Teaching "Leave It" with Live Things
First, it sounds like Murphy has already been reinforced for enjoying the behavior of chasing animals. You will most likely have success at reshaping these responses if you can also control the time he spends loose in the back yard, un-supervised. Remember that each time he runs for the squirrels and deer, he is being reinforced, and that reinforcement is tapping right into the Murph's hard-wired prey drive. So, management of Murphy's outside time will certainly make your job of behavior modification easier.
I'd consider approaching this just the same as if a dog were displaying fear/agression/overexcitement, etc. behaviors at other dogs he sees. Start with a low criteria, build up incrementally. Find out at what distance Murphy begins to respond, and begin your desensitization program five or 10 feet in back of that. That is, if Murphy is reacting to a squirrel at 50 feet, begin your desensitization at 60 feet away or so.
If Murphy is so excited about this now that he's upon his back legs pulling, then I'd advise you get a Gentle Leader or Halti to help manage the situation just until you have him a bit more responsive to you instead of the object of interest.
As soon as Murphy sees, smells or hears the distractor, he will begin his posturing, or his ritual for moving out and moving at the animal. Catch him just BEFORE he does this, and get his attention with rapid reinforcement and a high-powered primary reinforcer. If you are too late, catch Murphy's attention in some other way. He will most likely NOT respond to a simple verbal cue like the sound of his name when he is really focused on the other animal.
I like to use my body to break the obsession. I use my wheelchair and move slightly into the dog, not hitting him, but moving INTO his private comfort zone forcing him to give ME attention. I watch for that moment, quickly reinforce, then continue a high rate of reinforcement while still arcing into the dog, if necessary. This circling or arcing is really useful, as it breaks the obsession, sets the dog up to focus on the handler, and maintains the focus while the object of the dog's obsession is still in view: as you keep gradually moving INTO the dog, the dog continues to give YOU the attention.
You'll probably never convince Murphy that squirrels and deer are not madly interesting, but you CAN get him to look to you for leadership. And your leadership should clearly let Murphy know that giving YOU attention is far more rewarding than the thrill of fixating on the other animal. This will also help hone your skills of observation of Murphy's behaviors, and practice in watching for calming signals, and for those moments when you can capture his attention again.
Incrementally close the distance, moving closer to the object of obsession. This may take a while, and it's not going to happen in a couple of sessions, but you should be able to fairly quickly be able to break the obsessing and stop the lungeing at the end of the leash, and re-establish your leadership.
Good luck and keep us posted! You are not alone in having to deal with this problem. I have spent the last three years of my life working my service dog through these same things. And again, my dog was strongly reinforced during the entire first year of his life, when I was too ill quite often, to deal with the problem. By the time we began our desensitization program, he was truly obsessive.
He will most likely always have this as a default behavior, if left to his own. But I use management for those times he is off-leash. He gets no unsupervised time in the yard. He does get time, but I'm there to watch and provide leadership, if necessary. On leash, we no longer have a problem getting him to give me the attention. That's good enough for me. I don't expect him to be "perfect", only to respond when cued.
One more suggestion: Do you have Jean Donaldson's "Culture Clash"? If so, use listmember Stacy's excellent INDEX (found at http://kaylar.com/users/wmdog/keepers/) for this book and read all the sections on systematic desensitization. Her instructions are most detailed, easy to understand.
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