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I am confused about how to compute probabilities for linked genes.

The problem that I am solving is this:

  • P generation: AAbbddEEff X aaBBDDeeFF. If A and B are 40 centimorgan apart, what is the probabilty to get aabbddeeff in F2?

Here is what I have:

  • F1 is: AaBbDdEeFf.
  • The next cross it goes through is this: AaBbDdEeFf X AaBbDdEeFf.
  • To compute this cross, I drew the 2 chromosomes for AaBb (in coupling), and then the probability for a is 0.5 (A or a) and the possibility for no recombination is 0.6. So 0.5 x 0.6 = 0.3. The same goes for b, so aabb is: 0.3 x 0.3 = 0.09.
  • For ddeeff: 0.25x0.25x0.25 = 0.015625.
  • Multiplying these gives 0.09 x 0.015625 = 0.00140625.
  • Extending that and for 2 gametes gives this: (0.00140625)^2 = 0.00197x10^-3.

But the correct answer is not what I have computed, but instead is 0.000625.

I'm really confused with this question. If we know that only 2 of the 5 genes are linked, is it still correct to multiply: 0.09 x 0.015625 = 0.00140625? Maybe I should use a Punnett square somehow? Because in that case, the probability for a recessive homozygous is 0.0625 but I'm not sure it fits to this question.

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0.000625 looks right to me. On one chromosome, you have a 50% chance of a. Then you have a 40% chance of b (if and only if a crossover occurs). These multiply out to 20%. You multiply that by 50% for three unlinked genes to get 2.5% abdef.

Your approach was correct overall, but you used a 60% chance of b, so your final answer was too high by (60%/40%)^2. Don't let capital and small letters trick you - ab comes from a recombined chromosome.

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  • $\begingroup$ Thank you. Just to clarify, when you say: "ab comes from a recombined chromosome", it's only in the case that the alleles are in 'repulsion'? And for the unlinked genes I used 25% because I thought I need to use Punnett square (for example, if we want dd from Dd x Dd the chance is 25%). But the correct way is to say "50% chance of d/e/f", because I need to consider the chromosomes? @Mike Serfas $\endgroup$
    – user64444
    Feb 25 at 10:43
  • $\begingroup$ Repulsion is a sort of old-fashioned way to put it. Just think that A and b are physically linked by a strand of DNA inherited from one parent, as are a and B. The odds that these strands will be cut and spliced to make ab and AB is 40%. For the unlinked genes your math was accurate - I multiplied by 50% chance of d, e, and f, then multiplied the 2.5% chance of abdef by itself, while you multiplied by 25% chance of dd, ee, and ff one at a time, but it works out the same. $\endgroup$ Feb 25 at 12:26

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