I value your knowledge of beekeeping and may come to you in the future, since rumblings of beekeeping are abound at home and I'm in two minds about being COVERED IN BEES.
A few points:
Termites are not closely relate to the Hymenoptera. The bees, ants and wasps. Their closest living relatives are cockroaches, and they evolved their eusocial characteristics independently. When I have time I'll research the evolution of queen-led colonies in Hymenoptera, as I don't know it is happened once and has been secondarily lost in some species, or has evolved independently on multiple occasions. To wit: there are solitary bees and solitary wasps, but no solitary ants.
I don't know of any genetic barrier to the evolution of queen colonies in vertebrates. I think you're confusing the chromosomal determination of sex as it is in bees with what permits eusociality. As it is, there is a great many means of genetically determining sex in the animals of the world. The only problems I can see are in those that can change sex, and those (such as crocodiles) whose sex is determined by temperature during incubation. In chickens, for example, YY is male and XY is female. And the platypus (or was it the echidna?) has about a dozen X and Y chromosomes, of which only the last one matters to the sex of the individual.
From and evolutionary perspective, colonies are simple than they seem. Only the queens and the drones are present in the gene pool, the rest of the colony exist to aid them. It's like the way aunts will care for their nieces, indeed, both aunts and worker bees have a genetic evolutionary interest in their nieces and reproductively fertile sisters. The genes that make good workers are present in the queen, and effectively enhance the fitness of that queen even though they may not be expressed in her.
Another parallel can be made with the cells of the body. The transition from traditional sexual reproduction of the queens and colonies is similar to the one from single celled organisms to multicellular organisms. The cells of your limbs, your liver, brain, all of them except for the germ cells in your testes, have surrendered their reproductive capabilities, investing their genetic future in your gonads. They do still reproduce, but their own lineages are doomed. Occasionally they do go rogue, cease cooperating and adopt a more traditional Darwinian strategy, but this is called cancer and ultimately loses to natural selection when the host dies. And as you may know, hormonal imbalance in a bee colony can cause workers to start reproducing as though they were queens, which leads to colonial collapse.
Eusocial models may be considered the next paradigm after multicellularity, and another dimension of genetic expression. Like the extended phenotype proposed by Dawkins, where the genes of a beaver cause great environmental change by building dams, the genes of a queen bee directly enhance her fitness by being expressed in her infertile daughters.
Again, I see no genetic barrier to this in vertebrates such as birds, or molluscs such as squid. There may be other barriers. It, or the stages leading to it, may simply be less efficient and effective as a survival and reproductive strategy for such species than the traditional model they currently have. That may change in the future. Or not.
Thee are already documented many other organisms displaying eusocial organisation. Some are tricky to determine, being less clear cut and representing half-way stages, their evolution toward eusocial structure being incomplete. On top of the naked mole rate, these include a shrimp, a spider, aphids, thrips and ambrosia beetles.
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