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I should point out that I am not against the idea that collisions play no part. There is other 'evidence' that it doesn't. For example one might expect to see a relationship between an asteroids orbital elements and its periodicy. Slow rotators would be expected to have more opportunities to collide with other objects. I did a 3D log plot of the 3600 U>=2 targets Diameter, Spin Frequency, a and e and found a uniform distribution.
The only non uniform distribution was related to Diameter and a - the larger the semi major axis the larger the diameter of the asteroid in the dataset - but this is to be expected as an observational bias given that the magnitude of a target decreases with distance and amateurs (who do the bulk of the period determinations) have limits to achieve the required SNR for precision photometry.
Cheers
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