Richard Dawkins’ book, The Selfish Gene, discusses the mathematics of natural selection of eusocial insects.
Because the bees’ genes’ only hope of success is through the queen, the bees serve the queen’s offspring (the hive). In fact, the bahaviour that leads to the death of a bee, to the benefit of the hive, is caused by a gene (which is seeking its own success).
It is possible to hack this by killing the queen and installing a new one that is more distantly related to the workers (and which is more favourable to commercial beekeeping) but the gene is usually successful overall.
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