Explain how linkage decreases the amount of genetic variation in offspring?

Linked genes will decrease the amount of genetic variation in offspring because it violates Mendel's law of independent assortment.  When genes assort independently, alleles are able to be donated by parents at equal rates, whereas when genes are linked, then the likelihood of two (or more) genes passed together as a group is raised greatly, and genetic variation becomes dependent upon recombination, again, which is less likely than random independent assortment.

Assume a parent has:

A B
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a  b

If the genes are shown to assort according to Mendel's law, then offspring are equally likely to receive A;B, A;b, a;B, and a;b from that parent (all 25% likely).

Assume now that the genes are linked with a recombination frequency of 20%, now the probabilities of combinations are as follows:

80% A;B or a;b
20% A;b or a;B

therefore, 40% A;B, 40% a;b, 10% A;b, and 10% a;B.  That is, 80% likely to have two genes exactly like this parent instead of 50% likelihood when Mendel's second law is in play.

Thank you you are awesome!

@HannahQ
ummmmmm, confused! what does that have to do with the question?? (soz if it's obvious :/)

Thanks for the kind words.  If you're satisfied with the answer, please mark as solved.