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How Fast Does A Mutation Spread

Bailey's Pocket Mouse (Chaetodipus baileyi) is...

Pocket Mouse

The Rock pocket mouse (Chaetodipus Intermedius) is both sandy colored and black. They inhabit in the American southwest and I am writing specifically about those inhabiting Pinacate Peaks New Mexico. The natural predators of this mouse are owls. That is why their sandy coloration is beneficial to their survival. About 1.7 million years ago there were lava flows in the area that hardened into a dark almost black rock. Against that background the survival benefit from a sandy colored coat vanished. There is one mutation, totally random, which is why evolution works, that gives the mouse a black or dark coat. In 2003 the DNA of the mice was sampled from both variations of mouse and it was found the difference was in the Melanocortin-1 receptor (MC1R). Light colored mice have 2 light-colored genes while 1 or 2 of the genes are the dark variety in black mice.

How often a black mutation randomly appears depends on the mutation rate,  the reproduction rate and the population size. Considering the mutation rate, there are 2 Billion sites in the DNA of the mice, 10 sites in MC1R gene x 2 genes multiplying out to a 1 in 25 million chance that a mouse will have a black coat due to random mutation. Sounds pretty small doesn’t it? The rate of reproduction varies between 3-6 with an average being about 5 offspring per year per female. In a population of 5000 females that means there will be 25000 offspring per year. Multiplying the mutation rate by 25000 tells us that there will be at least 1 black mutation every 1000 years. Considering the pinacate lave flows are 1.7 million years old, that means the black mutation could have arisen at least 1700 times during that time span.

How long would it take to spread through the population? That depends on population size and s which is a selection coefficient (measure of advantage) it is a relative measure of fitness and a product of reproduction and survival. A 1% advantage is written as s= 0.01. An  s= 0.01 means at 1000 generations 95% of the population has the mutation and would be totally black. In real life, the survival advantage is over 10% which is written as s=0.1 and after a mere 100  generations 95% of the population would have black coats.

In conclusion, a 1% survival advantage is really not low or as some history deniers (creationists) would claim highly improbable. Mutations can and do spread faster than most people realize.

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