We successfully dealt with rodents in mulched beds using cats. The
problem plummeted to near zero. When coyotes killed our original
city-bred cats, the voles and pack rats came back with a vengeance. Then
we got barn-born cats who were completely country-savvy, and they
survived intact for the remaining 6 years we spent in
coyote/bobcat/hawk/owl country. The new cats restored the rodent-free
condition and hung out primarily in the garden. So we did the whole
experimental series to show that cats were the answer. They rarely went
after birds, being so well fed on voles. We also fed the cats in the house.
Good habitat for other predators is useful, but nothing helped like cats
did. We had a dog who killed pack rats and gophers in the garden.
Speaking of mulch and slugs, I have fewer slug problems (in the slug
ridden US Pacific NW) with mulch than without it. Mulch brings in birds,
predatory beetles, snakes, and other slug predators. With no mulch,
there is still slug habitat (my veggies) but no predator habitat.