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With dogs, I presume by 'agility' shows you mean the type that any dog can enter based on skill alone (obidience, tricks, course, etc.) and not the breed/type of dog. These types of shows don't exist for guinea pigs. Guinea pig shows are based solely on how well your pig conforms to the human-made ideal of breed type and ideal. The pig does nothing more than sit there and get examined by judges. Natural pig behaviors (eating, chewing, pooping, etc.) will score negative points, so a pig is often starved before the show.

Different breeds have different features that have come into being through many years and generations of human-selective reproduction. A coronet has a single rosette, placement of the rosette (location and symetry) is important and will score or lose points. Sometimes these features are detrimental to the pig itself, see the thread on 'lethal' guinea pigs for more info.

Non-altered is good, I have seen too many great dane's with their ears messed up from multiple operations or other dogs with tails missing, etc.