Nothing. Spiders should help control other pests in your trees, so learn to accept that they are your friends.
Are they spiders or caterpillars?
And if you don't believe Steve, here's Texas A&M on the subject of spiders and pecan trees:
They are about to kill the trees, the leaves are turning brown and 1 whole limb looks like it is dead, This is good?
Thanks Douglas, but that is not what these webs look like, It looks like white cotton candy, but tons of them!
Can you take a photo of this? It would answer a lot of questions. Also of the spider if you can.
Doesn't sound like your problem is spiders, but a photo might help.
If it looks like "sacks" hanging from the branches, it's probably webworms (aka as bag worms and tent worms). We had them in our 3 pecan trees in October 2010. Supposedly they aren't technically harmful to the tree except they strip the leaves and that's probably why your limb looks dead. (Seems to me that would stress the tree and one of our 3 trees did die, but we don't know if it was due to the webworms or something else.) If any of the sacks have fallen to the ground, look closely and you will see they are full of dead leaves. There are many links on the internet detailing methods for getting rid of the webworms. However, we didn't do anything and so far, they haven't come back. I included photos of one of our trees and a closeup of one of the sacks that fell on the ground, in which you can see the leaves.
Looks like caterpillars to me.
The webworm is a caterpillar in the larva stage but this process starts with a moth according to Wikipedia ( http://en.wikipedia.org/wiki/Fall_webworm ).
Thanks Shari..that is exactly what mine look like.. is there anything to do about those?
The tree needs to be professionally sprayed. Also I suggest that the webbed areas be cut out if possible.
These bugs will eat the foliage off of the tree. While it may not kill it right off, continued development will hinder its growth and eventually the tree will succumb do to the lack of leaves it needs to survive. In NJ area they do mass spraying of properties via aircraft as these bugs can wipe out large areas of trees in just a few years.
Fran, apparently there are multiple ways to get rid of them, depending on whether you want to use professionally or self applied pesticides, or whether you desire a more organic remedy. Only you can decide that. If you do an internet search for "webworms" or "pecan webworms," you will find all kinds of info on methods to rid your trees of them...or you can do like Woodbridge suggested above and just call a professional to deal with it but, depending on how many trees you have, that could get expensive in a hurry. As I mentioned above, we did absolutely nothing to our 3 affected trees--we were too busy dealing with more pressing projects on this 30 acre horse farm we bought-- and haven't had a recurrance of the webworms. With that being said, we haven't had many pecans since then either. Did the webworm problem cause that or was it coincidence? I don't know. However, we're not complaining because we quickly found out that picking hundreds of pecans up off the ground every day is not a lot of fun and shelling them is very time-consuming. Personally, if I want pecans, I'd rather buy mine already shelled at the grocery store, thankyouverymuch. ;)