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Backgound

My question has risen from this post made in 2014 on BioSE.

The question is how is genetic relatedness calculated for full sisters?

Genetic relatedness (r) is the probability that a random gene of the recipient will be identical to that of the altruist of close descendens.

This comes from the concept that an alturist sacrifises its reproducive life increasing the possibility that the reproductive life of its relatives are improved when rB>C (Hamilton's rule).

Now coming directly to the main thing: For full sisters of Hymenopterans where males are haploid(having only one set of chromosomes) and females are diploid(having a pair or two sets of chromosomes) r= 3/4 .

Problem

The following answer from the linked post explains how it is so:

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I was trying to find the mathematical basis of the formula the user has given. I presume the multiplication rule of probability must be applying to this.

But I'm not able to decipher the 'proportion' thing the user has used. Is it the probability of getting a gene that was inherited from one of the parent?

Then the 'shared' thing is the probability that the same gene was passed done to the other daughter from that parent?

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    And you did not ask this to the OP of the answer on Biology.SE because? You did not even mention this post to them? – 2017-02-06
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    No I didn't. I had just the same question as somebody had already asked the OP of the answer.I wasn't satisfied with his answer to those queries, so I decided to post here. – 2017-02-06
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    These are poor rationalizations. Be aware that failing to mention to the OP on Biology.SE that you are posting this could be considered by many as bad manners. – 2017-02-06
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    I'll inform him then and ask for apologies for not having informed earlier. – 2017-02-06

1 Answers 1

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Males are haploid: have singleton chromosomes.   A 100% proportion of this comes from their female parent, and 0% from any male.   They share 100% of their chromosomes with their female offspring, and they don't generate male offspring.

Females are diploid: have paired chromosomes.   A 50% proportion of which comes from each of two parents, a male and a female.   They will share 50% of their chromosomes with any one of their offspring, male or female.

So: 50% of a daughter's DNA is 50% their mother's DNA and the other 50% is 100% of their father's DNA.

On the other side, 100% of a son's DNA is 50% of their mother's DNA.

So: relatedness

  • relatedness of full sisters = $0.5\cdot 0.5+0.5\cdot 1 = 0.75$
  • relatedness of sister to full brother = $0.5\cdot 0.5 + 0.5\cdot 0 = 0.25$
  • relatedness of brother to full sister = $1\cdot 0.5 + 0 = 0.5$
  • relatedness of full brothers = $1\cdot 0.5 + 0 = 0.5$
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    I got it. Thank you. So my consideration that the product rule of probability has something to do with this, isn't right? I actually felt so because `Genetic relatedness (r) is the probability that a random gene of the recipient will be identical to that of the altruist of close descendens.` – 2017-02-06