How does crossing over in meiosis result in genetic variation?

Cross over is the first  way genes are shuffled to give rise to genetic diversity. Cross over takes place in sexual  reproduction.  The normal way that cross over occurs is chromosomes line up side by side and break off pieces of themselves, then trade those pieces with each other.

If they break the pieces at the same locus in the sequence of base pairs, the result is an exchange of genes called  genetic recombination and it ensures that the daughter cells produced  have a different genetic makeup from the parent cell and thus diversity occurs.

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