I agree with Roger but I'll throw in a few more observations.
First, I often find that thinner growth rings often have a worse ratio of summer to spring growth, simply becuase the spring ring is going to be about the same thickness while the summer growth can vary considerably. Also, older trees tend to slow down in growth rate it seems. I generally find thinner rings on the outer parts of bigger diameter trees, and you can see more vigorous growth in the tree's younger years. Might be that it is simply using up some of the nutrients avaialbe in the soil. Maybe a tree has a set lifespan like humans. Who knows. And of course there are exceptions, and they are worth looking for for the following reason.
Second, when you make a bow belly you are tapering thickness, and whenever you get to s pring ring you are at a bit of a step in terms of strength. That bit of spring ring that is exposed on the surface of the belly, is weaker than the surrounding summer wood, however slightly. I think maybe the spring growth mashes down to the density of the surrounding wood, but that takes just a bit of set for this to happen. For this reason, several thin growth rings would lead to several smaller steps, and a more gradual transition along the belly. At least when the total spring/summer ratio is the same as a corresponding thicker ringed piece of wood.
One more observation. It seems that sometimes within a summer ring you will find somewhat more of a porous nature, more of the light colored dots that are the spring-type vessels. These hollow vessels are not as strong as the deep yellow wood. So in evaluating your wood, don't just limit yourself to measuring (by eyeball) the spring/summer ratio. Look more closely.
Thats all assuming you're standing in front of a pile of already-split staves, trying to select a few of the best. If you've cut a tree and split it, whatever you got is going to make a bow. No need to be super picky after you've done all that work.
