Four Flats in the Desert

You may remember the goofy hikers. Now we've done an encore as the goofy bikers. Got our bikes out for a scenic ride through the desert on the trails in the State Park and ended up with four flat tires and a long walk home. Some kind of stealthy little Arizona ground plant with tiny spikes that jump on to your bike tires.  I know not to drive into a cactus, but how do you avoid what you can't see? Do the locals know about these things?