That's not true. The cockroaches you're referring to actually come from the tropics and can only survive inside buildings in the colder zones. Though they existed before man and now live in almost every country, the majority of them would go extinct if human dies out. Only the specimen in the warmer regions would survive. In colder regions, they are like parasites living off the human, by living inside its buildings, eating its food and using its transport vehicles for spreading across the globe. And as any parasite, it dies together with its host.
I dont know where you're from but where I'm from we have something called the bush cockroach which survives anywhere in coastal australia - much like Australians. I imagine there is a similar "race" of cockroach which can survive on any habitable landmass, much like ours. The bush cockroach was here long before people (or at least, european people) and my point stands even if it wasn't. We have food and shelter and the cockroach takes it and we cant stop it. This is an act of dominance.
If mites crawl onto a harvestman to get transported to whereever the harvestman goes, do you call it dominance? Do the mites
dominate the harvestman?
Also cockroaches don't often eat our food, they mostly eat what's left from our food, since our technology keeps cockroaches away from our food. (fridge, packing)
Also, did you mean this bush cockraoch?:
http://www.geocities.com/brisbane_hoppers/SmallBushCockroach.htmIf yes, then there is written, that they feed on pollen, honeydew and mould fungus, something which you don't find that often inside buildings. So that means, that this cockroach lives independently from human.
I think you're confusing quantity with dominance.
Quantity IS dominance. A human being on his own cannot control the technologies we boast about. One man can kill a wolf with a gun but a pack of wolves can take down a gunman. Noone could claim that man in the singular sense dominates the world, they mean that Man in the collective sense dominates the world. In any case, it is not the quantity of cockroaches that makes them dominant, it is our inability to control them. Dominance is control.
First: One single individuum can't be considered as a species. Even an equal number of individuums for both species isn't balanced. One bee is nothing, a bee-hive on the other hand can rout a pack of wolves. The hive is more than the sum of its parts.
Second: Give the man all the technology humanity achieved and he will be able to fight many many more wolves and still survive.
Third: 'Man' is not the same as 'a man'. 'Man' refers to humanity.
Fourth: If you say, humans aren't as dominant as cockroaches, then I'm allowed to say, that cockroaches aren't as dominant as mammals. Humanity is a single species. Comparing it's dominance to a whole order isn't 'fair'. It's quite obvious, that whole groups of different species are more dominant together than each single species of that group.
And last but not least: How do cockroaches control humanity? They can't even decide where to go, when they crawl onto a ship or plane. Also the only reason, why cockroaches are still alive, is that humanity does not see them as a serious threat. If we would use all our technology to wipe out cockroaches, then there won't be any cockroaches left soon. It's the same with any other animal, which hasn't got extinct by now: Rabbits and foxes are still alive, though farmers try to shoot them, so that they don't eat their crops or chickens. Applying your logic to these examples would mean, that rabbits and foxes are more dominant than humans and infact control humanity as a whole.