If you live in the Tucson metro and your house has been around longer than a decade, there's a real chance something has been in your attic at some point. The two most common offenders are pack rats and roof rats. They behave a little differently, but the effect on your insulation is similar enough that for our purposes we can talk about them together.
Pack rats are native to the Sonoran Desert. They're stockier, they hoard, and they build nests out of whatever they can carry. We've found nests stuffed with cholla buds, dog kibble, foil candy wrappers, eyeglass arms, you name it. Roof rats are an invasive species that's spread through southern Arizona over the last two decades. They're sleeker, they're climbers, and they show up wherever there's accessible fruit (citrus, pomegranate, fig). Both will happily move into your attic if there's an entry point.
What they do once they're up there is what costs you money. They compress insulation to nest in. They tunnel through it. They chew electrical wiring. They contaminate the material with droppings and urine. None of this is good for your R-value, your indoor air, or your house in general.