Sex and genetic shuffling: the details
Recombination introduces new gene combinations into populations.
Here is a quick and dirty review of the genetics of sexual reproduction.
We'll use human reproduction to anchor this because it's a familiar
topic, but the basic ideas transfer to other sexually reproducing organisms.
- Genes are located on long chains of DNA called chromosomes.
Humans have 23 pairs of chromosomes: one member of each pair was
inherited from the mother and the other from the father. Correspondingly,
we have two versions of every gene, one from the mother and one from
the father.
If people reproduced by taking 23 pairs of chromosomes from the
mother and 23 pairs of chromosomes from the father, the baby would
have too many chromosomes (46 pairs). So eggs and sperm carry only
half the usual number of chromosomes just 23 unpaired chromosomes,
carrying one version of each gene. When the egg and sperm get together,
the baby receives the normal 23 matched pairs.
When eggs and sperm are produced, the parent
cell first copies each chromosome, leaving the duplicate pairs attached to
one another. 
Producing eggs and sperm is our first opportunity for mixing and
matching genes. When the mother makes an egg, her chromosomes first
find their matched partners and exchange some DNA with each other.
That's called recombination. Because of this shuffling, genes from the mother's
mom and genes from the mother's father can wind up next to one another on the
same stretch of DNA. (The same thing happens in the father's sperm.)

Only after chromosomes recombine do
they segregate into different egg cells, so that each egg cell ends
up with one version of each chromosome.
- Meiosis, step one (click the image for animation):

- Meiosis, step two (click the image for animation):

When egg and sperm meet, the baby inherits a combination of genes
that is totally unique: it carries versions of genes from all 4 grandparents
plus any mutations that
occurred when the mother and father were making the egg and sperm.
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