Subject: What is the definition of a species for an asexually reproducing organism?

Biologists indicate that two organisms are the members of the same species if
they can sexually reproduce to make viable and fertile offspring. However, this
definition doesn't seem to hold much credence if you're an asexually reproducing
species. Furthermore, I understand bacteria of different species, and even
genera, can often exchange genetic information.

So how then are species defined for asexually producing organisms?

Re: What is the definition of a species for an asexually reproducing organism?