After 1 year, how much gap between members is acceptable in light framing?
I don’t see any pictures, but fastening boards together is based on: 1) shear loading, and 2) withdrawal loading. 

1) Shear loading is based on a.) thickness of fastener, b.) lumber species, and c.) support of fastener. 

Obviously, a.) the larger the fastener and b.) the denser the wood species, the more secure the joint connection. ALSO, c.) if the fastener is cantilevered, it’s shear strength is greatly reduced and the bending capacity of the fastener becomes a factor. Generally we consider the fastener’s shear “fully developed” if it’s not cantilevered more than 1 1/2 times the fastener’s (nail, screw, or bolt) diameter. When it exceeds the 1 1/2 diameter it can reduce the strength of the connection by as much as one-half. 

If it exceeds the magic 1 1/2 diameter we then worry about withdrawal. 

So, if the fastener has too big of gap or if the fastener is not fully penetrating into the adjacent member, then it is not “fully developed”.  However, seldom do we calculate the withdrawal of fasteners. 

So, if you’re worried about boards separating and the joint is weakened for shear loading, you need to determine if the connection needs to be at or near “full developed” strength. I doubt it is, especially in residential construction, because residential construction is way over designed. 

If this has occurred over a short period of time (less than a year) I’d recommend that it be “monitored “.  When we monitor a structural condition we install control points, such as strips of Formica (that won’t shrink or grow) with marks that can be photographed and documented. Keep a journal on a REGULAR basis, like monthly. Document outside temperature, inside temperature, humidity, etc.