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How Leopards get Their Spots Will Brennan

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One was developed by James Murray, and the other was developed by David Young ... if AD - w*ID = 0 leave the central cell unchanged. Model in Action. Young's model ... – PowerPoint PPT presentation

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Title: How Leopards get Their Spots Will Brennan


1
How Leopards get Their SpotsWill 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
  • 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)

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
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

8
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.

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
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

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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