I have been trying to control blackfly on beans by spraying infestations
on OTHER plants (mainly those two) as the beans grow, and it seems to
work.

I have not been "trying to control blackfly", I've been succeeding in
controlling them and I do not use sprays against them, so perhaps there
would be no infestations for you to spray if you tried what you're saying is
an old wives' tale next year.

| Given that there appears to be no formal herding of aphids, then yes,
| I wouldn't have thought that ants per se would increase the incidence
| of aphid colonization - merely take advantage of it and sustain it.

" . . . .thought . . . ."? If some are moved to pastures new . . . .

I've been keepng a very close watch on my plants (I have oodles of spare
time!) and have observed that an aphid or two first appear on the leaves of
the runner beans. These aphids, if I did not kill them, would give birth to
more live aphids until there's quite a patch of them - this too, is when I
often "squidge" them - and if I see an ant, out with the Nippon and put some
on the bamboo supports. If I did not squidge etc., aphids would suddenly
appear on nearby flower buds (not rain washed there unless water runs
upwards) and I'm convinced that ants would be responsible for moving them.
One such group of buds was removed straight away and out with the Nippon.

Many times I've tried to interest ladybirds in aphids which are "protected"
but they seem to know about the protection racket and will not attack them.
Perhaps other predators know of it too.

I agree that what I do does not equate to scientific proof and I do not have
enough money nor a large hermetically sealed environmental chamber in which
to conduct rigidly controlled experiments, but until someone comes up with a
good reason why I should not carry on the way I do, it's flypaper and death
to ants!

There is one more way to help reduce the aphids - peanuts. Peanuts to
attract bluetits, in a container having enough room for only one bird at a
time to get at them. The birds queueing up will clear aphids fairly well.

Regards

Ron