Thursday, April 28, 2005

 

let's do some simple maths/bio.

you have a dominant gene X and a recessive gene Y. so XX is perfectly healthy, XY is a bit unhealthy but not lethal, and YY usually don't live for too long. let's start with a small percentage, say 10%, of the given population with XY. A XY-XY mate has a 1/4 chance of a YY offspring, which sort of dies after a while; 1/2 of a XY, who lives on; 1/4 chance of XX which is perfectly healthy.

in the case of random matching:
P(XX) = 9/10 . 9/10 . 1 + 9/10 . 1/10 . 2 . 1/2 + 1/10 . 1/10 . 1/4= 0.9025
P(XY) = 9/10 . 1/10 . 2 . 1/2 + 1/10 . 1/10 . 1/2= 0.095
P(YY) = 1/10 . 1/10 . 1/4 = 0.0025
after eliminating the YYs since they die off, XY now occupies 9.52%
it seems that the recessive gene will slowly shrink in size, but as stated by some scientist long time ago, it will not be eliminated (which i guess is still a good thing, with evo in mind)

in the case of eliminating the XY-XY match:
P(XX-XX) = 0.8
P(XX-XY) = 0.2
P(XY-XY) = 0
thus
P(XX) = 0.8 + 0.2 x 1/2 = 0.9
P(XY) = 0.2 x 1/2 = 0.1
status quo.

hm. i dunno what to say. that was not what i was expecting. maybe i should check my workings again. ai, this spoils whatever i've concluded earlier this week =(

argh!

Zhengyu wrote at 6:41 PM.