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Posted by Amanda E on May 08, 2003 at 14:58:06:
In Reply to: Hmmm, let me see if I can rephrase one... posted by Hurley on May 08, 2003 at 10:53:22:
:...since that post rambled on and I was just having fun working problems. LOL What's causing the jam?
:Quick fraction review, feel free to ignore. :D
:Basic math tells us that to multiply fractions, you multiply the numerators across for the answer's numerator, and the denominators across for the answer's denominator. So, for example, multiplying 2/3 times 3/4 = 6/12...3/6...1/2. Adding them requires the denominators to be equal, so convert 2/3 and 3/4 to a common denominator, and the problem becomes 8/12 + 9/12 which then equals 17/12.
:OK, so...I'll lose my shorthand and express everything as aa bb cc.
:Let's say:
:a = amel recessive mutant
:A = wild type at amel locus>normal
:n = anery recessive mutant
:N = wild type at anery locus>normal
:If I want to figure numbers for a clutch from Normal het snow x Snow parents, I'd express the parents as: AaNn (female normal het snow) x aabb (male snow)
:So, from this, we know that the chance of getting each gene is:
: *AaNn *aann
: 
:a = 1/2 a = 1/1
:A = 1/2
:and
:n = 1/2 n = 1/1
:N = 1/2
:So, from this we know that the chances of getting
:aa = 1/2 (1/2 x 1/1 = 1/2)
:Aa = 1/2 (1/2 x 1/1 = 1/1)
:AA = Not possible (1/2 x 0/0 = does not exist)
:nn = 1/2
:Nn = 1/2
:NN = Not possible.
:
:Alright, what are the possible combos using these 2 mutations?
:Normal (AANN, AaNN, AANn, and AaNn)
:Amel (aaNN and aaNn)
:Anery (AAnn, Aann)
:Snow (aann)
:
:So, let's take the simplest one...snow.
:Chance of getting a snow:
:aa = 1/2, nn = 1/2.
:
:1/2 x 1/2 = 1/4 aann.
:aa x nn
:
:Chance of getting an anery:
:
:Chance of getting AA or Aa? 0/0 + 1/2 = 1/2
:Chance of getting an nn? 1/2
:1/2 x 1/2 = 1/4 Axnn.
:
:Chance of getting an amel:
:aa = 1/2
:NN or Nn = 1/2
:aaNx = 1/4
:
:Chance of getting a normal:
:AA or Aa = 1/2
:NN or Nn = 1/2
:AxNx = 1/4
:Note: I use x to mean that it doesn't matter if that letter is 'A' or 'a'.
:Summary:
:Snow (aann) = 1/4
:Anery (Axnn) = 1/4
:Amel (aaNx) = 1/4
:Normal (AxNx) = 1/4
:OK, so I only took into account phenotypic outcome in this one...
:Want to do one with figuring genotypes this time?
:
:Same genes, let's do Normal het snow x Anery het amel, for spice.
:AaNn x Aann
:
:1/2 a ___1/2 a
:1/2 A __1/2 A
:1/2 n ___1/1 n
:1/2 N
:
:Chances on the A's
:
:(1/2 A x 1/2 A) = 1/4 AA
:(1/2 a x 1/2 A) + (1/2 A x 1/2 a) = 1/4 + 1/4 = 2/4 = 1/2 Aa
:(1/2 a x 1/2 a) = 1/4 aa
:Checking myself to make sure I got that right...1/4 + 1/2 + 1/4 = 4/4. Yep. :)
:
:Chances on the N's
:
:(1/2 N x 0/0 N) = NN not possible.
:(1/2 n x 0/0 N) + (1/2 N x 1/1 n) = 0/0 + 1/2 = 1/2 Nn
:(1/2 n x 1/1 n) = 1/2 nn
:1/2 + 1/2 = 2/2...all there. :)
:Chance of snows (aann) = 1/4 aa x 1/2 nn = 1/8 snows.
:Chance of amels (aaNn + aaNN) = (1/4 aa x 1/2 Nn) + (aaNN not possible) = 1/8 amels (100% het for anery).
:Chance of anerys (Aann + AAnn)
:(1/2 Aa x 1/2 nn) + (1/4 AA x 1/2 nn)
:= 1/4 Aann + 1/8 AAnn
:= 2/8 + 1/8
:= 3/8 anerys (67% het for amel).
:The 3/8 anerys being comprised of 2/8 Anery het amel and 1/8 Anery ...so you can express the Anerys as 67% (2 of 3) chance het amel.
:Chance of normals (AaNn, AANn, AaNN, AANN)
:
:Aa + AA = 3/4, NN + Nn = 1/2
:= 3/4 x 2/4 = 6/18
:= 3/8 Normals
:Of the 3/4, 2 are Aa, 1 is AA, so 67% chance het amel
:Of the 2/4, 2 are Nn, 0 are NN, so 100% chance het anery
:= 3/8 Normals het anery (67% chance het amel)
:
:...and a last check to make sure everyone's accounted for: 1/8 + 1/8 + 3/8 + 3/8 = 8/8.
:Summary:
:
:1/8 Snow
:1/8 Amel het anery
:3/8 Anery (67% het amel)
:3/8 Normal het anery (67% het amel)
:
:
:Here's to hoping a different look at the same material lifts the logjam. :D After a while, you can just look at the crosses and do them in your head...and that's a great party trick. ;)
:
:Hurley