genetics - 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?

Answer

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.r_MD=1/2

2.r_MS=1/2

3.r_DM=1/2

4.r_DF=1/2

5.r_FD=1

6.r_FS=0

7.r_SM=1

8.r_SF=0

case 1:

r_DD=(r_DM*r_MD) + (r_DF*r_FD)

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

r_DD=3/4 case 2:

r_DS=(r_DM*r_MS) + (r_SF*r_FD)

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

r_DS=1/4 case 3:

r_SD=(r_SM*r_MD) + (r_DF*r_FS)

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

r_SD=1/2 case 4:

r_SS=(r_SM*r_MS) + (r_SF*r_FS)

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

r_SS=1/2