Should I mention undergraduate research history when writing a resarch statement for a faculty position? I am a PhD student applying to academic faculty positions in mid-sized institutions in the United States. I am writing research statements for ecological/environmental positions with a major focus on my current (graduate) research and my plans for extending my research in the future. However, I had almost 5 years of research experience prior to coming to grad school (4 of the 5 were while I was an undergraduate). 

My question is, should I mention or incorporate in any way the research I was involved with as prior to graduate school? I am especially curious about work done as an undergraduate. 

Also, does the quality of work matter? for example, I researched and published an undergraduate thesis but also worked as research assistant on a number of projects.
Do you feel that your undergrad research is a significant part of your research profile, or tied in with your current research interests?  If so, then yes.  If not, then I don't see it adding much value to your research statement.  For research schools, you want your research statement to be impressive, not watered down with minor results.  I was involved in 1-2 (unpublished---1 became a paper, which got accepted, but I decided not to publish) research projects as an undergrad, but I did not even think to mention them in my research statement.
Note any papers you published will appear on your CV, so the committee will already see these.  

However, one place you might mention it is in connection with the prospect of supervising undergrad research.  You can say what a good experience it was for you, and how you would like to be involved in it on the other side now.  This could come up either your teaching statement and/or your research statement, depending on your application.  (I might put it in my research statement if the projects I was already discussing lead to good projects for undergrads.)  This could be a boon, depending on how much the departments you're applying to value undergrad research.