# How to calculate relatedness in haplodiploid organisms (mainly full sisters and full brothers)?

I have tried to calculate the relatedness for haplodiploid organisms, but cannot understand the calculations behind full sister and full brother.

(taken from Wikipedia: haplodiploidy

I have managed to solve the other cases. Since female will have ZZ:

female will share 1/2 of her genes with daughter

female will share 1/2 of her genes with son

female will share 1/2 of her genes with mother

female will share 1/2 of her genes with father

Since male will have only Z:

male will share 1 (100%) of his genes with his daughter

male won't share anything with his son (unfertilized eggs leads to male in haplodiploidy system)

male will share 1(100%) of his genes with his mother

male won't share anything with his father (unfertilized eggs leads to male in haplodiploidy system)

Even though I figured out how others work, I wasn't able to calculate r for fullsister fullbrother? How can it be 3/4,1/4,1/2,1/2?

• Is this a homework question? If so, you should sow us the work you've done so far, including the ones you already figured out. Commented Sep 25, 2014 at 10:35
• The table is taken from Wikipedia: Haplodiploidy, right? If so, you should include a reference. Commented Sep 25, 2014 at 10:46

It is useful to think in terms of the proportion of genetic material that an individual gets from each parent and the amount of this genetic material that will be shared with another individual (on average), and then sum this together i.e. as:

$relatedness = prop_{mother} * shared_{mother} + prop_{father} * shared_{father}$

A female will share 50% of the genetic material from the mother's side and 100% if the material from the father's side with her full sisters: $0.5*0.5 + 0.5*1 = 0.75$

A female will share 50% of the genetic material from the mother's side and 0% if the material from the father's side with her brother: $0.5*0.5 + 0.5*0 = 0.25$

A male will share 50% of the genetic material from the mother's side with his sister (and doesn't get any from the father's side).

A male will share 50% of the genetic material from the mother's side with his brother (and doesn't get any from the father's side).

Remember also that this only holds if the female has only mated once.

• A female will share 50% of the genetic material from the mother's side and 100% if the material from the father's side with her full sisters--then it should be 0.5*0.5+1*1 right? and A female will share 50% of the genetic material from the mother's side and 0% if the material from the father's side with her brother: 0.5∗0.5+0*0 right? Commented Sep 27, 2014 at 18:14
• A female still gets 50% of her genetic material from each parent, so it should be 0.5 in both calculations. The first case you suggest would lead to a relatedness of 1.25, which is clearly impossible. Commented Sep 27, 2014 at 23:10
• Yes but are we using 0.5 because 1.25 is impossible? Commented Sep 30, 2014 at 14:00
• No, because 50% (0.5) of the genetic material in a female comes from each parent. Commented Sep 30, 2014 at 14:16
• okay relatedness=propmother∗sharedmother+propfather∗sharedfather Does this generalised statement apply in all cases other than haplodiploidy to calculate relatedness? Commented Oct 1, 2014 at 6:27

This is a relative thing in haplodiploidy system.

r = Mother's side + father's side(in this case)

D--Daughter

S--Son

F-Father

M-Mother

Note:

You can get the below things from the question image itself.(All that you need to do is to read male and female appropriately as son,father,mother,daughter based on the context.So simple!)

1.rMD=1/2

2.rMS=1/2

3.rDM=1/2

4.rDF=1/2

5.rFD=1

6.rFS=0

7.rSM=1

8.rSF=0

case 1:

rDD=(rDM*rMD) + (rDF*rFD)

rDD=(1/2*1/2)+(1/2*1)

rDD=3/4 case 2:

rDS=(rDM*rMS) + (rSF*rFD)

rDS=(1/2*1/2)+0*1

rDS=1/4 case 3:

rSD=(rSM*rMD) + (rDF*rFS)

rSD=(1*1/2)+(1/2*0)

rSD=1/2 case 4: