Wide Pine Gaps

I have an old home (built in 1840s) with original wide pine boards in the dining room floor. The floor is currently clear coat (with probably polyurethane). I want to re-sand and refinish this floor. My question is this: Parts of the floor have some pretty wide gaps between the wide pine boards. In a few places the gaps are as wide as 3/8" between the boards. It looks like whoever finished this floor the last time, tried to fill these gaps with wood putty. This stuff is now crumbling and generally looks like crap. Should I remove the fill entirely and leave the gaps for authenticity? (there is a subfloor underneath so it would not be exposed to the crawl space) Or is there some better method of filling these gaps? I guess I'm looking for some opinions on what would look best.

Thanks for your advice!

 

When the floor boards shrink and swell, and wide plank shrinks and swells pretty good, it compromises any filler used during finishing. That wouldn't happen if the humidity levels inside the home were kept real constant throughout the year.