If I used 'motorcycle, atv, and trailer tires' as the link text, and someone searched for motorcycle tires, would a search engine go 'ok, we have that phrase in the link'?
If it did count it, would it carry as much weight as if the whole link was just 'motorcycle tires'?
I want to suggest 'not', but I've no evidence other than a sneaking suspicion based on something similiar I've done on my site that's not perfectly correlated with what you've said.
Personally I wouldn't try and refine it quite that far. Specifically, try and get some links that say motorcycle tires, atv tires, etc. mix it up. Worry more about the authority/heaviness of the sites that link to you. Then create specific pages for each type of tire, with appropriate links. i.e. I'd have a central page on 'motorcycle tires' and another central page on 'atv tires', and link to those pages from your home page using that text. Hopefully then the second level pages rank on those terms.
Then from the secondary pages (and martinibuster I think is also talking about this) you start linking out to 26" yamaha atv tires, 28" yamaha atv tires, yamaha mud tires, bear paws for yamaha atv's, 26" arctic cat tires (for those that can only afford to drive arctic cat)...and so on.
that's not quite what you were asking I know. But my unscientific preference is to use links to give my site 'weight' without worrying too much about anchor text, then use internal links and on page text to rank for specific terms.
My gut reaction is your sites you should spend as much or more time on long tail terms. I own a couple of arctic cat ATV's and when I need new tires and go shopping with credit card in hand, I probably won't search on 'atv tires'. I'll probably do the following:
"arctic cat 400 2008 atv mud tires"
"arctic cat 366 2008 atv road tires"
"arctic cat 400 28 inch atv tires bear claw"
Those are the funky terms you want to rank on to hit the shoppers :).
That being said, mix it up a bit, get some links of each type of text and I wouldn't worry about it text beyond that. It's my opinion that if you try and go that granular with anchor text that first it won't look natural to the algorithm and secondly if it ranks today due to anchor text, then tomorrow they could change the ranking factor. But an authority site today speaking on a subject (with onpage text) will still be an authority site tomorrow.