Hi Rich
Sorry I had it in mind yours was mainly Sweet chestnut. (Which of course squirrels do go for as well, but have a preferrence for birch over S.C., S.C. produces callous wood much more quickly than other trees and typically very successfully heals wounds- though these healed wounds are subsequently a favoured site for further squirrel attentions!)
Beech and hornbeam are of course major targets as well - sorry about my confusion over what you were working with.
Grey Squirrels were introduced in late Victorian times but have really only been a severe problem since the 1940s in most areas. (the stripping isn't feeding as used to be thought, it's an antagonistic territorial behaviour- two squirrels meet interact to identify dominance and then when they sepearate they ti some territorial marking i.e. stripping - they have no significant natural predators here, and so end up living at such high densities in some years that they are encountering other squirrels very frequently and so doing lots of stripping damage!)
Trees respond to squirrel bark stripping (if the stripping hasn't gone all the way around the stem) by producing callous wood to physically heal the damage, but also by producing chemicals that are moved into the exposed sapwood, these contain anti-fungal and antibacterial agents.
It's interesting (well if like me you're a tree nerd it's interesting!) that squirrel wounds tend to heal better than physical wounds made in other ways. The squirrels strip the bark, and usually the dividing/growing layer of cells called the cambial meristem, but do very little damage to the sapwood that they expose. This sapwood is left intact and fully functioning - so that the movement of protective chemicals into that sapwood is very efficent. Most squirrel wounds (obviously not if it's completly round the stem) heal very well. The timber will usually have been damaged in terms of its potential value in the future, but the tree itself often survives and grows very well if it isn't in too much shade. (this doesn't apply to birch or rowen)
You probably find cutting crossections through healed hornbeam that there is very little rot in the rings below each healed bit of squirrel damage? Where you cut a ring through healed damage at the base of a tree that has been damaged by timber extraction machinary etc. (and where the sapwood has been damaged beneath the bark) you would find that often there is significantly more and deeper rot/discoluration to the growth rings below any healed wounds.
Squirrels can change the relative proportions of broad leaved species over time in mixed woodlands - In our woods they give hornbeam,lime and sweet chestnut the advantage (which heal very well) over birch (which is less able to prevent the exposed wood from rotting by natural chemical means before the callousing physically heals and seals the wound, and when the wood beneath is weakend by decay the top of the tree blows out in the wind). The birch grows again from the point below this damage but is reduced in height compared to its neighbours so it then gets less light than they do and so is rapidly outcompeted by them as their canopies close above it.
One of the best studies of this is Peterken's work in Lady Park wood where squrrels have given ash a competitive advantage over beech - the beech are rarely killed but once they're topped by the ash their chances of becoming a dominant canopy tree are very limited.
