1. How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

2. Spots and Stripes  Skin coloration is caused by melanin  What is the cause of specific patterns such as spots and stripes?

3. Modeling animals  Spot and stripe arrangement are random and distinct, yet share a definite pattern…  This led mathematicians to realize that there must be some way to model the phenomena

4. Models Emerge  Two models emerge: –One was developed by James Murray, and the other was developed by David Young  Both models both incorporate the same elements however: reaction- diffusion

5. Young Model  Young’s model is based off of cellular automata modeling  Young has 4 assumptions on his model: –There are two types of cells; colored(D) and uncolored(U) –The colored cells secrete 2 morphagens; an inhibitor(I) and an activator(A)

6. Diffusion of Morphagens  As the D cells release the A and I morphagens, they diffuse throughout the environment  Near the D cells, there is a higher concentration of A, but this is inverse with its distance from D

7. What’s it all mean?  Cell type is determined by the concentration of the morphagens in its area  If over a U cell, A>I then the cell will switch to a D and start producing morphagens  Conversely, if over a D cell, I>A, then it will change to a U

8. How does this explain the patterns?  if AD - w*ID > 0 set the central cell to D,  if AD - w*ID < 0 set the central cell to U  if AD - w*ID = 0 leave the central cell unchanged.

9. Model in Action  Young's model Young's model  The shape of the patterns can then be changed by inputting different variables for the area of the model

10. Murray’s model  Also based on reaction-diffusion, but concentrated on the rate of diffusion as opposed to concentration  Also had two chemicals; an inhibitor and an activator working on the cells

11. Speed is of the essence  The chemicals work at different speeds; –The activator is slower –While the inhibitor is faster  This disparity in speed allows the inhibitor to surround the activator during diffusion, causing a spot.

12. An Analogy  Forest Fires mimic this same dynamic  Fires burn first, but diffuse slowly.  Firefighters respond, spraying untouched trees surrounding the fire with anti- inflammatory chemicals, containing the fire in Spots

13. Theory in action  By changing the rate of diffusion then, the pattern will be different.  Murray also found as Young did that shape plays a role in the development of the pattern

14. Spots vs Stripes  Since spotted leopards and striped tigers are about the same adult size, he concluded that it must happen during development  i.e. the zebra resembles a long thin pencil like shape during development, resulting in its stripes

15. Harmony  Although Murray and Young used slightly different methods to model the formation of spots and stripes, they both agreed that it can be solved through mathematical modeling