[ExI] biology term

[Anders]

We can model it like this: assume the probability that one chromosome 
has the mutation is p. The risk of having two copies is p^2, one copy 
2p(1-p). When you have one copy you have fitness y, with two fitness x, 
and fitness 1 if one has none. Finally, there is a probability q that a 
new mutation will make a chromosome to switch to the mutation.

Given this, the next generation will have (1-q)^2(1-p)^2 + y(1-q)p(1-p) 
chromosomes without the mutation (first term matings between 
non-carriers, second matings between heterozygous people). There will be 
xp^2 + y(1-q)p(1-p) + (1-(1-q)^2)(1-p)^2 + yqp(1-p) copies (matings 
homozygos people, heterozygous, mutations in non-carriers and in 
heterozygous carriers).  Normalizing we get

p = [ xp^2 + y(1-q)p(1-p) + (1-(1-q)^2)(1-p)^2 + yqp(1-p) ]/ 
[(1-q)^2(1-p)^2 + y(1-q)p(1-p) + xp^2 + y(1-q)p(1-p) + 
(1-(1-q)^2)(1-p)^2 + yqp(1-p) ]

I need to catch a flight, so I do not have the time to do the algebra, 
but if you do this right (I may have dropped a term or a factor 
somewhere) you will get an equilibrium p dependent on x, y and q. q 
refills the population even if there is no heterozygous advantage.


On 2016-10-12 05:10, spike wrote:
>
> With the topic of Lee Corbin coming up, I am reminded of the last discussion
> we had, which has been nearly a year ago.  I may bring up topics for the
> next couple of months or more as I think of them: things he and I discussed
> when together.
>
> I don't know the terminology in genetics which is why I can't look up the
> answers, but I think we have some biology hipsters here.
>
> When a mutation is recessive and each parent carries one copy, there is
> about a 25% chance the offspring will inherit both copies of the mutation.
> In the case of a lot of genetic diseases, if either copy is the
> non-mutation, then the disease is not expressed.  So if two carriers of that
> mutation mate, then the offspring have about a 50% chance of being a carrier
> and about a 25% chance of being free entirely of the mutation.
>
> In the case of Tay-Sachs disease, it is known that some populations (such as
> Ashkenazi) have a number of carriers, so the Jewish couples have a known
> risk of suffering the heartbreak of a Tay-Sachs baby, who will not survive
> to bring them grandchildren.
>
> Given that a mutation is detrimental in some cases, why does that mutation
> survive in a population?  A theory that Lee Corbin and I kicked around is
> that in every case where a mutation carries the risk of causing infant death
> in a homozygote, there should be some health benefit somehow to the
> heterozygote carriers.  In the case of Tay-Sachs, that benefit is an
> increased resistance to tuberculosis.  Another example is sickle-cell anemia
> gives the heterozygote carriers increased resistance to malaria.
>
> Biology hipsters, what is that phenomenon called?  If I don't know the name
> of something I could waste hours Googleing around and finding nada.  Lee
> didn't know the term either.  That kind of disease, expressed only in
> offspring of two carriers, should have a name.  There might be a name to the
> theory that all such maladies must have some corresponding benefit,
> otherwise the mutation would gradually disappear due to reduced viability of
> the offspring.
>
> spike
>
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-- 
Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University