When changing fields, should I focus more on describing past research or connecting it to the new area in my statement of purpose? I want to change my field from molecular biophysics to theoretical ecology. While they are basically required some same basic background (physics, math, programming), the rest is quite irrelevant. In my current draft of this part, about a half is about this the problem and the result of the work, another half is for my contribution and what I've learnt. Having said that, should I focus less on describing the work and leave space for the thing that will be useful for the next research?

Below is copy from Choosing research ideas to include in a statement of purpose.


  What have you already done? What problems have you solved, or at least worked on? What independent projects have you been part of? What were your key contributions? What did you learn? What did you teach the world? How do your results compare to what was already known? What original ideas are you most proud of? Be specific, technical, credible, and confident (but not arrogant). Refer the reader to your web page for more details. Have a web page with more details: preprints, project reports, source code, videos, etc.
I am going to focus my answer on your original question statement (but without getting involved in editing the official title of your Question):

When changing fields, should my past research be written in a way that brings out the maximum relevance to the new area?
In my current draft of this part, about a half is about this the problem and the result of the work, another half is for my contribution and what I've learnt.

Good.  This is exactly what they're looking for, in that section of your essay.

Having said that, should I focus less on describing the work and leave space for the thing that will be useful for the next research?

No, you can let the &quot;previous work&quot; section stand alone.  That's the section where you show the committee that you have done good science, and that you can speak about it in an understandable way.
Just to make sure we're on the same page -- your essay is going to have another major section, where you get to be imaginative about what you would like to do in the new field, right?