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

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

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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

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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

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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)

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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

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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

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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.

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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

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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

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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.

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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

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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

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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

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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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