I was asked this by some schoolchildren. Here's my best shot.
The gene that expresses stripeyness in tigers is the same gene that expresses spottiness in leopards. All big cats carry very similar gene pools, and the individual genes are expressed differently in each species. (In the case of stripeyness in the big cats, it is governed by the genes controlling the size of the animal.)
If the same applies to hymenoptera, then hornets, wasps, bees, hoverflies etc will all (?) carry the stripeyness gene, expressed differently in each species. For example, apis and bombis express very different degrees of stripeyness.
Honeybees are mildly stripey because there is some mild survival value to carrying and mildly expressing the gene. Hornets are very stripey because there is big survival value to strongly expressing the gene. That's why bees are stripey - a bit obvious, really.
Is that right?
How and why did the gene arise, and what did it originally code?