Chromosomes in diploid animals
In diploid animals
both the male and female have two sets of chromosomes; the female egg contains
one of the two sets and the male sperm contains one of his two sets. So when
fertilisation occurs the fertilised egg again contains two sets of chromosomes;
half from the male and half from the female. So the average degree of
relatedness between sisters and brothers is 50%.
Chromosomes in haplodiploid animals
animals the male has only one set of chromosomes as he develops from an
unfertilised egg, so every sperm contains the same one set of chromosomes, in
other words he passes on 100% of his genes in each sperm.
The female however is
diploid so has two sets of chromosomes, and each egg will contain one of these
As males develop from unfertilised eggs this means that sons will
have 100% for their genes in common with the female, and in bees this will be
the queen. This also means that male bumblebees have no father as they do not receive any genes from him at all. . Also the queen passed on only half her genes to her son so she is
related to him by just 50%.
So to recap all males are related to the queen 100%. All males are fatherless. All queens are related to their sons 50%.
The workers (females) will also have received one
set of the possible two of the queen's chromosomes so they will be 50% related
to her, and they will also have received the one set that their father had. And because the male (father) had just one set of chromosomes to pass on he is 100% related to his daughters.
This makes females (queens and workers) 50% related to their queen and 50% related to their father. And fathers 100% related to their daughters.
the difficult bit, the relatedness between sisters. Each sister receives one of
a possible two sets of chromosomes from the queen, and these make up half her
genes, so there is a 50% chance that 50% of her genes will be the same as her
sister's. So that's 50% x 50% = 25%, or 1/2 x 1/2 = 1/4.
Then both sisters get
the same set of genes from the male (their father) as he has only one set. So half their genes
are exactly the same, and if you add this half to the 25% from the queen you
get a relatedness of 75% between sisters.
This means that sisters
(workers) are more related to each other than they are to their mother (queen),
father or even any daughters they could have. So if a worker wants to pass on her genes it makes sense for her to pass them on through sisters who will be raised as queens as they will have 75% of her genes. If a worker did have daughters they would get just 50 % of her genes.
So, should a worker also be better to raise her brothers to pass on her genes rather than having sons of her own. Well the answer to this is no. All her brothers are just 25% related to her - they are in effect half brothers as they had no father. They have just one set of their mother's chromosomes, so there is a 50% chance that they will share 50% of their sister's genes - 25%. This means that if the worker lays her own unfertilized (male) eggs they will be 50% related to her as they will have one of her 2 sets of chromosomes. It is this that leads to the chaos and breakdown of harmony in a bumblebee nest towards the end of summer.
However there is one major
assumption here and that is that the queen mates with only one male, and we
know that this is rarely the case in honeybees, and probably not in some of the
other social insects.