15
How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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

Embed Size (px)

Citation preview

Page 1: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

How Leopards get Their Spots

Will Brennan

How Zebras Get Their Stripes

Page 2: 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?

Page 3: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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

Page 4: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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

Page 5: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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)

Page 6: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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

Page 7: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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

Page 8: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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.

Page 9: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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

Page 10: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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

Page 11: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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.

Page 12: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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

Page 13: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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

Page 14: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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

Page 15: How Leopards get Their Spots Will Brennan How Zebras Get Their Stripes

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