1) The verb ‘to dod’ is on record from the early thirteenth century when it was used in connection with having one’s hair cut, and by <i>c</i>.1440 it occurred with reference to trees that had been polled or lopped (OED).
It is found in Yorkshire from the sixteenth century, perhaps with that meaning, although 'decayed' is also a possibility: 1545 lxxx dodded trees sold … for fyre wodd, Spaunton. However, it cannot easily be distinguished from a number of similar words, all of which had to do with trees which had lost their branches, usually through decay or age, and the OED has individual entries for each of these. Several of the examples given are relatively late and the list includes: doddard, doddered, dodderel, doddle, dotard and dottard, doted and dotterel. The examples of 1568 and 1603 are from Yorkshire sources, and references in the county’s records suggest that these words are difficult to separate in meaning. For example, in the Accounts of the Woodward General, 1544-5, the entries are in the same hand and ‘dodded’ which has already been quoted is paralleled by olde dotted trees and olde dotterd trees. An Almondbury survey of 1584 has a few old doted trees which are good for nothing except it be for the fire. A list of woods in Bilsdale for 1642 has dodderell okes, dotterd okes and dodderd okes and accounts for Pickering Forest have similar forms: 1608 dottards, 1660 old Dotterells. The words may have been used interchangeably but they do not have a common origin: ‘dotard’ and similar terms derive ultimately from the verb ‘to dote’, that is to be out of one’s wits or weak-minded. It had come to be used of trees by c.1420.