How Leopards get Their Spots Will Brennan

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How Leopards get Their SpotsWill 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

• Youngs 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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Whats it all mean?

• Cell type is determined by the concentration of
  the morphagens in its area
• If over a U cell, AI then the cell will switch
  to a D and start producing morphagens
• Conversely, if over a D cell, IA, then it will
  change to a U

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How does this explain the patterns?

• if AD - wID 0 set the central cell to D,
• if AD - wID
• if AD - wID 0 leave the central cell
  unchanged.

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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

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Murrays 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