Ignoring the reinforcer
Thank you all for this fruitful discussion about squirrel chasing (and herding and similar behaviors).
You can view something your learner wants to do very badly as "competition" for the treats you carry, a behavior flouting your level of control. That would be the intuitive and historical way. Or, you can view it s a powerful potential reinforcer, and set things up so your learner gets paid with a chance to enjoy that reinforcer for behavior that you want—which may in fact include ignoring that reinforcer. That's the science of it. Chris Puls's shaping of "leave it" in a beagle, earlier this week was a good example:
I just spent an hour working with my beagle, using the training steps I laid out for "leave it." He was completely OFF leash the whole time. He started out having difficulty looking away for more than one second from the treat held in my hand out to my side (eye contact game). By the end of the session, he was walking over and around treats on the floor! While off leash! AND he was doing "leave it" on treats I deliberately dropped on the floor!
Working on getting the eye contact when I presented the hand with the treat in it took half of the session, just to get the eye contact solid for 10+ seconds, even while my hand with the treat was moving a bit and regardless of where my hand was placed in relation to him.
After the LONG time of working on getting him to look away from the treat in my hand, things progressed a bit faster. When I switched to the treats in a Ball jar lid in my hand though, I had to start over and have my thumb over the treats. He went through the steps faster this time than he did with just the eye contact first steps.
Soon I was able to put the treats in the lid right near him after I said "leave it" and he was looking right at me, even though they weren't protected by my thumb. We took a break here (so I could cut up more treats) and played a short game of fetch the toy, but he kept running right back to the training area with his tail wagging so I knew he was still ready to learn.
I moved to a few different places/positions with the lid in my hand but when I stood, it was really hurting my back to bend over (to get the lid close to the floor where it would end up). I ended up taping the Ball jar lid onto the end of a dowel so I could offer it low to the ground and remain standing.
Then I did some reps where I held the lid and set it on the ground. I kept my hand near the stick that was still attached just in case. When I felt he was ready/reliable I removed the stick I had taped on. He would look at the lid when I put it down and immediately give/hold eye contact. Yea!
I upped the criteria by asking him to come past the lid to get the reward/treat after I clicked. I was able to get quite a distance away and he was still not going for the treats, even though there was no way I could have protected them. This is farther than we have ever gotten! And his behavior was a LOT more reliable than ever before.
Next, I removed the rim of the lid, so the top part was flat on the floor. No problem. I guess it still looked enough like the lid even though it was now just a flat disk on the floor with the treats on top. Problems arose when I dumped the treats off that lid and onto the floor. I didn't break down the criteria enough and he scarfed up all the food.
We tried again with loose food on the floor while I was much closer and able to move a foot in to protect the food (only had to move my foot a bit toward the food when I thought he was going to try it and after that, he didn't try to get it again). It was VERY clear that he REALLY wanted to! But I was also comfortable trusting him to respond to the behavior that had been the most rewarded: eye contact.
Imagining what's possible
The crossover trainer—and I am one, too, after all—often comes to clicker training with a background where success has included correction. For years, in seminars and classrooms I have been faced with the telling phrase, "I don't see how you could possibly..." followed by an example, often drawn from extensive expert experience.
"I don't see how you could possibly train x to do y under circumstance z, without punishment," the person says. The declaration is often made as a kind of ultimatum or challenge. "There! See that? There's no clicker answer to that!"
The key is not in the x-y-z of the example, but in the opening phrase, "I don't see how..."
The person really doesn't see how another way is possible, and that's the only issue here. Nor should the person be expected to; it took Skinner et al a long time to come up with the underlying principles of operant conditioning, and it has taken all of us dog trainers a decade or more to devise, use, and teach how to apply the principles effectively in challenging situations.
Meanwhile, the challenger deserves empathy. This situation, when new information is replacing old information, resembles the process called extinction, in which previously reinforced behavior is no longer reinforced. Extinction is a very unpleasant process for any organism. The experience often arouses anger, even in lab animals.
A squirrelly reward?
On the ClickerExpo list you have been doing the "clickerly" thing—helping people through the extinction curve by explaining and teaching the shaping/cueing approach to managing behavior around strong attractions. One does this, of course, by incorporating the attractions into the shaping plan. The example someone gave of the collie with sparrows in the barn was super!
Going from that collie to terriers in the woods is just a shaping staircase; if you want to do it, it can be done, but it involves a lot of steps. For me, that's too much like work. My practical solution is a mix of training and management. The backyard is fenced, and there the dogs can bark and chase squirrels all they want. Outside the front door, on the sidewalk, we enjoy a shaped behavior of stalking squirrels, with an occasional brief "chase" reinforcer. In the woods, my poodle, whose lust for squirrels is mitigated by his general timidity, can be off-leash, because he was quite easily shaped to come when called, even from squirrels. My 17-year-old border terrier, however, stays on-leash in the woods. From her standpoint, it's a lot better than no woods at all.