WHY COULD INSECTS THIS LARGE NEVER EXIST?YouTube Tarantula Trailer

• Exoskeleton too weak

• When shed exoskeleton when molting, collapse under weight

• Limits on nest size

• Respiratory capacity

Clicker Question warmup

As the radius of a cell increases, the surface area to volume ratio of the cell

a) Increasesb) Decreasesc) Stays the samed) Insufficient data to answer this question

A Review: Surface Area/Volume and Maximum Cell Size

Volume of a sphere

= 4/3πr3

Surface area of a sphere

= 4πr2

Surface to volume ratio

= 3/r

Relationship of Surface Area to Volume as a Function of Cell Radius

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5

Cell Radius

Surface Area / Volume

nutrients

wastes

Respiratory System of Insects

•Exoskeleton with waxy cuticle prohibitssimple diffusion through epidermis•No blood vessels, so no lungs•Tube system that carries O2 from surfaceto cells and takes up CO2

Tracheal tube system

Tracheal volume data Length of Beetles Tracheal volume

(as % of body volume)

17mm 1.9%18mm 2.1%27mm 3.3%47mm 5.7%60mm 7.4%62mm 7.6%80mm 9.9%129mm 15.8%

Graph the data and determine the relationshipbetween tracheal volume and beetle body length.

•What is the mathematical formula describing the relationshipbetween these two variables?A) x2 + y2 = 0B) y = mx + bC) y = log xD) y = 1/x

•What does this information tell us about insectsize and tracheal system size?

Let’s do some math!

SMALL INSECT

Oxygen depleted if tube diameter stays the same

Large Insect

Tracheole volume larger to accommodate needs

SUMMARY OF THE PROBLEM

LARGE INSECT

•Based on your data, what is the theoretical maximum length of a beetle?

The largest living beetle today actually is 170 mm.•What do you think limits the body volume that an insect can devote to the tracheal system?

One step further…

During the Carboniferous (350 mya) there were insects much larger than any found on Earth today. •Develop a hypothesis from this observation.•How would you test your hypothesis?