Pokemon-go – In Pokemon Go when selecting a wild Pokémon does the colored circle have any significance

Based on the caption of this image, it looks like the pink circle shows up once you have clicked on the Pokémon on the map, as a means of letting you know that you've clicked on it.

I just tested it and this seems accurate. It seems like this is to let players know that their click was registered and for which Pokémon (if there are multiple close together).

In addition, from this comment,

if you run from a Pokémon, the pink ring will stay for a little while.

Here is another user reporting that it is simply a UI update:

When catching wild Pokemon, I noticed a purple ring closing in on the Pokemon that I tapped on. I believe this is a new feature from the newest update. Doesn't seem to have any game play effects.

Here is another:

So you know which pokemon you are selecting if there are multiple!

Some anecdotal evidence:

In the image, I'd actually gotten a connection error after tapping the Rattata, and while I waited for something to happen, I tapped the Pidgeotto as well. The pink ring appeared around both, but did nothing. Only after minimizing the app and reopening it to regain connection did tapping on the Rattata again do anything (it started the wild encounter).