Reckless crossing is more likely to lead to healthy dogs than excessive in-breeding. So between the two extremes I’d prefer the former.
I’m a big fan of bulldogs. It’s a shame what has been done to the English bulldog through excessive pure breeding and exaggeration of traits. Here’s a pure bred English bulldog from an earlier time:
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A modern English bulldog:
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So no, I don’t believe in purity for purity’s sake. I believe in breeding to make a healthier end result, which means introducing fresh genes from time to time.
The best bulldogs today are crosses, either fresh crosses or bulldogs that were crossed several generations back.
A couple of mine: this one is an English bulldog F1 cross to a French mastiff and further back also had Staffordshire infused in.
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This one was generational, meaning he bred true to his kind and was last crossed several generations previous. His distant ancestors besides English bulldog were American bulldog, bullmastiff, and pit bull.
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I’m not a big fan of shelters. Primarily because in modern times they’re mostly repositories for random pit bull crosses that IMHO should be all put down if they aren’t wanted both for safety’s sake and for practicality. Those dogs are physically quite healthy but it’s Russian roulette as to how dangerous they are. Yes, temperament is first and foremost a function of genetics. I’m convinced you can take a dog born with good temperament and make it dangerous with poor raising but you won’t make one born with a bad temperament safe. People seem to find the notion that some dogs are born bad as unfair, as if fairness actually exists in nature. It doesn’t, and yes some or even many dogs are born dangerous.