My question is about the classic study cited below (*) and available as a free pdf download from
http://www.genetics.org/content/28/6/491.full.pdf+html
At page 495 the authors use the "average division time" of bacteria dt, divided by ln(2), as the time unit in the equations
(1) dN_t...
tert-butyl bromide reacts with HOH to give HBr and the corresponding alcohol ,
C
C-C-C
OH
But tert-butyl alcohol reacts with HCl to give tert-butyl chloride.
HBr is a "stronger" acid than HCl. Is this part of the explanation of the different reactions?
Our formulas give the same sequence, bearing in mind you are looking at males and I am looking at the whole population, so my result x 2 = yours. Also our numbering is different. My index 1 is your 2.
You: 1 - (-1)^n / 3
n=1 1/2
n=2 3/12
n=3 9/24
n=4 0,3125
n=5 0.34375
n=6 0.328125
Me...
For the items above the [snips]--yes, you have consistently said 1/3 of the males and that is correct. Just wanted to be sure.
My formula is taken directly from the table above it--you can read the sequences d_n, e_n right off the table. Each column gives the numerator of d_n, e_n, and the...
1/3 of the males, you mean? And 1/6 of the population...? I noticed below your said the approach to 1/3 was for xY, but I get 1/3 for XY and 1/6 for xY, with xY as an "afflicted" male? I assumed that was because you were only looking at the males.
My recurrence formula gives both d and e. d is...
Well, the easiest way is to construct the following three lists:
1--- 3--- 5--- 11---21
3--- 5--- 11---21---43
8---16---32---64---128...
If d_1 is 1/8 and e_1 is 3/8,... inductively, d_6 will be 43/256, and e_6 will be (128-43)/256.
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This is an easy...
While I am looking for your simpler formula for affected males, it may be that the equations are the simplest possible for studying the effect of differing starting proportions generally. For example, we might ask what is the effect on the ultimate proportion of d = xY when we vary the starting...
Better not shout Eureka yet, but I've now got a simple formula that for F1, F2, F3, agree with your calculated figures. Tell me whether your computer calcs. give you for x/(x + X) ratio in the males, F4 0.3125, F5 0.34375 ? I did not use Mathematica nor even a scientific calculator.
Note the...
"...BTW I got 48 not 46 in F3."
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Yes it's 1,2,48, 10240,...,etc. "Worked for me in Mathematica" means that I programmed the equations in Mathematica and entered a set of initial conditions (a vector). It's easy to do the first few generations by hand but to see the variables...
The last set of equations quickly shows a:b:c:d:e approaches 1:4:4:3:6, but on reviewing your note, I finally see that if we know that the proportion of x:X in each generation is 1:2, we can use elementary probability to get these (equilibrium) ratios. For example, probability of being a female...
xx=a, xX=b, XX = c, xY=d, XY=e.
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In good conscience, in case someone tries to do this, I will put down in terms of a,...,e the equations that actually finally worked for me in Mathematica.
a' = 2ad+bd
b'=2ae+bd+be+2cd
c'=be + 2ce
d'=bd + be +2ad...
" If you as you now say you begin with one pair there is a definite chance they will produce things like only xY male progeny, only XY male progeny or for that matter only male progeny or only female progeny, chances that diminish the larger the population."
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I should have been...
Thanks.
No, I'm starting from Xx*XY, a carrier female and a normal male. If we started with a large population I think we'd have H-W conditions and statistical stability. Instead, we begin with one pair. We can take as our original vector F_2 = {0,1,1,1,1}, or F_1 = {0,1,0,0,1}. Each...