Question
Thank you very much. We will take your advice and try to catch the culprit in the live trap with fruit. I have seen mice in the yard, but not rats. Could mice do this? Have you ever seen an animal cleanly peel many lemons like this?  The fruit is not even bitten into. Is there anything we can put on the bougenvilla or tree to deter him that will not harm our dogs? The dogs don't appear to hear anything and they usually hear everything! (beagles)
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Followup To
Question -
A few weeks ago we found that our large bougenvilla had been destroyed by some kind of animal as the ends were chewed down and a lot of the branches were chewed into. There were tons of little one inch spinters left on the ground.
Now, today, after 3 days of rain, we found that our lemon tree, which is close to the bougenvilla, had many lemons that were neatly peeled and either left on the tree or on the ground, the majority of which not even bitten into.
Do you have any idea what this could be and what we can do about it? Mice, rats, squirrels, possums, one raccoon, have been seen in our yard.
(I would prefer trapping over killing.)  
We live in Venice, California.
Answer -
Hi Eric Brandt,

It is a little difficult to identify the culprit by your info. A rodent (rat, squirrel, rabbit, etc) will leave clean sharp chisel like bite marks. Raccoon and opossum, leave ragged chew marks. Deer leave semi ragged chew marks.

If I had to guess, I would say rats.

I make electronic animal deterrents that will work for some of these pests. see my info site at:

http://HomeTown.AOL.com/DCJincks/MyHomePage/Business.html

They would not help against rats or squirrels.  For them I would get a cage type live trap and bait it with fruit.  I often catch offending rats within a few hours to a day if the trap is located near their nest or habit trail.

Hope this helps.

Dan Jincks

Answer
The beagles add to the likely hood of being rats. I have seen rats selectively take parts of fruit etc. They might like the peel but not the fruit! Rats can be very sneaky and can get out on the ends of small branches.  Study the teeth size to be sure something smaller like mice are not the culprit. I have differing species in my area, but never seen mice act as you describe. Squirrels are a possibility, but my local ones would take the whole fruit off if interested.