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If an individual has a new chromosome, which is very unlikely to happen, he will not have any luck in finding a sexual partner with this same trait. How will the offspring inherit this trait. And given that extra/fewer chromosomes are often undesirable traits (e.g. Turner Syndrome) how can it propagate?

I assume that humans and rats have different number of chromosomes, so a common ancestor must give a lineage where some individuals had a different number of chromosomes than their parents.

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You are right that a person with an abnormal number of chromosomes will be unlikely to find an "equal" partner to mate with. This does not prevent a chromosome aberration from spreading though, and it is not necessary that the mutation is initially beneficial for it to spread. While it is true that many chromosomal aberrations may be detrimental and cause various syndromes, a chromosome split or multiplication may also be netural except for the matter of reproduction. A change in chromsome number will not be inherited deterministically, but can give rise to various new permutations in the offspring due to the mechanics of chromosome segregation during meiosis.

You can find a good explanation at Scienceblogs.com: http://scienceblogs.com/pharyngula/2008/04/21/basics-how-can-chromosome-numb/ :

The net result [of a chromosome split] is that although this individual is fine and healthy, a significant number of his or her gametes may carry serious chromosomal errors, which means they may have reduced fertility. They aren’t sterile, though; some of their gametes will have the full complement of genes, and can similarly produce new healthy individuals who will probably have fertility problems. (...) So our two chromosome individual will have a reduced fertility as long as he or she is breeding with the normal one chromosome organisms, but those split chromosomes can continue to spread through the population. They are not certain to spread — they’re more likely to eventually go extinct — but by chance alone there can be continued propagation of the two chromosome variant. Which leads to another misconception in the question: something doesn’t have to provide a benefit to spread through a population! Chance alone can do it. We don’t have to argue for a benefit of chromosome fission at all in order for it to happen.

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