To add something interesting to the story, just one data point aka anecdote though:
8 years or so ago we got a aphid attack on my plum tree that I killed off with spray (systemic. IIRC, so it would kill of those bugs even when it didn't hit them directly.)
A couple of years later the aphids where back and I wouldn't spray it again so I started looking for alternatives.
One thing I figured out was I had also a ant problem in the same tree, so I got rid of those and that helped quite a bit but had to be repeated from time to time.
A couple of years later ladybugs started to show up and this year I counted 6. Considering each of them can eat 100 aphids a day or so they are very welcome :-)
A few possible explanations, won't go into rating them:
- maybe it was all random
- maybe ladybugs are more sensitive to insect spray than aphids are (would make sense since they prey on aphids and systemic insecticides could/would accumulate up in the food chain.)
- maybe the ant colony had been keeping the ladybugs away the first year the aphids attacked (I don't know but it is widely known that ants and aphids often form a symbiotic relationship so it wouldn't surprise me a bit if they also defended their source of yummy sugar.)
- maybe my plum tree was just to small to pick up a collection of ladybugs the first year.
From totally unscientific observations I made as a young child: the ants actually deploy and protect the aphids like cattle. I remember seeing ants literally carry ladybugs away from the aphids.
I pruned my roses a few years ago and within minutes the cut stems were seething with aphids. I tried to get rid of them with some mild bug spray (iirc it was pyrethrum or similar) but they just ignored it, and I needn't have bothered because within half an hour there were dozens of ladybugs eating the aphids. It was amazing how fast both species homed in on their respective targets.