Flatbread, this idyllic Iceland type of breeding you refer to takes place in the Middle East. Locals randomly mate their dogs together, either deliberately or accidentally, and the cute puppies are generously shared out to family members and friends and a very large percentage of them get dumped when they get past the cute puppy stage, and the kids get a brand new puppy to replace it, because puppies are always being born here and therefore dogs are disposable.
(If they are lucky, they stay with their family, but chained up outside even through 50 degree summers because Muslims supposedly aren't allowed to bring animals into a house, but anyway I digress).
Our dog was found in a park, which is a common dumping ground (because lots of white immigrants go there and the more caring dumpers know the pup may well get rescued) when she was 10-12 weeks old. Others get dumped at the beach, or tied up outside expats' houses. I have personally witnessed 2 persian cats thrown out of the boot of a car in the park.
As I have said before, she is a mutt, but I have no idea how strong her genes are - she could be the result of a father-daughter mating or brother-sister mating.
Many more dogs still are just 'released into the wild' (I know this for a fact after speaking to one Arab who had done exactly that because the dog got 'too noisy' and she would be better off 'with nature').
So we literally have strays on every single street, breeding willy nilly. It's the same with the cat population.
I am sure a bit of natural selection goes on - I work with a charity and it seems that the survivors are the feistiest, most aggressive dogs - they have to be to survive the heat, lack of water and food and kids throwing rocks at them (seems to be a national sport here). It's the same with cats - you wouldn't even want to take a kitten in for rehoming if it was born to a street cat. Natural selection in the wild produces aggressive, wary animals.
All of the street dogs are ugly, dog-shaped dogs which we know from experience people don't want to give homes to :(
I think that Flatbread has raised some genuinely interesting topics for debate in this thread, but she has totally de-valued her points by (a) trying to defend her own irresponsible breeding and (b) this stupid idea that natural selection is relevant to the UK dog population. Come to the Middle East and see how well dogs do when they're left to breed in a 'natural' way. When dogs are in such over-abundant supply, they become a disposable commodity and lose their value to people, and even become a pest.