dna - How distantly related are eusocial insects? Aren't members of a species much more related than 1/4, 1/2, or 3/4?

In evolutionary genetic comparison, you are talking about members within species. They will share almost all genes, because if they didn't they would belong to a different species.

However, within species there exist different versions of the same genes, called 'alleles'. When we say that you are 0.5 related to each of your parents, we mean that statistically, 50% of your alleles should be those which your father has, and 50% of your alleles are those passed down from your mother.

Eusocial insects have different mechanisms. Bee males are produced without fertilisation, meaning that they only have one copy of each bee gene. When the male produces sperm, it only has this one set, so all sperms end up carrying the same set of alleles.

Females on the other hand have the normal double set, with two different versions of each gene. So if you look at one gene, half of the female's egg should have one version and the other half should have the other version. All females of one hive are produced by the same queen and the one male that she mated with. Remember, the male only has one set, so the versions coming from the male are the same in all female offspring.

This means a female's genes are made up of: 50% from the father (these are the same across all females) and 50% from the mother (where half the females have one version and half have the other version). Statistically, this means that looking at one gene, there is a 75% chance that two bees will have the same version of that gene.