[ExI] biology term

[Anders]

I found the book in my office, the relevant section starts on page 124.

If the fraction of chromosomes with allele A is p and the remaining 
q=1-p have allele a, then if the fitness of AA is w1, Aa w2 and aa w3, 
the possible equilibrium fraction is p=(w2-w3)/((w2-w1) + (w2-w3)) 
(beside the obvious cases of p=0 and 1). If the fitness w2 is set to 1 
and w1=1-s and w2=1-t we get the nice formula p/q = t/s, which is valid 
even if they both are negative (i.e. there is a heterozygous 
disadvantage) but it is not a stable equilibrium.

On p. 131 they show that adding mutations does not change the situation 
much: the equilibrium doesn't shift much for reasonable mutation rates. 
This also means that if there is no heterozygous advantage at 
equilibrium mutations will only add a small fraction of the allele.



On 2016-10-14 08:43, Anders wrote:
> On 2016-10-14 01:26, spike wrote:
>>
>> In the old days before the internet, we worked out equations like 
>> this.  Now
>> notice I first Googled, then asked my community of gurus (found the 
>> answer
>> that way) but didn't start with trying to derive the equation. The 
>> object
>> lesson was not missed: next time, calculate first, wait for that 
>> approach to
>> fail, then look up the answers.  I was lazy because biology isn't my 
>> area of
>> expertise.  Had it been an orbit mechanics question, I mighta calculated
>> first.  Now... no more lazy for the spikester.
>
> To be fair, this kind of genetic equation is a mess, and if one is not 
> careful there will be confusion. I would suggest grabbing a copy of 
> "The Genetics of Human Populations" by Luigi Cavalli-Sforza - this is 
> an awesome pre-genomics book, describing the classical state of the 
> art. I know it solves balanced selection in one of the early chapters.
>
> Or, one can have fun and make a Monte Carlo simulation. Little agents 
> with two chromosomes swim around, randomly mate, mutate, and their 
> offspring survive at different rates...
>
> I would try to hack that together right now, in fact, but I need to 
> rush to a tutorial. I got a student! Muhahahaha!!! So I guess this can 
> be left as an exercise... :-)
>

-- 
Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University