1 cm X 1 cm X 1 cm = 1 cm3 Surface to Volume Ratio: 6/1 or 6:1 (6 parts surface area exposed per unit volume)

2 centimeter cube Surface area = 2 cm X 2 cm X 6 = 24 cm2 Volume = 2 cm X 2 cm X 2 cm = 8 cm3 Surface to Volume Ratio: 24/8 or 3:1 (3 parts surface area exposed per unit volume)

Surface Area = Length X Width X Number of Sides Volume = Length X Width X Height

Surface Area = Length X Width X Number of Sides Volume = Length X Width X Height

3 centimeter cube Surface area = 3 cm X 3 cm X 6 = 54 cm2 Volume = 3 cm X 3 cm X 3 cm = 27 cm3 Surface to Volume Ratio: 54/27 or 2:1 (2 parts surface area exposed per unit volume)

Size of Cube Surface Area Volume Surface to Volume Ratio

1 cm 6 cm2 1 cm3 6:1

2 cm 24 cm2 8 cm3 3:1

3 cm 54 cm2 27 cm3 2:1

1 centimeter cube Surface area = 1 cm X 1 cm X 6 = 6 cm2 Volume = 1 cm X 1 cm X 1 cm = 1 cm3 Surface to Volume Ratio: 6/1 or 6:1 (6 parts surface area exposed per unit volume) 2 centimeter cube Surface area = 2 cm X 2 cm X 6 = 24 cm2 Volume = 2 cm X 2 cm X 2 cm = 8 cm3 Surface to Volume Ratio: 24/8 or 3:1 (3 parts surface area exposed per unit volume)

Surface to Volume Relationship

• The larger the animal the lower the amount of surface area exposed in proportion to volume. – Thus there is less heat loss through the skin per

unit volume

• The smaller the animal the greater the amount of surface area exposed in proportion to volume. – Thus small animals lose more heat per unit

volume than large animals.

The rufous hummingbird weighs about 3 grams, roughly the same as a penny. Heart rates: Resting = 250 beats per minute Feeding = 1200 beats per minute Body Temperature: 105 – 1080F

Torpor Due to their small size hummingbirds have a huge problem with heat loss if environmental temperatures are cold.

Bermann’s Rule

• As you go up in elevation or you move towards the poles the temperature?________

• As you go up in elevation you move towards the poles you would expect the body size (or average weight) of an animal to?_________

Bergmann's rule (“B” = Body Size) • Big animals → have larger body masses → more heat is being

produced. • The more cells an animal has → more internal heat will be produced. • Big animals → have a smaller surface area exposed relative to their

body mass (volume) → less heat is being dissipated.

Adult male polar bears weigh between 550 to 1,200 pounds. Exceptionally large individuals weigh as much as 1,700 pounds.

Allen's rule (“A” = Appendages) The long and narrow box (B) has the same volume but 1.75x greater surface area exposed than the shorter and compacted box (A). The greater the surface area exposed (box B) → the faster body heat will be lost to the environment.

A Surface Area = 96 Volume = 64 Surface to Volume Ratio = 1.5:1

B Surface Area = 112 Volume = 64 Surface to Volume Ratio = 1.75:1

A

B

A and B have same volume. B has 1.75 times greater surface area.

• In 1877, the American biologist Joel Allen observed that the length of arms, legs, and other appendages also has an effect on the amount of heat lost to the surrounding environment.

• Among endothermic animals, individuals in populations of the same species living in warm climates near the equator tend to have longer limbs than do populations living further away from the equator in colder environments.

• A body with relatively long appendages → is less compact and → has more surface area exposed.

• The greater the surface area exposed → the faster body heat will be lost to the environment.

• http://anthro.palomar.edu/adapt/adapt_2.htm

Allen's rule (“A” = Appendages)

Hot versus Cold Climates • You are measuring the average weight, ear

lengths, and leg lengths of two populations of coyotes; one in Alaska and one in Joshua Tree National Park (desert).

Hot versus Cold Climates • You are measuring the average weight, ear

lengths, and leg lengths of two populations of coyotes; one in Alaska and one in Joshua Tree National Park (desert).

• Which population would you expect to have a higher average weight?

• Which population will have an average longer ear length?

• Which population will have an average shorter leg length?

Surface to Volume Ratios

• What is the advantage of having a smaller body size in the desert? – Hint: Do you want to retain heat or lose heat on a

hot day in the desert?

Why are cells so small?

Cell # 1 Cell #2

1. Which cell has a greater surface area exposed in proportion to volume? 2. Which cell will be able to get more oxygen across its cell membrane in proportion to volume? (The cell needs to get oxygen from the environment across the cell membrane to the mitochondrion to make ATP)

Surface to Volume Ratios SMALLER CELLS HAVE MORE SURFACE AREA EXPOSED IN PROPORTION

TO VOLUME than large cells → smaller cells are more efficient at transporting material across their cell membrane

The Smaller the object,

the Larger the SURFACE AREA EXPOSED PER UNIT OF VOLUME → more efficient to exchange its internal content with the environment

Mouse to Elephant Curve

• Why would you expect a mouse to have a higher metabolic rate per unit body weight than an elephant?

• Which would you have to feed more per unit body weight, a mouse or an elephant?

Kit foxes are the smallest foxes in North America. They have exceptionally long ears, a slender body, long legs, and a long tail. What habitat in California would you expect this fox to be found in?

• Does the body plan of the kit fox follow the principles of Bergmann’s and Allen’s rule? Explain.

• Average weight is 3.5 to 7 pounds

• Large ears: 2.8 – 3.75 inches

• Body without tail: 18 – 21 inches

• Tail: 9.85 – 13.4 inches