The dot is added in the .lbx (specifically english.lbx) file where we find amongst others
editor = {{editor}{ed\adddot}},
editors = {{editors}{eds\adddot}},
That means that the abbreviated versions include a dot. And there are many more abbreviations for certain roles that include a dot.
If you only need to change a few stings, you can use \DefineBibliographyStrings in the preamble of your file.
\DefineBibliographyStrings{english}{%
editor = {ed},
editors = {eds},
}
With that command, however, you cannot change the full and abbreviated versions of the string separately. Additionally, if you need to change lots of strings, your preamble might get bloated.
Alternatively, you can define an .lbx of your own. Create a new file called english-dotless.lbx where LaTeX can find it with the content
\ProvidesFile{english-dotless.lbx}
\InheritBibliographyExtras{english}
\DeclareBibliographyStrings{%
inherit = {english},
editor = {{editor}{ed}},
editors = {{editors}{eds}},
}
\endinput
and all the other strings from english.lbx you need to change.
Then in your document issue \DeclareLanguageMapping{english}{english-dotless} and your new file will be used instead of the standard English strings. (Of course this method works for all languages that have existing .lbx files.) For more on custom .lbx files see Changing another language “et al.” to “et al.” as well as What is the most appropriate way to configure biblatex for use with an unsupported language?.
\DefineBibliographyStrings{english}{editors=eds\nopunct}seems to handle that. – Gareth Walker Jul 23 '16 at 09:23\nopunctshouldn't normally be necessary there, I believe. It is only needed to suppress punctuation that might follow, not instead of punctuation if you don't want any. – moewe Jul 23 '16 at 10:37