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How Leopards get Their Spots Will Brennan

How Leopards get Their Spots Will Brennan. How Zebras Get Their Stripes. Spots and Stripes. Skin coloration is caused by melanin What is the cause of specific patterns such as spots and stripes?. Modeling animals.

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How Leopards get Their Spots Will Brennan

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  1. How Leopards get TheirSpotsWill 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 • 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

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